Class 10th Mathematics CBSE Solution
Exercise 6.1- Fill in the blanks using the correct word given in brackets: (i) All circles are…
- Give two different examples of pair of similar figures and non similar figures…
- State whether the following quadrilaterals are similar or not:
Exercise 6.2- In Fig. 6.17, (i) and (ii), DE || BC. Find EC in (i) and AD in (ii)…
- E and F are points on the sides PQ and PR respectively of a PQR. For each of the…
- In Fig. 6.18, if LM || CB and LN || CD, prove that
- In Fig. 6.19, DE || AC and DF || AE. Prove that bf/fe = be/ec
- In Fig. 6.20, DE || OQ and DF || OR. Show that EF || QR.
- In Fig. 6.21, A, B and C are points on OP, OQ and OR respectively such that AB…
- Using Theorem 6.1, prove that a line drawn through the mid-point of one side of…
- Using Theorem 6.2, prove that the line joining the mid-points of any two sides…
- ABCD is a trapezium in which AB || DC and its diagonals intersect each other at…
- The diagonals of a quadrilateral ABCD intersect each other at the point O such…
Exercise 6.3- State which pairs of triangles in Fig. are similar.Write the similarity…
- In Fig. 6.35, ODC ~ OBA, BOC = 125 and CDO = 70. Find DOC, DCO and OAB…
- Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at…
- In Fig. 6.36, qr/qs = qt/pr and 1 = 2. Show that PQS ~ TQR.
- S and T are points on sides PR and QR of PQR such that P = RTS. Show that RPQ ~…
- In Fig. 6.37, if ABE ACD, show that ADE ~ ABC.
- In Fig. 6.38, altitudes AD and CE of ABCintersect each other at the point P.…
- E is a point on the side AD produced of a parallelogram ABCD and BE intersects…
- In Fig. 6.39, ABC and AMP are two right triangles, right angled at B and M…
- CD and GH are respectively the bisectors of ACB and EGF in such a way that D…
- In Fig. 6.40, E is a point on side CB produced of an isosceles triangle ABC…
- Sides AB and BC and median AD of a triangle ABC are respectively proportional…
- D is a point on the side BC of a triangle ABC such that ADC = BAC. Show that…
- Sides AB and AC and median AD of a triangle ABC are respectively proportional…
- A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the…
- If AD and PM are medians of triangles ABC and PQR, respectively where ABC ~…
Exercise 6.4- Let ABC ~ DEF and their areas be, respectively, 64 cm^2 and 121 cm^2 . If EF =…
- Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O.…
- In Fig. 6.44, ABC and DBC are two triangles on the same base BC. If AD…
- If the areas of two similar triangles are equal, prove that they are congruent…
- D, E and F are respectively the mid-points of sides AB, BC and CA of ABC. Find…
- Prove that the ratio of the areas of two similar triangles is equal to the…
- Prove that the area of an equilateral triangle described on one side of a square…
- ABC and BDE are two equilateral triangles such that D is the mid-point of BC.…
- Sides of two similar triangles are in the ratio 4: 9. Areas of these triangles…
Exercise 6.5- Sides of triangles are given below. Determine which of them are right triangles.…
- PQR is a triangle right angled at P and M is a point on QR such that PM QR. Show…
- In Fig. 6.53, ABD is a triangle right angled at Aand AC BD. Show that: (i) AB^2…
- ABC is an isosceles triangle right angled at C. Prove that ab^2 = 2ac^2…
- ABC is an isosceles triangle with AC = BC. If ab^2 = 2ac^2 prove that ABC is a…
- ABC is an equilateral triangle of side 2a. Find each of its altitudes…
- Prove that the sum of the squares of the sides of a rhombus is equal to the sum…
- In Fig. 6.54, O is a point in the interior of a triangle ABC, OD BC, OE AC and…
- A ladder 10 m long reaches a window 8 m above theground. Find the distance of…
- A wire attached to a vertical pole of height 18 m is 24 m long and has a stack…
- An aeroplane leaves an airport and flies due north at a speed of 1000 km per…
- Two poles of heights 6 m and 11 m stand on aplane ground. If the distance…
- D and E are points on the sides CA and CB respectively of a triangle ABC right…
- The perpendicular from A on side BC of aABC intersects BC at D such that DB = 3…
- In an equilateral triangle ABC, D is a point on side BC such that bd = 1/3 bc…
- In an equilateral triangle, prove that three times the square of one side is…
- Tick the correct answer and justify: InABC, AB = 63 cm, AC = 12 cm and BC = 6…
Exercise 6.6- In Fig. 6.56, PS is the bisector of QPR of PQR. Prove that qs/sr = pq/pr…
- In Fig. 6.57, D is a point on hypotenuse AC of ABC, DM BC and DN AB. Prove that:…
- In Fig. 6.58, ABC is a triangle in which ABC 90 and AD CB produced. Prove that…
- In Fig. 6.59, ABC is a triangle in which ABC 90 and AD BC. Prove that ac^2 =…
- In Fig. 6.60, AD is a median of a triangle ABC and AM BC. Prove that: (i) ac^2 =…
- Prove that the sum of the squares of the diagonals of parallelogram is equal to…
- In Fig. 6.61, two chords AB and CD intersect each other at the point P. Prove…
- In Fig. 6.62, two chords AB and CD of a circle intersect each other at the point…
- In Fig. 6.63, D is a point on side BC of ABC such that bd/cd = ab/ac Prove that…
- Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above…
- Fill in the blanks using the correct word given in brackets: (i) All circles are…
- Give two different examples of pair of similar figures and non similar figures…
- State whether the following quadrilaterals are similar or not:
- In Fig. 6.17, (i) and (ii), DE || BC. Find EC in (i) and AD in (ii)…
- E and F are points on the sides PQ and PR respectively of a PQR. For each of the…
- In Fig. 6.18, if LM || CB and LN || CD, prove that
- In Fig. 6.19, DE || AC and DF || AE. Prove that bf/fe = be/ec
- In Fig. 6.20, DE || OQ and DF || OR. Show that EF || QR.
- In Fig. 6.21, A, B and C are points on OP, OQ and OR respectively such that AB…
- Using Theorem 6.1, prove that a line drawn through the mid-point of one side of…
- Using Theorem 6.2, prove that the line joining the mid-points of any two sides…
- ABCD is a trapezium in which AB || DC and its diagonals intersect each other at…
- The diagonals of a quadrilateral ABCD intersect each other at the point O such…
- State which pairs of triangles in Fig. are similar.Write the similarity…
- In Fig. 6.35, ODC ~ OBA, BOC = 125 and CDO = 70. Find DOC, DCO and OAB…
- Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at…
- In Fig. 6.36, qr/qs = qt/pr and 1 = 2. Show that PQS ~ TQR.
- S and T are points on sides PR and QR of PQR such that P = RTS. Show that RPQ ~…
- In Fig. 6.37, if ABE ACD, show that ADE ~ ABC.
- In Fig. 6.38, altitudes AD and CE of ABCintersect each other at the point P.…
- E is a point on the side AD produced of a parallelogram ABCD and BE intersects…
- In Fig. 6.39, ABC and AMP are two right triangles, right angled at B and M…
- CD and GH are respectively the bisectors of ACB and EGF in such a way that D…
- In Fig. 6.40, E is a point on side CB produced of an isosceles triangle ABC…
- Sides AB and BC and median AD of a triangle ABC are respectively proportional…
- D is a point on the side BC of a triangle ABC such that ADC = BAC. Show that…
- Sides AB and AC and median AD of a triangle ABC are respectively proportional…
- A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the…
- If AD and PM are medians of triangles ABC and PQR, respectively where ABC ~…
- Let ABC ~ DEF and their areas be, respectively, 64 cm^2 and 121 cm^2 . If EF =…
- Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O.…
- In Fig. 6.44, ABC and DBC are two triangles on the same base BC. If AD…
- If the areas of two similar triangles are equal, prove that they are congruent…
- D, E and F are respectively the mid-points of sides AB, BC and CA of ABC. Find…
- Prove that the ratio of the areas of two similar triangles is equal to the…
- Prove that the area of an equilateral triangle described on one side of a square…
- ABC and BDE are two equilateral triangles such that D is the mid-point of BC.…
- Sides of two similar triangles are in the ratio 4: 9. Areas of these triangles…
- Sides of triangles are given below. Determine which of them are right triangles.…
- PQR is a triangle right angled at P and M is a point on QR such that PM QR. Show…
- In Fig. 6.53, ABD is a triangle right angled at Aand AC BD. Show that: (i) AB^2…
- ABC is an isosceles triangle right angled at C. Prove that ab^2 = 2ac^2…
- ABC is an isosceles triangle with AC = BC. If ab^2 = 2ac^2 prove that ABC is a…
- ABC is an equilateral triangle of side 2a. Find each of its altitudes…
- Prove that the sum of the squares of the sides of a rhombus is equal to the sum…
- In Fig. 6.54, O is a point in the interior of a triangle ABC, OD BC, OE AC and…
- A ladder 10 m long reaches a window 8 m above theground. Find the distance of…
- A wire attached to a vertical pole of height 18 m is 24 m long and has a stack…
- An aeroplane leaves an airport and flies due north at a speed of 1000 km per…
- Two poles of heights 6 m and 11 m stand on aplane ground. If the distance…
- D and E are points on the sides CA and CB respectively of a triangle ABC right…
- The perpendicular from A on side BC of aABC intersects BC at D such that DB = 3…
- In an equilateral triangle ABC, D is a point on side BC such that bd = 1/3 bc…
- In an equilateral triangle, prove that three times the square of one side is…
- Tick the correct answer and justify: InABC, AB = 63 cm, AC = 12 cm and BC = 6…
- In Fig. 6.56, PS is the bisector of QPR of PQR. Prove that qs/sr = pq/pr…
- In Fig. 6.57, D is a point on hypotenuse AC of ABC, DM BC and DN AB. Prove that:…
- In Fig. 6.58, ABC is a triangle in which ABC 90 and AD CB produced. Prove that…
- In Fig. 6.59, ABC is a triangle in which ABC 90 and AD BC. Prove that ac^2 =…
- In Fig. 6.60, AD is a median of a triangle ABC and AM BC. Prove that: (i) ac^2 =…
- Prove that the sum of the squares of the diagonals of parallelogram is equal to…
- In Fig. 6.61, two chords AB and CD intersect each other at the point P. Prove…
- In Fig. 6.62, two chords AB and CD of a circle intersect each other at the point…
- In Fig. 6.63, D is a point on side BC of ABC such that bd/cd = ab/ac Prove that…
- Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above…
Exercise 6.1
Question 1.Fill in the blanks using the correct word given in brackets:
(i) All circles are __________. (congruent, similar)
(ii) All squares are ___________. (similar, congruent)
(iii) All ____________ triangles are similar. (isosceles, equilateral)
(iv) Two polygons of the same number of sides are similar, if (a) their corresponding angles are _________ and (b) their corresponding sides are ___________. (equal, proportional)
Answer:The solutions of the fill ups are:
(i) Similar
(ii) Similar
(iii) Equilateral
(iv) (a) Equal
(b) Proportional
Question 2.Give two different examples of pair of
(i) Similar figures
(ii) Non-similar figures
Answer:Two examples of similar figures are:
(i) Two equilateral triangles with sides 1 cm and 2 cm
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)
(ii) Two squares with sides 1 cm and 2 cm
![](data:image/png;base64,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)
Now two examples of non-similar figures are:
(i) Trapezium and square
![](data:image/png;base64,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)
(ii) Triangle and parallelogram
![](data:image/png;base64,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)
Question 3.State whether the following quadrilaterals are similar or not:
![](data:image/png;base64,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)
Answer:The given quadrilateral PQRS and ABCD are not similar because though their corresponding sides are proportional, i.e. 1:2, but their corresponding angles are not equal.
Fill in the blanks using the correct word given in brackets:
(i) All circles are __________. (congruent, similar)
(ii) All squares are ___________. (similar, congruent)
(iii) All ____________ triangles are similar. (isosceles, equilateral)
(iv) Two polygons of the same number of sides are similar, if (a) their corresponding angles are _________ and (b) their corresponding sides are ___________. (equal, proportional)
Answer:
The solutions of the fill ups are:
(i) Similar
(ii) Similar
(iii) Equilateral
(iv) (a) Equal
(b) Proportional
Question 2.
Give two different examples of pair of
(i) Similar figures
(ii) Non-similar figures
Answer:
Two examples of similar figures are:
(i) Two equilateral triangles with sides 1 cm and 2 cm
(ii) Two squares with sides 1 cm and 2 cm
Now two examples of non-similar figures are:
(i) Trapezium and square
(ii) Triangle and parallelogram
Question 3.
State whether the following quadrilaterals are similar or not:
Answer:
The given quadrilateral PQRS and ABCD are not similar because though their corresponding sides are proportional, i.e. 1:2, but their corresponding angles are not equal.
Exercise 6.2
Question 1.In Fig. 6.17, (i) and (ii), DE || BC. Find EC in (i) and AD in (ii)
![](data:image/png;base64,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)
Answer:(i) Let us take EC = x cm
Given: DE || BC
Basic Proportionality Theorem: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.
Now, using basic proportionality theorem, we get:
= ![](data:image/png;base64,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)
![](data:image/png;base64,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)
x = ![](data:image/png;base64,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)
x = 2 cm
Hence, EC = 2 cm
(ii) Let us take AD = x cm
Given: DE || BC
Basic Proportionality Theorem: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.
Now, using basic proportionality theorem, we get
![](data:image/png;base64,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)
![](data:image/png;base64,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)
x = ![](data:image/png;base64,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)
Hence, AD = 2.4 cm
Question 2.E and F are points on the sides PQ and PR respectively of a Δ PQR. For each of the following cases, state whether EF || QR :
(i) PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm
(ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm
(iii) PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm
Answer:(i)
![](data:image/png;base64,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)
Given :
PE = 3.9 cm,
EQ = 3 cm,
PF = 3.6 cm,
FR = 2.4 cm
Now we know,
Triangle Proportionality Theorem: If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.
So, if the lines EF and QR are to be parallel, then ratio PE:EQ should be proportional to PF:PR
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![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Therefore, EF is not parallel to QR
(ii)
![](data:image/png;base64,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)
We know that,
Triangle Proportionality Theorem: If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.
So, if the lines EF and QR are to be parallel, then ratio PE:EQ should be proportional to PF:PR
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Hence,
![](data:image/png;base64,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)
Therefore, EF is parallel to QR
(iii)
![](data:image/png;base64,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)
In this we know that,
Triangle Proportionality Theorem: If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.
So, if the lines EF and QR are to be parallel, then ratio PE:EQ should be proportional to PF:PR
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Hence,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEYAAAAvCAMAAABpC0wkAAAAAXNSR0IArs4c6QAAAG9QTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjqQOmaQOma2OpDbZgAAZgBmZpDbZrbbZrb/kDoAkGYAkGY6kLbbkNv/tmYAtmY6tpA6ttv/tv//25A627Zm27aQ2////7Zm/9uQ/9u2//+2///bvlF91wAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABwUlEQVRIS+1W21aDMBCEWita8dKqwUotSP7/G81eQpZAtniO8mL3oWcpw2R3NmTIst+KJodYvzo+SvN8c0qTT8BvEF2v3jK7dz+UZnZH/ycihnflPdFcfUAhzz7NDKRpmhheQQFuceiBaIxaBzIL+KBsKsrAGpDavVoLYiR8x3Cow1Y53GwLpy/wKSHgqLaH13BxDYNCldpbZUyAieBbXtKE8Yo0WU8C3pW9rGcmjcwC7ieN/7dFLyml3YMmzgjue8JJYzSw+b70zWcCXKSgGO5fqKukV4E25XQIuEjV0V5u/j8FDJ+qYXMlNOhxUfIz+DICz25qmXIWX0XYoDttXtxsH7UaRq65fiK4sMG22Byyo3rixCZrDZ9XwTXpoCVDS59ckWu2BZ5zwgaZGK0vFQPXhPWYJthgW5BJqDSRa/LnA7k3uSb5+JmmBq7pnnxnJYMNchVcZfpQ700WDfRAwN4GvbR18JAJqqFrWn8ZbJBpulIb1MA1nZQshHRNagq/uJIRu6ZXQHhf49Sy1Yp35TRT7JrcwsD7ju775o4lm2YZu6bJt+PN6ltV2ppzC/T9VF/NOSxO+WKqyHnPXlB/qMA3Abgj5oZcPk4AAAAASUVORK5CYII=)
EF is parallel to QR
Question 3.In Fig. 6.18, if LM || CB and LN || CD, prove that
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
Given: LM ll CB and LN ll CD
From the given figure:
In ΔALM and ΔABC
LM || CB
Proportionality theorem: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion
Now, using basic proportionality theorem that the corresponding sides will have same proportional lengths, we get:
(i)
![](data:image/png;base64,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)
And in ΔALN and ΔACD corresponding sides will be proportional
Therefore,
(ii)
From (i) and (ii), we obtain
![](data:image/png;base64,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)
Hence, Proved.
Question 4.In Fig. 6.19, DE || AC and DF || AE. Prove that
![](data:image/png;base64,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Answer:![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/4RDuRXhpZgAATU0AKgAAAAgABAE7AAIAAAAMAAAISodpAAQAAAABAAAIVpydAAEAAAAYAAAQzuocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAGFobWFkIGF2YWlzAAAFkAMAAgAAABQAABCkkAQAAgAAABQAABC4kpEAAgAAAAM0OQAAkpIAAgAAAAM0OQAA6hwABwAACAwAAAiYAAAAABzqAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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)
![](data:image/png;base64,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)
Given:
Basic Proportionality Theorem: If a line is parallel to a side of a triangle which intersects the other sides
into two distinct points, then the line divides those sides in proportion.
In triangle ABC, DE is parallel to AC
Therefore,
By Basic proportionality theorem
......(1)
In triangle BAE, DF is parallel to AE
![](data:image/png;base64,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)
Therefore,
By Basic proportionality theorem
...... (2)
From (1) and (2), we get
![](data:image/png;base64,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)
Hence, Proved.
Question 5.In Fig. 6.20, DE || OQ and DF || OR. Show that EF || QR.
![](data:image/png;base64,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)
Answer:To Prove: EF ll QR
Given: In triangle POQ, DE parallel to OQ
Proof:
In triangle POQ, DE parallel to OQ
Hence,
Basic Proportionality Theorem: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.
(Basic proportionality theorem) (i)
Now,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQEAAAAYCAMAAADNnLgoAAAAAXNSR0IArs4c6QAAAK5QTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OgBmOjoAOjpmOjqQOmaQOma2OpC2OpDbZgAAZjoAZjpmZjqQZmaQZma2ZpCQZpC2ZpDbZrbbZrb/kDoAkGYAkGY6kGaQkJBmkLaQkLa2kLbbkNv/tmYAtmY6tmZmtpA6tpBmttvbttv/tv//25A625Bm27Zm27aQ2////7Zm/9uQ/9u2/9vb//+2///b0H36UAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADyklEQVRYR+2XW3vaMAyGY7oysq0rK926A6PrDoR1a9MQQsn//2OTPsmHGLJQnnKXXACWZfnVwXJIkv7pI9BHoI/AnhHIhmWnZmZO7juVjqgg+0cUe0CtjDFfu7jq2ahLJUl2KLFxY178wuL1N2MGX/iXiqeBTRGdiaYMjNlj08CE7B9RhMM2gNyEJGKxnl10exxr7FqUD+ZJfU0fSVKlw7ukMDAMcQaxfVi0nsk05pPN5GkQsn9EEQxbAfIdtVt0l8V2hKp0u5ZgfMXWNhPJEI4TxFUaeghRPRMYYVqEEerOiOwfUfhhKwCY6oUZlkU6EBfqGUqQhKOEhPMk1xNepOb0x9uyqb18Y05/vmdHhb66NOad8orDiIBmPBNHWdyMgHQaJL9ZyRYDbJ5A0ZzI7h9R6JCWtgKg1h7mq5PvU00QazPO73lOwuo1txfFm5I3o6Z2QYeoSjm/OZSKwVRTSAMpZPZaVOS3isVbfbTkcxQfD+qZVpSwycKcjDNBgGZFdv+IQoaojTYAJIiW8wnMtPXY9gGhywlyJlXltSEEvizCvDtYbJxySLO6jS+K+laNW0DBQFTQCf3hxG48ExNgPwsVNkJH4RthO4DScohd17A9yN6BPpVJ9YoRvbaeaBx05HtYPhbugOfsyik3eKTQZkLEd74CXNBEjY1WYzcNDI4AZpVAc+tFsn9E4btpO4B4Cedd11hJfbqIYFMJpzYsH3gcdEfGLWRw9tfCu9cIe8CkyklcR28YMpRupYfOGhEM8iAmcNUpaUBuFNVSiBCKErJtAA0SnHddQ+vCRQTjuNShLciSJH/CLbs65AE2E9aEWKtSVbVafRsI6gMYvCYmsCkPIhNTuPOoEdgBoF4i6y4t+kNLQSewv3QGry3OoMlgkQT0QQMf3Exa3igBiJs3gb3JUALRhYbd+CMmsBEQKIGOKHyltQJk2gjxQjmqb3BaSXv94d41NIrx+qakz7L4NLmoPsoEtDm0yysuU1a6IqWXZX071gyqcR6tiJJ6Il6+IJak2E7FDj7+Sceo1GCZFO40WXJriQlQWxbK7t+gECFoWgDIOnqu1pHtThXd+3fBrZxjYpXSO21mxhwLgLGQVMebidwPPF5fmsFnvYDIuL/w6CY3Z2h+KmZLdo9qErwTN5ZxQM7JJkIXETREun9EIUM8uwF08uCvNb8J+f7xdDsSvP8+e6h0mTjiPF4g9vrb1AKx2P5PEmu6dn5EPw43nfFhWTT+4RxurGWl68fPbvk5DNb0h9ecN15tnsNswwb6Rf/0EegjcLQI/AP51KUmn4ducgAAAABJRU5ErkJggg==)
Hence,
(Basic proportionality theorem) (ii)
From (i) and (ii), we get
![](data:image/png;base64,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)
Therefore,
EF is parallel to QR (Converse of basic proportionality theorem)
Hence, Proved.
Question 6.In Fig. 6.21, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR.Show that BC || QR.
![](data:image/png;base64,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)
Answer:To Prove: BC ll QR
Given that in triangle POQ, AB parallel to PQ
Hence,
Basic Proportionality Theorem: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.
(Basic proportionality theorem)
Now, ![](data:image/png;base64,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)
Therefore,
Basic Proportionality Theorem: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.
Using Basic proportionality theorem, we get:
![](data:image/png;base64,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)
From above equations, we get
![](data:image/png;base64,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)
BC is parallel to QR (By the converse of Basic proportionality theorem)
Hence, Proved.
Question 7.Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX)
Answer:Consider the given figure in which PQ is a line segment drawn through the mid-point P of line AB, such that PQ is parallel to BC.
![](data:image/png;base64,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)
To Prove: PQ bisects AC
Given: PQ ll BC and PQ bisects AB
Proof:
According to Theorem 6.1: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.
Now, using basic proportionality theorem, we get
![](data:image/png;base64,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)
![](data:image/png;base64,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)
[As AP = PB coz P is the mid-point of AB]
![](data:image/png;base64,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)
AQ = QC
Or, Q is the mid-point of AC
Hence proved.
Question 8.Using Theorem 6.2, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side. (Recall that you have done it in Class IX)
Answer:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAisAAAG4CAYAAACEtKdYAAAABGdBTUEAALGPC/xhBQAAAAFzUkdCAK7OHOkAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAAZiS0dEAP8A/wD/oL2nkwAAAAlwSFlzAAASdAAAEnQB3mYfeAAAINJJREFUeNrt3X201XWB7/HPkSMEqICQoiYe0VIgr5g1KGpgZtnqyVqM2YNZ6aqr6TTmHZsZpxVO02TOmp6msTv3Nis0tSdnZAwNlqRYKJozBgFaMeHRQvEBQU5AIrDvH4pX5JzDedy/32/v12st//Ccfc757r1cx/fa+7N/p6VWq9UCAFBSexV9AACA7ogVAKDUxAoAUGpiBQAoNbECAJSaWAEASk2sAAClJlYAgFITKwBAqYkVAKDUxAoAUGpiBQAoNbECAJSaWAEASk2sAAClJlYAgFITKwBAqYkVAKDUxAoAUGpiBQAoNbECAJSaWAEASk2sAAClJlYAgFITKwBAqYkVAKDUxAoAUGpiBQAoNbECAJSaWAEASk2sAFAXK1euzOTJkzN58uSsXLmy6ONQIWIFgLpYvHhxduzYkQ0bNmTBggWp1WpFH4mKaKn5rwWAQbZ+/fqcd955Oeyww7Jt27asWbMm//qv/5oxY8YUfTQqwDMrAAy6VatW5Z577skpp5yS008/PQsXLsz9999f9LGoCLECwKDavn175s2blwMOOCBTpkzJsccem2OOOSY333xznn322aKPRwWIFQAG1RNPPJElS5ZkxowZaWtry0EHHZRp06blzjvvTHt7e9HHowLECgCDasWKFVm4cGFmzJiRYcOGZejQoXnb296WZcuWZfHixUUfjwoQKwAMmmeffTbz5s3LtGnTctxxx7348SlTpmTmzJm55ZZbsn79+qKPScmJFQAGzaOPPpp7770306ZNy8EHH/zixw888MCccsopWbhwYR544IGij0nJtRZ9AAAa1+23355777039957b77+9a93epsFCxbkhBNOyJAhQ4o+LiXlOisADIpNmzbloosuyr333puzzjorw4cP3+Xzzz33XObPn59t27blu9/9bg4//PCij0xJeWYFgEHx29/+NnfddVdmzZqVz372s7s9c1Kr1TJixIhceumluf3223PeeecVfWRKymYFgAFXq9WycOHCrF27NqeddlqnL/G0tLTkrW99ayZNmpTFixdn06ZNRR+bkhIrAAy4DRs2ZPHixZk2bVomT57c5e3a2toybdq0LFiwwB83pEtiBYABd//99794bZXx48d3ebuRI0fmne98Zx577LHMmzcv27dvL/rolJCBLQBQap5ZAQBKTawAAKUmVgCAUhMrAECpiRUAoNTECgBQamIFACg1sQIAlJpYAQBKTawAAKUmVgCAUhMrAECpiRUAoNTECgBQamIFACg1sQIAlJpYAQBKTawAAKUmVgCAUhMrAECpiRUABsyiRYty6qmn5pBDDk9LS0taWlpy8smn5pJLLin6aFRYS61WqxV9CACqb/bs2bniiity6KHnZuzYmRkxoi1J8tRTi/LEE3Ny0EFjcsMN387UqVOLPioVI1YA6LfZs2fnyiu/muOPn5uxY2fu9vnnntuQlSv/POvX/0d+97uHMnr06KKPTIWIFQD6ZedLP9On39FpqLzUPffMzEknjclNN91U9LGpELECQL/MnDkzq1e3ZerUOXu87ebN7fnJTw7PL37xCy8H0WMGtgD0y6pV7Xt8RmWnESPaMmrUYVm6dGnRx6ZCxAoA/fLoow+/OKbtiaFD29Le3l70sakQsQJAXQ0ZUvQJqBqxAkC/TJ8+I089tajHt1+79s7MnDmz6GNTIWIFgH55wxum5onHv53nntuwx9uuXv3V7LvvKONaekWsANAvl3/8g9lv7y1ZubL7q9Ru3Lg0q1dfkWuvneM6K/SKWAGgz5584L7c/63P5zNvnZSnHv9e7lkyI5s3t+92u9Wrv5qf//zUzJr17px55plFH5uKcZ0VAPpkZ6ikVsv2bc9l0x+35sv/9VTu+cXyjBp1WIbu3ZaWbMsTT92VkcNH5robrhMq9IlYAaDXXh4qqe3IMR/4dMa+5tj8csXK/HLFiiz76W3Z0P6rTD3swEybcVreeNHniz42FSVWAOiV7kLlpTa0/ypL53wxe7UOzYhx4/PGv/lW0UenomxWAOixnoZKkuwzfkKSpFbbkS1PP5FtWzYVfXwqSqwA0CO9CZUkaX3FiLxi9LjkhSfwN65ZXfRdoKLECgB71NtQ2Wmf8RNSq+1Ikjz92xVF3w0qSqwA0K2+hkrywktBtVpSq6XDMyv0kVgBoEv9CZUkGd02KUlSq9XS8ehDRd8dKkqsANCp/oZKYmTLwBArAOxmIEIlMbJlYIgVAHYxUKGyk5Et/SVWAHjRQIdKYmRL/4kVAJIMTqgkRrb0n1gBYNBCJTGypf/ECkCTG8xQSYxs6T+xAtDEBjtUdjKypT/ECkCTqleoJEa29I9YAWhC9QyVxMiW/hErAE2m3qGSGNnSP2IFoIkUESqJkS39I1YAmkRRobKTkS19JVYAmkDRoZIY2dJ3YgWgwZUhVBIjW/pOrAA0sLKESmJkS9+JFYAGVaZQSYxs6TuxAtCAyhYqOxnZ0hdiBaDBlDVUEiNb+kasADSQModKYmRL34gVgAZR9lBJjGzpG7EC0ACqECqJkS19I1YAKq4qobKTkS29JVYAKqxqoZIY2dJ7YgWgoqoYKomRLb0nVgAqqKqhkhjZ0ntiBaBiqhwqiZEtvSdWACqk6qGyk5EtvSFWACqiUUIlMbKld8QKQAU0UqgkRrb0jlgBKLlGC5XEyJbeESsAJdaIoZIY2dI7YgWgpBo1VHYysqWnxApACTV6qCRGtvScWAEomWYIlcTIlp4TKwAl0iyhkhjZ0nNiBaAkmilUEiNbek6sAJRAs4XKTka29IRYAShYs4ZKYmRLz4gVgAI1c6gkRrb0jFgBKEizh0piZEvPiBWAAgiV5xnZ0hNiBaDOhMqujGzZE7ECUEdCZXdGtuyJWAGoE6HSOSNb9kSsANSBUOmakS17IlYABplQ6Z6RLXsiVgAGkVDpGSNbuiNWAAaJUOk5I1u6I1YABoFQ6R0jW7ojVgAGmFDpPSNbuiNWAAaQUOkbI1u6I1YABohQ6R8jW7oiVgAGgFDpPyNbuiJWAPpJqAwMI1u6IlYA+kGoDBwjW7oiVgD6SKgMLCNbuiJWAPpAqAwOI1s6I1YAekmoDB4jWzojVgB6QagMLiNbOiNWAHpIqAw+I1s6I1YAekCo1IeRLZ0RKwB7IFTqy8iWlxMrAN0QKvVnZMvLiRWALgiVYhjZ8nJiBaATQqU4Rra8nFgBeBmhUiwjW15OrAC8hFApByNbXkqsALxAqJSHkS0vJVYAIlTKxsiWlxIrQNMTKuVjZMtLiRWgqQmVcjKy5aXECtC0hEq5Gdmyk1gBmpJQKT8jW3YSK0DTESrVYGTLTmIFaCpCpTqMbNlJrABNQ6hUi5EtO4kVoCkIlWoysiURK0ATECrVZWRLIlaABidUqs3IlkSsAA1MqFSfkS2JWAEalFBpDEa2JGIFaEBCpbEY2SJWgIYiVBqPkS1iBWgYQqUxGdkiVoCGIFQal5EtYgWoPKHS2IxsEStApQmV5mBk29zEClBZQqV5GNk2N7ECVJJQaS5Gts1NrACVI1Saj5FtcxMrQKUIleZkZNvcxApQGUKluRnZNi+xAlSCUMHItnmJFaD0hAqJkW0zEytAqQkVdjKybV5iBSgtocJLGdk2L7EClJJQoTNGts1JrAClI1ToipFtcxIrQKkIFbpjZNucxApQGkKFPTGybU5iBSgFoUJPGNk2J7ECFE6o0BtGts1HrACFEir0lpFt8xErQGGECn1hZNt8xApQCKFCXxnZNh+xAtSdUKE/jGybj1iBklu3bl3OOOOMtLS0dPrPiSeemCuvvDJPPvlk0UftEaHCQDCybS6tRR8A6JlJkyblrLPOyvDhw1/82Pbt23Pffffl7//+7zNv3rzMmTMnRx55ZNFH7ZJQYaDsM35CnvrV/Ua2TUKsQEVMmDAhF198ccaOHbvLx2u1Wq6//vqcc845ufnmm3PJJZekpaWl6OPuRqgwkJ4f2c41sm0SXgaCimtpacmb3vSmzJw5M0uWLMnGjRuLPtJuhAoDzci2uYgVaADDhg3LsGHD0tHRkW3bthV9nF0IFQaDkW1zESvQANasWZNHHnkkkydPzr777lv0cV4kVBhMRrbNQ6xAhW3bti1Lly7N7Nmz8/vf/z5nnHFGhg4dWvSxkggVBp8r2TYPA1uoiAULFmTcuHGdfm7//ffPl770pbzpTW8q+phJhAr1YWTbPMQKVERnb10eMmRIXvva1+Z1r3tdDjjggKKPmESoUD+djWxbh48s+lgMArECFdHVW5fLRKhQTztHts9uXJ/k+ZHt/kceU/SxGAQ2K8CAECoUwci2OYgVoN+ECkUxsm0OYgXoF6FCkZ4f2cbItsGJFaDPhApFcyXb5iBWgD4RKpSBK9k2B+8GgpIbO3Zs5s+fX/QxdiFUKJN9xk/IH59Zl+T5ka13BDUez6wAvSJUKBsj28YnVoAeEyqUURlGtjt27MiSJUvyqU99KkcffXRaWlrS1taW888/P0uWLMmOHTuKfpgqTawAPSJUKKuiR7YdHR25/PLLM3369KxevTqXX3557rjjjnz+85/P448/nunTp+fiiy/O008/XfRDVVk2K8AeCRXKrMgr2W7ZsiV//dd/nRtuuCHXX399zj777Oy11/9/HuCDH/xg/u3f/i1/8Rd/kSS56qqrMnKkPwnQW55ZAbolVKiCoq5k+7Of/SzXXHNN/vIv/zLve9/7dgmVJNlrr70ya9asXH755bn66quzYMGCoh+qShIrQJeEClVRxMh2y5Yt+fd///dMnjw5s2bNypAhQzq9XUtLS97+9rdn5syZmTt3bjo6Oop+uCpHrACdEipUSREj2yeeeCLLly/PMccckwMPPLDb244bNy7HHXdcli5dmjVr1hT9cFWOWAF2I1SomiJGtk899VQeeuihTJgwISNGjOj2tkOHDs2YMWOyfPnyrFu3ruiHq3LECrALoUIVFXEl2z/+8Y957LHHenz7iRMnFvb4VJ1YAV4kVKiyeo9sX/GKV+Sggw7q8e1Xr3bBur4SK0ASoUL11XtkO27cuBx++OF55JFHsnnz5m5vu3Xr1qxfvz7HHHNMxo4dW/RDVTliBRAqNIR6j2zHjx+f17/+9Vm+fHkef/zxbm+7bt26LF++PEcddVSvno3heWIFmpxQoVHUe2Q7bNiwvOtd78oDDzyQH/zgB9m2bduLn1u5cmXe+9735pZbbsmzzz6befPmZeHChTnzzDMzatSooh+qynEFW2hiQoVGUsSVbE8++eR8/OMfzxe+8IWMGzcu5557blpbW3PUUUflvPPOy6WXXpoxY8bksccey4UXXpgzzzyz6IepksQKNIGlS5fmzjvvzIYNGzJ69OjMmDEjhwx9TqjQcGqjDsySpQ/moae35NYnr8ibZp2TGTNmZPTo0YPy84YNG5Yrrrgiw4YNy/nnn5+5c+fmrLPOyqGHHpqnn346Bx10UBYtWpQkmTp1aoYNG1b0Q1RJLbXaC+/zAhrOhg0b8tGPfjRz587N/vvvn1qtlpaWljz99NOZfsT4fPotx2b4kAgVGsKPbp2f8/7nhXlu27bsu+++SUtLNm3anL333jvXXnvtoD6rsWPHjixdujTXXHNNFixYkF//+tc56qijcsopp+Tcc8/NmjVr8pnPfCZ/+qd/mssuuyyvfOUri364KkWsQAObMmVK1q5dm1e/+tXP//J+QUdHR3794AMZtXdy9dknCBUq70e3zs/Z534sEydO3O16JqtXr87q1atz0003FfoyTHt7e77yla/kHe94R04//fSCH7FqESvQoGbPnp0vfelLOeGEE9Lauvsrvtu2bcvddy3OJ895X/7uS/9Q9HGhz555ZmOOmvr6vPKAA7q88Nrq1avz5JNP5pFHHhm0l4QYPDYr0KB+8IMfZMKECZ2GSpK0tram7fCJ+f6Pf5Ijj7mh6ONCny1bviLPbt3a7RViJ06cmEcffTSLFi0ycq0gsQIN6sEHH8zxxx/f7W323Xff/OY3v8kt8/3Zeqpr1X//NiNHjtzj7fbZZ58sXbpUrFSQ66wAAKXmmRVoUJMmTUpHR0fGjBnT5W06Ojpy0PjxefsZby36uNBny5avyJzr9vxS5h/+8IdMnTq16OPSB2IFGtQ7Tj05X/+/387BBx/c5cD2kUceyacv/mQ+8qEPFH1c6LNnntmYG77/w6xevbrbgW1ra2tmzpxZ9HHpAy8DQQN68oH7ctqwtRm/34gsvf+/0tHRscvnOzo68stly9J22IRcftmlRR8X+mXUqP3yrav/6cW3KL/czo9/5zvf8U6givLWZWgwL72E/sZNW/Llhb/MPQ89mf3HjEktSUuSp9evzzve9tb8n3/6WkaN2q/oI8OA+NGt83P+hRdn2/bt2WfkiNRqtfyhoyOtra257obvGtZWmFiBBtLV3/pZs7U1P73r7jzzzMaMGrVf3njS9PyP104p+rgw4J55ZmN+etfd+em8G7Oh/Vc5cvz+Oe0tZ+SNF32+6KPRD2IFGoQ/Sgj/34b2X2XpnC9mr9ahGTFufN74N98q+kj0g80KNAChArvaZ/yEJEmttiNbnn4i27ZsKvpI9INYgYoTKrC71leMyCtGj0teePFg45rV/fyOFEmsQIUJFejaPuMnpFbbkSR5+rcrij4O/SBWoKKECnRvn/ETnn9mpVZLh2dWKk2sQAUJFdiz0W2TkiS1Wi0djz5U9HHoB7ECFSNUoGeMbBuHWIEKESrQc0a2jUOsQEUIFeg9I9vGIFagAoQK9I2RbWMQK1ByQgX6zsi2MYgVKDGhAv1jZNsYxAqUlFCB/jOybQxiBUpIqMDAMbKtPrECJSNUYGAZ2VafWIESESow8Ixsq0+sQEkIFRgcRrbVJ1agBIQKDB4j2+oTK1AwoQKDz8i22sQKFEioQH0Y2VabWIGCCBWoHyPbahMrUAChAvVlZFttYgXqTKhA/RnZVptYgToSKlAcI9vqEitQJ0IFimVkW11iBepAqEDxjGyrS6zAIBMqUA5GttUlVmAQCRUoDyPb6hIrMEiECpSPkW01iRUYBEIFysnItprECgwwoQLlZWRbTWIFBpBQgXIzsq0msQIDRKhA+RnZVpNYgQEgVKA6jGyrR6xAPwkVqBYj2+oRK9APQgWqx8i2esQK9JFQgWoysq0esQJ9IFSguoxsq0esQC8JFag+I9tqESvQC0IFGoORbbWIFeghoQKNw8i2WsQK9IBQgcZiZFstYgX2QKhA4zGyrRaxAt0QKtC4jGyrQ6xAF4QKNDYj2+oQK9AJoQKNz8i2OsQKvIxQgeZgZFsdYgVeQqhA8zCyrQ6xAi8QKtB8jGyrQaxAhAo0KyPbahArND2hAs3LyLYaxApNTahAczOyrQaxQtMSKoCRbTWIFZqSUAF2MrItP7FC0xEqwEsZ2ZafWKGpCBXg5Yxsy0+s0DSECtAZI9vyEys0BaECdMXItvzECg1PqAB7YmRbbmKFhiZUgJ4wsi03sULDEipATxnZlptYoSEJFaA3jGzLTazQcIQK0FtGtuUmVmgoQgXoKyPb8hIrNAyhAvSHkW15iRUaglAB+svItrzECpUnVICBYGRbXmKFShMqwEAxsi0vsUJlCRVgoBnZlpNYoZKECjAYjGzLSaxQOUIFGCxGtuUkVqgUoQIMJiPbchIrVIZQAQabkW05iRUqQagA9WJkWz5ihdITKkA9GdmWj1ih1IQKUG9GtuUjVigtoQIUwci2fMQKpSRUgKIY2ZaPWKF0hApQNCPbchErlIpQAcrAyLZcxAqlIVSAsjCyLRexQikIFaBMjGzLRaxQOKEClI2RbbmIFQolVICyMrItD7FCYYQKUGZGtuUhViiEUAHKzsi2PMQKdSdUgCowsi0PsUJdCRWgKoxsy0OsUDdCBagaI9tyECvUhVABqsjIthzECoNOqABVZWRbDmKFQSVUgCozsi0HscKgESpA1RnZloNYYVAIFaBRGNkWT6ww4IQK0EiMbIsnVhhQQgVoNEa2xRMrDBihAjQiI9viiRUGhFABGpWRbfHECv0mVIBGZ2RbLLFCvwgVoBkY2RZLrNBnQgVoFka2xRIr9IlQAZqJkW2xxAq9JlSAZmNkWyyxQq8IFaBZGdkWR6zQY0IFaGZGtsURK/SIUAGanZFtccQKeyRUAIxsiyRW6JZQAXiekW1xxApdEioAuzKyLYZYoVNCBWB3RrbFECvsRqgAdM7IthhihV0IFYCuGdkWQ6zwIqEC0D0j22KIFZIIFYCeMrKtP7GCUAHoBSPb+hMrTU6oAPSOkW39iZUmJlQAes/Itv7ESpMSKgB9Y2Rbf2KlCQkVgP4xsq0vsdJkhApA/xnZ1pdYaSJCBWBgGNnWl1hpEkIFYOAY2daXWGkCQgVgYBnZ1pdYaXBCBWBwGNnWj1hpYEIFYPAY2daPWGlQQgVgcBnZ1o9YaUBCBWDwGdnWj1hpMEIFoD6MbOtHrDQQoQJQX0a29SFWGoRQAag/I9v6ECsNQKgAFMPItj7ESsUJFYDiGNnWh1ipMKECUCwj2/oQKxUlVADKwch28ImVChIqAOVhZDv4xErFCBWAcjGyHXxipUKECkD5GNkOPrFSEUIFoJyMbAefWKkAoQJQbka2g0uslJxQASg/I9vBJVa6cf3116elpaXTf2bOnJlvfvOb2bRp8F6bFCoA1WBkO7haiz5AFVx00UV51ate9eK/b926NXfeeWcuvPDCrFixIldddVVGjhw5oD9TqABUR2cj29bhA/v/hWYmVnrg7LPPzkknnbTLx/7qr/4qV155Za666qq8973vzWmnnTZgP0+oAFTLzpHtsxvXJ3l+ZLv/kccUfayGIVb6qLW1Naeeemo++9nPZu3atb362vb29jz88MNZtGhRkqStrS1tbW2ZMWOGUAGoqI6ho/Kr3/93VqzdmFufvCKve/M7X/zd3lMbN27MD3/4w9x4442566670tHRkdNOOy3vf//7c/bZZw/4s/hVIVb6YfPmzUmSfffdt8dfM2fOnPzZn12Sjo4NGT9+RrZvT7Zubc8zzzyct502I+cdNTz7DG0VKgAVct33vp9PX/mdbNqyKQeMm54dq57MNT/6XJ555uGceeaZ+fa3v53Ro0d3+z2WLFmSCy64IBs2bMiHPvShfPrTn06S3HLLLbnsssvyox/9KP/yL/+SAw88sOi7W3dipQ927NiRVatW5Wtf+1re85735MQTT+zR1334wx/JjTfOzcSJszNx4p/v8rnNm9tz37IPZ9HP7sxV7z0uE8eOFCoAFXD+J/88N908P0cc8Xed/m6/666P5NBDD8/PfnZHpk6d2un3+OUvf5kLLrggbW1t+ed//ucccsghL37uzW9+c971rnflYx/7WP72b/92UHaSZefdQD1w8skn7/JOoCFDhuToo4/OPvvsk2984xt55StfucfvMWfOnNx449z8yZ8s2u0/5iQZMaItJ57404w78Kz8w22/ESoAFXDd976fm26en2nT7uzyd/sJJyzKmDHvzgc+8NFOv8eWLVty9dVXJ0m++MUv7hIqSdLS0pIZM2bkE5/4RL7zne/knnvuKfpu151nVnrg5e8G2r59e+67777ceuut2bRpU7785S/n1a9+dZdf397enk996pJMnDg7++03tdufNWXKV7Pk7p/kf89dmMsvEysAZfXw736X//XXs3PEEVf06Hf7PfdMzezZszN79uxdPrdq1arcfvvtmTVrVl7zmtd0+vVDhgzJW97ylixatCjr1q0r+q7XnVjpgc7eDVSr1XLHHXfkYx/7WP7xH/8xX/nKVzJ8+PBOv769vT0bN27otLpfbu+9R+fA8edlwfy5+cS7Ti36rgPQheW/WJ6Ojmd6/Lv9gAM+kttuW5SXtUoefPDBrFq1Kscee2yGDBnS5fc4/vjjs2DBgqLvdiHESh+1tLTkxBNPzBlnnJG77747Dz/8cI4++uhOb7to0aKMH9/zNfi4cTNz991XZMX3vlb03QSgC//x89/mgHHTe3z7nb/bX+43v/lNkuzyDD67Eiv9MHz48BxyyCFZvnz5Hp+W2769999/r9ahRd9FALrQsteQ7KgN6f83Yo/ESj9s2bIla9asyfHHH9/tW8na2try3HMP9/j7bt7cnnGj9s9+hx5R9F0EoAtta7dm68oHenz7zZvbc/DBh+328dZW/yveE49QP/z85z/P/Pnzc+qpp+aggw7q8nZtbW3ZsKE9mze3Z8SItj1+33XrFuWkmadk+qVeBgIoq62LFuUL3z+1V7/b3/CGqbt9fMqUKUmS3//+90XfpdISKz3wve99L4sXL97lY8uWLcu8efMyceLEXHLJJd2+533mzJl597vfnbvv/mhOOOGObn/WunWL8rvfXZObb/5F0XcbgG4M1O/2I444IpMmTcqyZcsya9asLke2jz76aC6++OJMmzYtn/zkJ5vqWitipQe+8Y1v7Pax4447Lpdddlk+/OEPZ8KECXv8HnPmzMmrXtWWpUs/milTvpK99x69223WrVuU++9/Tz73uc91eeEgAMpjIH63H3nkkTn99NNz66235pxzzsmkSZM6/Vn33Xdfbrvttpx00kkZMWJE0Xe9rlpqtVqt6EM0i6VLl+YDH/hI1q59Jgcc8JGMHTszSS2bNz/8QnXPyec+97nd3oMPQHkNxO/2//zP/8ysWbMyderU3a5gmyQrVqzI+eefn9bW1lx33XVpa2sr+m7XlVipsw0bNuSrX/1qbrttUe6++84kycEHH5Y3vOH5iwV5RgWgevr7u71Wq2X+/Pm54IILkiQf+tCHMmPGjGzdujU//vGP893vfjeHHnpovvnNb/b4T7w0ErECACXxyCOP5Nprr80tt9zy4mX1Z8yYkVmzZuX9739/xo4dW/QRCyFWAIBS84cMAYBSEysAQKmJFQCg1MQKAFBqYgUAKDWxAgCUmlgBAEpNrAAApSZWAIBSEysAQKmJFQCg1MQKAFBqYgUAKDWxAgCUmlgBAEpNrAAApSZWAIBSEysAQKmJFQCg1MQKAFBqYgUAKDWxAgCUmlgBAEpNrAAApSZWAIBSEysAQKmJFQCg1MQKAFBqYgUAKDWxAgCUmlgBAEpNrAAApSZWAIBSEysAQKmJFQCg1MQKAFBqYgUAKDWxAgCUmlgBAEpNrAAApSZWAIBSEysAQKmJFQCg1MQKAFBqYgUAKLX/B6bDyiWkganFAAAAJXRFWHRkYXRlOmNyZWF0ZQAyMDE4LTA2LTE1VDA5OjE1OjIyKzAwOjAw1pFssQAAACV0RVh0ZGF0ZTptb2RpZnkAMjAxOC0wNi0xNVQwOToxNToyMiswMDowMKfM1A0AAAAASUVORK5CYII=)
To Prove: PQ ll BC
Given: P and Q are midpoints of AB and AC
Proof:
Let us take the given figure in which PQ is a line segment which joins the mid-points P and Q of line AB and AC respectively
i.e., AP = PB and AQ = QC
We observe that,
![](data:image/png;base64,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)
And,
![](data:image/png;base64,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)
Therefore,
![](data:image/png;base64,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)
Basic Proportionality Theorem: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.
Hence, using basic proportionality theorem we get:
PQ parallel to BC
Hence, Proved.
Question 9.ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that ![](data:image/png;base64,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)
Answer:The figure is given below:
![](data:image/png;base64,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)
Given: ABCD is a trapezium
AB ll CD
Diagonals intersect at O
To Prove = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAsCAMAAAAelGUHAAAAAXNSR0IArs4c6QAAAIdQTFRFAAAAAAAAAAA6AABmADo6ADqQAGa2OgAAOgBmOjpmOjqQOmaQOma2OpDbZgAAZgBmZjoAZjpmZpC2ZpDbZrbbZrb/kDoAkDo6kGY6kJA6kLbbkNv/tmYAtmY6tpA6tpBmttv/tv//25A625Bm27Zm27aQ2////7Zm/9uQ/9u2/9vb//+2///bR+0lDgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAB1UlEQVRIS+1WaVODMBDNYivWox61tVqqlWIB4f//PrNHQsJwxBmn/VDzgQnk7ePt5nhR6o9bvZoeiLJcA0SLEXYXVK5jgMmzjUiBmYp4ulMZ3A1SuSDpL01A9fhKTNX8Uj+twG4+F1TNMa66/zTQ7TK9wJck2uCnhF76mguSvoUW1wdiKmKUNMLkglhe0+qXjUpRTQ6U73B2Lkj6lirXBc6RSbIyf+1OzwW1ylDNQTfNZLSkLK27uaC2+BTnHHXKAM/HCBOBWkzFFU5UEWsdLHZQkg/igISXX72i8u9xNeb6UW+hWbBdwlxQDgtVv/PSUWuItJqcCqUyvfJnu/7UaMQF7XGr3AwUY4Trf/i8KpDglqQmy28gfQttdfpC+vBwtBL/JrujiTrRj/SJgrMsZ0OICTcYjp29iXTylS92qBATdjEYW66MaZPX8ZkcYsIeRmLFahNUw+MhJuxhEnIPygo59BFePuCnEBP2MBRrTaTQZzFEZAMhJuxhyJKsJkxVDCLEhD0MX0yMeVOqVKYQE/YxXCa5aLDhuUyDJuwZtZileC2nin4YZsKuUXOsmQO6pWQxyQwxYc+Ddez3R3zLN0u6qUye2EdDTLjBcKzdKyfa7Wf72x+qODFXVWmxIAAAAABJRU5ErkJggg==)
Construction: Construct a line EF through point O, such that EF is parallel to CD.
![](data:image/png;base64,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)
Proof:
In ΔADC, EO is parallel to CD
According to basic propotionality theorem, if a side is drawn parallel to any side of the triangle then the corresponding sides formed are propotional
Now, using basic proportionality theorem in ΔABD and ΔADC, we obtain
![](data:image/png;base64,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)
In ΔABD, OE is parallel to AB
So, using basic proportionality theorem in ΔEOD and ΔABD, we get
![](data:image/png;base64,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)
From (i) and (ii), we get
![](data:image/png;base64,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)
Therefore by cross multiplying we get,
![](data:image/png;base64,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)
Hence, Proved
Question 10.The diagonals of a quadrilateral ABCD intersect each other at the point O such that
Show that ABCD is a trapezium
Answer:The quadrilateral ABCD is shown below, BD and AC are the diagonals.
![](data:image/png;base64,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)
Construction: Draw a line OE parallel to AB
Given: In ΔABD, OE is parallel to AB
To prove : ABCD is a trapezium
According to basic proportionality theorem, if in a triangle another line is drawn parallel to any side of triangle,
then the sides so obtain are proportional to each other.
Now, using basic proportionality theorem in ΔDOE and ΔABD, we obtain
...(i)
It is given that,
...(ii)
From (i) and (ii), we get
...(iii)
Now for ABCD to be a trapezium AB has to be parallel of CD
Now From the figure we can see that If eq(iii) exists then,
EO || DC (By the converse of basic proportionality theorem)
Now if,
⇒ AB || OE || DC
Then it is clear that
⇒ AB || CD
Thus the opposite sides are parallel and therefore it is a trapezium.
Hence,
ABCD is a trapezium
In Fig. 6.17, (i) and (ii), DE || BC. Find EC in (i) and AD in (ii)
Answer:
(i) Let us take EC = x cm
Given: DE || BC
Basic Proportionality Theorem: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.Now, using basic proportionality theorem, we get:
=
x =
x = 2 cm
Hence, EC = 2 cm
(ii) Let us take AD = x cm
Given: DE || BC
Basic Proportionality Theorem: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.Now, using basic proportionality theorem, we get
x =
Hence, AD = 2.4 cm
Question 2.
E and F are points on the sides PQ and PR respectively of a Δ PQR. For each of the following cases, state whether EF || QR :
(i) PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm
(ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm
(iii) PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm
Answer:
(i)
Given :
PE = 3.9 cm,
EQ = 3 cm,
PF = 3.6 cm,
FR = 2.4 cm
Now we know,
Triangle Proportionality Theorem: If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.
So, if the lines EF and QR are to be parallel, then ratio PE:EQ should be proportional to PF:PR
Therefore, EF is not parallel to QR
(ii)
We know that,
Triangle Proportionality Theorem: If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.
Hence,
Therefore, EF is parallel to QR
(iii)
In this we know that,
Triangle Proportionality Theorem: If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.
So, if the lines EF and QR are to be parallel, then ratio PE:EQ should be proportional to PF:PR
Hence,
EF is parallel to QR
Question 3.
In Fig. 6.18, if LM || CB and LN || CD, prove that
Answer:
Given: LM ll CB and LN ll CD
From the given figure:
In ΔALM and ΔABC
LM || CB
Proportionality theorem: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion
Now, using basic proportionality theorem that the corresponding sides will have same proportional lengths, we get:
(i)
And in ΔALN and ΔACD corresponding sides will be proportional
Therefore,
(ii)
From (i) and (ii), we obtain
Hence, Proved.
Question 4.
In Fig. 6.19, DE || AC and DF || AE. Prove that
Answer:
Given:
Basic Proportionality Theorem: If a line is parallel to a side of a triangle which intersects the other sides
into two distinct points, then the line divides those sides in proportion.
In triangle ABC, DE is parallel to AC
Therefore,
......(1)
In triangle BAE, DF is parallel to AE
Therefore,
By Basic proportionality theorem
...... (2)
From (1) and (2), we get
Question 5.
In Fig. 6.20, DE || OQ and DF || OR. Show that EF || QR.
Answer:
To Prove: EF ll QR
Given: In triangle POQ, DE parallel to OQ
Proof:
In triangle POQ, DE parallel to OQ
Hence,
Basic Proportionality Theorem: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.
(Basic proportionality theorem) (i)
Now,
Hence,
(Basic proportionality theorem) (ii)
From (i) and (ii), we get
Therefore,
EF is parallel to QR (Converse of basic proportionality theorem)
Hence, Proved.Question 6.
In Fig. 6.21, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR.Show that BC || QR.
Answer:
To Prove: BC ll QR
Given that in triangle POQ, AB parallel to PQ
Hence,
Basic Proportionality Theorem: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion. (Basic proportionality theorem)
Now,
Therefore,
Basic Proportionality Theorem: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.Using Basic proportionality theorem, we get:
From above equations, we get
BC is parallel to QR (By the converse of Basic proportionality theorem)
Hence, Proved.Question 7.
Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX)
Answer:
Consider the given figure in which PQ is a line segment drawn through the mid-point P of line AB, such that PQ is parallel to BC.
To Prove: PQ bisects AC
Given: PQ ll BC and PQ bisects AB
Proof:
According to Theorem 6.1: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.
Now, using basic proportionality theorem, we get
[As AP = PB coz P is the mid-point of AB]
AQ = QC
Or, Q is the mid-point of AC
Hence proved.
Question 8.
Using Theorem 6.2, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side. (Recall that you have done it in Class IX)
Answer:
To Prove: PQ ll BC
Given: P and Q are midpoints of AB and AC
Proof:
Let us take the given figure in which PQ is a line segment which joins the mid-points P and Q of line AB and AC respectively
i.e., AP = PB and AQ = QC
We observe that,
And,
Therefore,
Basic Proportionality Theorem: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.
Hence, using basic proportionality theorem we get:
PQ parallel to BC
Hence, Proved.
Question 9.
ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that
Answer:
The figure is given below:
Given: ABCD is a trapezium
AB ll CD
Diagonals intersect at O
To Prove =
Construction: Construct a line EF through point O, such that EF is parallel to CD.
Proof:
In ΔADC, EO is parallel to CD
According to basic propotionality theorem, if a side is drawn parallel to any side of the triangle then the corresponding sides formed are propotional
Now, using basic proportionality theorem in ΔABD and ΔADC, we obtain
In ΔABD, OE is parallel to AB
So, using basic proportionality theorem in ΔEOD and ΔABD, we get
From (i) and (ii), we get
Therefore by cross multiplying we get,
Hence, Proved
Question 10.
The diagonals of a quadrilateral ABCD intersect each other at the point O such thatShow that ABCD is a trapezium
Answer:
The quadrilateral ABCD is shown below, BD and AC are the diagonals.
Given: In ΔABD, OE is parallel to AB
To prove : ABCD is a trapeziumAccording to basic proportionality theorem, if in a triangle another line is drawn parallel to any side of triangle,
then the sides so obtain are proportional to each other.
Now, using basic proportionality theorem in ΔDOE and ΔABD, we obtain
...(i)
It is given that,
...(ii)
From (i) and (ii), we get
...(iii)
Now for ABCD to be a trapezium AB has to be parallel of CD
EO || DC (By the converse of basic proportionality theorem)
Now if,⇒ AB || OE || DC
Then it is clear that⇒ AB || CD
Thus the opposite sides are parallel and therefore it is a trapezium.Hence,
ABCD is a trapezium
Exercise 6.3
Question 1.State which pairs of triangles in Fig. are similar.Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form:
![](data:image/png;base64,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)
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)
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)
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)
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)
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KL4NNddqSYHqZaQ1x3xiMdch61oU2X3Rhy0IHSYs2w1iTTIiO+DLAi4Ir7rljIpUuX8Pvo0ShXujSKFHwHtarXxPvvvYcCOXOgSa1qmDplOmYcCEFb+fsl1liVrzijEEtrEZJ5Z1w4r4OQGl6GSNm3N11yo9A6C3KIMjVLrISIJ7iXXzREYPJxB+pttSKNT3Sj1kLLTfhOiG3rZQ/Mel7RMw2vJ5Rg0WwaB9hE4wlDrY1m1eTxmi1S5dWft0Rgv2hjbGE/RzZ4uqVKxaQ1sm1EubVm/LI3Oq3xzpQtj8eD6dOmoWSxYnIUx/ChP8Jvmx9Wr16NAf36oUTRoqjxwftYNG8ugk0uLD8XoYZ7cUgRc/EZhOyzwwbfKx7VRl/b9RreAFrgC065kHuVGSVXmbD6tOvJh/7k7x0VK37IHjvKigyyPxi9BFXWmDH2iAMHwyJg0/GVZxLeTShR0YG/evQHzzWotOHGmy34XszqIRwWJBs83WAZxbRmF+K0S6MHB+WQ877xl81erBVLPI3tTp8+jW6du6B4kaIY9fPPuHjxIiLCI+B2u3FZLJfu3boh05tv4ovWrWA1GFTTyRMiCBzgVU2E5A0RktflbxUTS2jkPjsOXveoczQ0niYszkj8LWs0i8hDjU0W7LnylNLf5W+ahDT85e/3EnnNs9SkZDPNkujvNeeEUymGuj/YswWvJpRIUa12yoKsLiSiKttjjtfElE7NuSfyM3sNsYYkn5DIx1ssGLzfjhUX3TjDWpV7qGYbN25Ereo1ULnie9i+fftdry+YP1/I5l1Uq1IVx44cvvk8RwwHyHcaJn8nKyvuZ4Uho/zt9+U7jj3mxFXtBtN4igixReCHXTakWWxE8wArLhjCn+4XEuP9vDkCS8+60THAhhfoBpsThsJiPXUXC3/dORcs2g32zMCrCYX59POOO9Xie1uskBYiIJ/LImwuxyeBYqHstKPbfgdGiRm9UEz7g8Gee3chvgW+vr6oW6cOqlSujN27d9/1+pLFi5U7rHrVqjh+/Phdrxvk70w741LxlFxMmRRiyyza1zfy3RbJ85fNmlg0njxOi0LzqSg3rKXqvNcOuxd11Q66Ea5k9aONFqQmscw1oKJY+z8esCsljck0GkkbXk0oZmcUftpjwxuy+D70teDI9XCYXUyLBG44xbx/hGSrK1euoGf3HioY//tvv+Hy5ctiEUUiPDxcBeu/69MHuXPkwJcdOsBsNsf/OSLAk444UVWEOMPi6FqXAkIw/ffYsZ0Ep4VE4wmCMcZCK00qy6rvYQe8zacUGRGl2sIM2m1HESGTVAuNqnNFnfVmjD/mwAmxqDwe7QdLqvBqQmGwu3NAdHZVHbEErnKCnHIIR8UIyp0LL/q5qKjIOEeYRkREwOVyKeIgZkybjnfy50fF8uXx808/wd/fH5s2bcKPQ4eiTMmSqF2jJpYuWaoC+PeCMzwKh0X7+lFIhBkt7A322mKjKsb865ADp4R0wjWvaDwBrLjsxmtLjHh+Thh+PuH0yu9I0TTGtMnvLHKdc6kRKUVm0i8zovVWK1addeG6Q8dXkiK8mlAu2SPx3iYLUsww4OOdNgSHGnD66CHs3rkD+/bsVsee3f9/7Nq5E3v37MGZM2dgs9lu+yz+TsLw8fHBvn37FLlcvXoVw4Q8CuTJi3y586BmteqoUvl9FBarpVzpMhg3dixMJlOC52sH2yKxXoSkp3zXnCLUz4m1kl2slboiJDOOOxGiZ69oPE5ERik37Ouy5kqIYsM2KN6MKLFWGF+Zd9qFFlusSOdjUNMi6eJuu92GzfL93dpaSVLwakLZGxaO3Gs5GMuMfjvD4Oe7Bf179UDr5i3wRbt2tx0d2rXHZy1bolOHDmJVLIHZYrn5OXuEZIYOGYJv+/TB33//jV9HjcJvo0djx44duHTxIv6aMBEd23+Bj5s0VUfXzp0x7b//cP78+Yf63ucNEZgV5EKrbVY1nCjFTAMKiIB/u9uGjSIkJrs2VzQSHzbR6n8+7EC6ZSY1kuFwcHjS+OJCLOxCMUa+ex1RIDkEj16JDzZY8KtY+NuvejSxJBF4LaEww2v5eRdyrbbg3TVOTNh2Hr/98gsK58uDV59/EWleT3XzSCvHW+nSI90bqZULa8G8+Sr9l7h27Sp69eiJgnnzKUKhdTLkhx/wbuEi6PjFFwgKClLnMW6ye9cu7Nu7V/2cGMv3ZKgHQ/fbUXq9WbWjeHm+AZVXmzFahGRPSDjsOhdfIxHBLtw9dthU+nynAKsa15CUQNLYcdmNzrtsKLTKjJcWGPGayAxnsfx30qVcx5G6UatXw2sJhdkp/xx34m1ZWDW3RmDMit34+ssvUeydgsiXM5cQQmFFCsVijrzy3NuZMqNOrVrYL6RBGAwG/Dt1KsqXLoO6tetgq68vHA4H1q5Zo9xbBYRkGC8xGo3qfLq2ohLZcWvzRGLXNY8aclRwpVnVrqQTcqm/wYyZIiSXrBEI154wjUTA8evh+NzXqiyUwfvsMCRBFyvFj7HTFWdc+HyLFZmWGVVMMqPITNttFuVSNsjeEKWNfK+E1xKKwR6J0QfsyLTSgjbCD79OW456dWqjY7u2mDBuHBYtWqRSe+neYlzks1atULRQYbE+BiM4OFh9xratW1VMJGP6N9GpY0ecOHFCPU9XVvu27ZDy5VdQ/cNqCAwMfLz/jFhbjK/Qp/1NgA1vLzLifwsMyLXCjDb+VqwS4THpXHyNR0TAJQ+qigXMJo0TTjgRkYTdRLRWTonFNS3IiVpi4b8wNzq+UmitWcUot19xa1LxQngtoXBYz7fbbaJtmdF5rxPT56/EwL59sXXLZmV5RDKTK+ZcNnjs0b07KpQth8WLFit3Fy2NmTNmIlvmLMolxrjI8WPHbp7f+etv8PLzL6B40aKqOaTFann8/5R84dOGcEw95kSTraJJCqkwcF9GNoFv9thVZX9S3gQ0ni7+Pe3CW7KmUi4xwYcB+WdgKTGFmDUqPx10qOF3z8024Pl5BlQXC//HIw4cuxGe6F4FjYeH1xLKkdBwNJIFRHP3+31mHD0ahEMHDiAy4m6/8M5du9CsSROxYD7CkcNH1HMWiwXjxo5Dvly5kSFtOiGQr3Hs6FH12rVr1/DVl52Q6pVXlets5PDhqvXKkwKn5zEI+ct+O6qut+DlBQZVPUwhmXzcqVKQXTq+ovEA4J464KhDdW7IsMwE35BnqyN2uMgDE1paiJKpxhBzwqrITdsAK3zEwj/DDhXaYnnq8FpC2XLVg3ysQBdt5NeTzmgtJA5NhIWI48ePx3sVKqBXjx6wmKMtDQbWh//4o4qtMGAfF6GkTvka3smXHz26dY+zGv5xwyba1zYRkk7+VmRYbsJrzMVfZFQZOj6ibYbYIxGhh3ppJABUQLqJgsLC2sprzDh4I2kF5BOC2PjKfNkPWG2fRvaHl0Vmsi42Kleyn+wZ5nh692k8GXgtocw658KLPtH9uiadjT+fnu6rdm3aoFKFipg7Z66qLyEuXLigakwSQijdunTFsRh32JNGREQULlgisOCMOzqgKv/zS3LkXWVG90ArtgrhOLUbTOM+CLNGoN1Om4ozfLXNigvPcOsfh5DncWME/hZr/n0hT7rA2F289Dozhu62Y59Y/7qQ+OnAOwlFFsOYky68wG6+K0zYeCVu850V7wcOHEDND6ujcf2GOHTo0M3X6MLydgvlVkSFR6nWMuOOOlFtg1lNmHxpvgHvr7dg0AE7dov2pVMmNeJePMBpsUgaC5G8tcyEMQftqonpsw6bKxLbZG/ot9eu9gm6wdLKnlFri1U1aj3/tBtjJkN4JaGw++iAAw68scSIdr4W1VQuzgVls2HWzJmoUK4cevfoeTP9l0iohcL6lK6dn56FcicYhGSF8He7bCiz1qxcGLTSmm62YNYpF06LZhaliUXjFtAV5HvejQqyXnKvMqlGqS73kyUUu92Oq1evKdlyOZ9sy5dQsc4WnnKqQXp5V0T3MUu/yICu221Ycd6Fy2zZpEXmicArCYUFWe1lcbBAq/d2q8r4igtM/+3auYtyd/0zdeptrzGGMmLYsPsSSqH8BdC7Zy+cPHnSq66BVbSvDefcaCJaZ8al0bn4uYRg2fto7QU3gu06CKkRDU5knC6WbXZZHwXXmLFeFJLI8Cezg9JLQG8Axz2MGD5C9cSbN2cuDh48qPrmPUkEC3H8d8yBihssyCDXgmMuii43YYAoZ/5X3DDp+Mpjh1cSCjOgOEiLgepfDzribVXi7+en6kxafNIcO3fuvO21MIMBY/74UxFKfFler7/8CooVKYLRv/wq2tUVr7sOHtkUWB087bgT9TaYlX+c3VlLrDZhoAjJvhAPwrW1kuzhkTUwar8dKecbUHS9BTtDntxQrTNnz+KnESNQsWw51bm7xLvF8G6hwmj5aXPVX+9Jw+qOwv4b4Rh7yI6KIif/8zEg7WIjKq8z4w/ZS04ZwnXTyccIrySUzaKBlxfTPbOYrzPEfA+PQ9ui9jN75kyULPouBg0YiOvXr98uZB6PvD4LObK+jbSp3ritDoXnfvPV13jl+RdQqngJzJ83D3aH3WtvklM0q11CssMPOVCJQcg5YUgjxPKhkO4fhx0ICg3XmlcyhisyCm132JBiehhKbbbiwhPsFffvP/+o1HzWe3Xq0BHfffstSgqp5JXnfv3lF4SEhDyVa2K0R3cz7rbLjkLLjHhOZCbrEhMa+lkx/YRTjZ3QIpP48EpCYZXvW6JtZVxpwrqrnjjThRkj6d+vH8qXKYPZs2ap9OE7sXP7DtSpUROZ3sygGkjGxknOnzuHdp+3QcqXXlZTG/fu3ZMkFpfdGYn1593KN1xkZXR8JYMQS5ttVlXUdlEP9UqWCJZ18YGsgRdm3EDrQBtsT8hqtVqtSlFjP73PW7dWbuOwsDD8Pvo3vCuWf4N69VQD1qeJqyITTDNmR4rcS01CLAbkWWpEF5GhxRfduGHTfuPEhNcRCssuuhxwIMWMMORabVYdh+PC+nXrULtmLdSvW/cud1csont5/YNK5Ssq4li9erUqeFy5fLmaxPhO/gIqzsLzktQGYmEuvgutfK3IsSy6Vif1EiP67rYjUAj4Bod6afUrWYC61t7r4Si10YL0PgaMPWCH6wnFT0geX335JbJnfRv9+vZVcUvK14xp01CqRAlU/aCK6p/31K+RbCrnDBGYcsShGk1mWBI9CC/3SrrU7TggFr6Kr2g8MryOUCyyGbbeZVMVvzU2WHDGEhGHEEVh3JgxKFakqDKxaa3ELWxRapEPGTwYVd5/Hz8MGgQ/Pz8M7N9fZYb17NEDp06dSpKtGzjUK0iEhAO8yqwSzWuBUZFK2dUmDNtjx5FQDyK18vXMgzG0teddqsdVXlEuODLb84AWSmxT1AeRA57r9ngwWGSKMUomxvzx+x+YOGEimjRspOIo7PLtTckuLCQ+IOQ7XOQjz3IT/icyk16sFg7CG3/YgQvsZqx55ZHgdYTCqYxNAqx4Zb4BPeQxOA5/MDWjMX/+qcxsNom0WO7dhyso6KSab/Lzzz+r942SxymTJ+PIkSNJ/gbSV7z5igcD99lRXISELVzeWmRCw60WFcy/ZNJusGcZDnck5p10Km27nGyMm865EqxIsOfduXPn1FC6nTt2qPENF86fvznRND6wmJhjHg4fPoxNGzeifdu2yPJWRhWUL/lucWTJkBFVRYFbtWKl6u7tbbgme8zyi250225DrsVG5Qajpf+pnxUz5FqG2rTMPCy8i1BEOzh63YPqWyzILJrDJNG+LXGYoqw32b17N7Zu3apmwcdWx98LzJPfv38/1q1dq4ohbXb7o3xN1ZzSm3DDGoGlp11oF2hV6aMpZocpX/FXO2xYfN6NEIsWkmcR7FJNN1dGkZc6vlYcTUAPLxIGp5r+9++/6Pf990rBmjljBkb/+iv6y+/TRfmi1X+nxWIQRW7Z0qVqLhEVsr//+kuskt/VCIgu33yDZo2boHH9Bviq45eYPm0aQu9IlPE2XBALnwH6RlutSL+Qg/DCUECIpedeOzZedqt6OI0Hg1cRCs339aJhFV9jRiE51px1qdRZbwC1OZrv69auw0IfH/gs8MHmTZtULUxCCO1J4aIxHBOEiOtsNCNjTHwlnzxy3r1vsAcGpxaSZwlXrZHo7m9FygVGtBLl4XoCZqBwrDVJpHDBgqhQtiwmjB+Pbdu2YeyYMShbqhRKFSuGSZMmwWQ23XyPS9b/vLlz8UGlSmjwUV3lGZg6ZQrer/ge6tSshWXLlqlYZmBAgJKJpORGPmNlZw6gpl843lphQ4r5RpRbbcJYkaPdN8Jh041aEwyvIhSHJ0pZJVlEwy61wYLAKx4VUHvaIGFwHj0nPNI3zFz7UsWKo2K5cujTqxd27dql0pS9BXa5jmzrPeqAAzlWmlQ34zcWGZFntRm/01dsjFDFcBpJHyflXlZbZ1YW6Tf77Ai/T983bvRsUVSrRg28kOI5dGjfXqX2Mg2fLuCOHTogW5YsaP7JJ3LewZvvoVVPCyRX9hwYNvRHRUq0ctq0ao1c2bKjV8+eKh4ZV7aldyMKLqcLwQYbAs5b0GeHFWmXm/HqQhNSi9VSZr0Zs4KcuCbEreMr94dXEYpFNIEhu+xqVO57nIkd+vQXp0c0M/qWOaDrrbTp1VTIj2rVVhlmzLWn8LX57HN1jrdpZddtkcpX3Es01+yLjWpOd1axVj73s2LeSZfyJWskbfhfD0dWthuZEYY+h+4fr7hx4wamTp6iElpeeu55lfZrjolB2h0OjBwxUnWWoPWyaOFC9TwH1jGxpUCefChdsqRK0ye43vt/3xepXk2pZhHNmzdPtUNKKrBZrdi4YQNGDhuKb9q1wZB+/TB/9RbMEZOly043UonVx2ywfKvMaC0yww7gZu0Guye8ilCMQiifyI2jcFSTx+tecPNYVc+UyDw5cqiAIwP7WzZvwaZNm/CjaGpF3imkiIXV9te91Gd8SbTYGaJlMeiYeZFR9ToqvNykZnevv6iFJMlC9Jdll9xII/cyq48BU4Pu3+okeqzDMEUo6VOlxocfVMH06dNVjJH47dfRSPVKSryZOo0qDCZogX9QqbKafFqzenVVCByLH4cMUfVc+XPnwcABA3D23NkkceksQiarVqxA00aNkTljRvU/5M2RHd06tIXf+nU4fMmCSXI96/tahVgMKuu0mFj7A/c7sOOqR40o17gbXkUo520RKL7JgheFUDrstnlFqyr6hd9/rxIyZ3gLQ0V4wm6pWblw4SIG9OuP/EIodWrWhr+/n1ffbDbZ/P2AHVU3mNXclefEEqy0xoTfDjuwUzRdm87FT1JgI9EpoihwoFb1tSZsv+y+73uY0BJroaR/IzVyZs2GunXqKGuESSsM0ud8OztqfFgNu3ZE13etXrVKZXClS/UGalarjrlz5tz8vB+HDEXq115H7uw58OnHH2P79sAkce2Y1NOm9Weqk0blChXR8Yv2+KhWLbHC8uDzVi1x7NB+dd7ea+EYsseGsuvMSOVjxCtitdQV+Rl31KFavLj0aInb4D2EIvfFP9iDAnLjMsuNm3TEO9IN16xejcIFCiLH22+rzsZ3Yt7ceSKA2fB2xszwWbDAu++2XGOLaFbbr7oxaKcNxUXjSinEknKhARXXWzDjhBNXrTq+klTAAPzQfXakW2pC8y0WHElAhhfdVNu2blWFvuwgkT1zVuSXTZSWR6cvv8THzZqhVYsWWCUk4nREdw3muiahkIDiIpQ306RVn0UrZZHPwiRx7ZjhRu9CudJllMUVEhKsMtPY248jLZYs9Im5XtH9wbZcdKvGrPmXGfH6QqOSm/qbLVh51qUSXXTNVzS8hlDcwvQLz7iQa7UJRcSEXx7k8orv5bfNTy2wNKlS4a+JE297zRPuUemT7GX0XvkKKic/SSAyCtdkM1p13o0Oflak9DEoX3EeIZh2IjTL5D5YdTaY1+OcIRxdA6O7cncTBeGyKWExRwbUZ8+erayQTOmFVLJkVZo61zGD9VOmTLlZP8IUY3YSLiqbL91g8REK4y6ML86bPTdJXDv2GcuZPbtKNGBLJhLtju3bUad2beTJnlMRzm0iExGF8+YILD/nQqutVlVInEIs/GKrzei5w4a159yqJii5w2sIxSYb2NRjDry9woQq683wv+h+5M9kwSOLr1h7smH9BrVw2H/oXojNdvH388e14GCcOXMWnzb7WGlgLKRkARjdBhTKNWvWoGnjxmIm51VZLqdPn05ad1/W//Hr4RhzzIlGom29oWbbG1B6jRl999qx+ZL7ic/V0Eg4DoeE45NNZqQRQvlJLHrnA/j1PeHhGPXTz8idI4dyZWUUQsgsa5xZjH169VbuL2YucqOlhXI/QmF8hdleC+bNTxLXjgkE71WoiPJlymLE8OGqLdPPI39CmVKlVAfztbJnxCczB1ltf9ihLJTMi41I42NEVbHwRxyMjq+EJ2M3mNcQSqgtEj/JJpZBzPeP/Sw4FfrwabjUrnbu2Im/xaJgvj1nNPwki+WnESOV/5izGu6s4GVq8NGjRzFn1mxM+vtvjB83XkzgGarehNoMLRAG31u1aInfR49WBV0N69VHpgwZVNsJCt39yMprIRbL/mseDJfrX36DGa9y9PKcMFRZa8a4404cCYtQ/noN78Kqix4UFjJ5VTY1NlRNaF6r0+lUqcO9RQmi64utUkqXKCmEkEMRS0FRkDhniGnABGUgIRYKOw5zFsqTAv8Pq9WS4OxKEiQTZ6hosnDzz9//RLnSZZFTiLBMyVLqGlSqWFHtFyyYvudnhUdh+wU3WvtakMInOoPyRbFY6m20YOpJJ44bItR47+QGryGUc6YIdBJTkr7JLnttD12lysXF4qrWsvGXLFYc33/3naqo37B+PTq2/0IFI1lPcuDA/tved+LkSTUzpUqlyopQtmzZgq7fdEbV9z/A0MGDVRM8kgoFiwc1ObrCKssCZLZXfP3EkgyioutX/K648bW/FTmE2F9daMRLcj8+2WJRbrCr9kgdX/EijDnlwv9kE0sh96nXbjtOhIWrflX3agxKFxZbrbT57DNkz5oV3/XpgwNijVDxorZOtxWtDa7xFcuXK3liwF7FUO5BKLTg6TJbuMDnsf7PrHNhBf6+ffuwfOlSIbA5KiZ07erVeGvB+Dyz2zg/afmyZVgve8GRw4exZ89eldVGi4RxUnZHHj9unPI0RCYgKMK5Ta23WfCcXP9XRU7ejJGZN4TgP9tqUYPwwlxR8LKmGo8VXkMo+0LDUXm1WWUeDT7qfOhuudQ+2AqC2hIFhKYtLQdqMrQquPBzZsumOqLGgtbKOFlIuXPkFNIoj107d6r3sBMx3QHM8uJEyJUrV6pMr9YtW6Ht55+rnxm8vHLlildVyz8KomJ8xYuEQJqJ9sX78dICI/KtMKF5oA2+yg2mrZWnDU5kHHLEgRT05YuGnGm5CbU2WfD7AQeOhsY/RIp9uCaI9V2i6LsoJJsoe9wRV2VD5jiIooUKKWuDWVtUrJhOTGIhwcQXlE/zWiqVmNKgbl34bdv22P5nkkmAvz+6d+kqit/7+EDkslKFCvhQlL4e3brBV5TAOwsrKZdM8e/Qrj2+/KKDCrzTxfVxkybqMSgoSHkstgcEKpJhnU5CLB6DPQL99tvxlhDJa2Ilfr/HhmnHnPhos8jMXIMahldglQlf7rRh1xVPnDOdnkV4DaGskYv+5pLoQqJG26xYddaF06JxPUilPP3CTAdsVL8BXouZdbJ2zf/7QleuWKEWPuc39O/bV4TrulqAe0VTafHpp3j5fy+gXp2PcD0kVJ3/14QJSPniS8iSMZOyUk6J5nJZNJ29e/cqHzPN4qTYqThBEGLZdz0cPwu519ogQjI7TN2bymLS/3LQgT3Xkrev+GmDs3G+2+/Ac7JxvSFHynnRtRLc4OqKpf+bkM0uuUd3ti46eOCgWO8tkEeUJ7ZMWSVKUiy2BwaqIl1aKHx9pGy4HO1ABYsBfKbO85EtWGIxdPAQVbdSMG8+9P3uu5tussQGe+exePizli2Va6p08RKK9Dg8741XUyoFki48EsKt4Hjib776Srmre/fqpWKqMzmYr1gxVBTlcf36dQ8sw27RHf855kCWZUa8KITeLsCKINmrwuWe7AgJx0CRD3YwVjIj96WGEP0oeY6xl2d2v4iB1xDKzHMuvCyEwjGmb3LMrWhcnUQjnhjkwh7RuNwJ0IrZb4uBchZrcZEVL/KuLPLvVW8hghoMCeX1V17Ft717Izj4GsxmE34b/Zvyob76wktKywq7EabOny+C827hIioLplzp0liyeHHy27nEXPcXq6TXLpvqsUYXS5oFBjQVTeyfICfOGCMU+Wg8WVwzh6PDDhteX2xEQyH5vqIJtwmwoZBY+c/LPUotB8doTz4Zc49iQC28XZs2KsW3bu06KhgdCyabjBg2Qrm22D2Yo31Z+U53EsmC72G8MLawkdp//7798NJz/1PuX2r/TFZ5HOCI7nFjx+KTps3kOw7H/PnzVFFltaofClnkUjJdS6wnusJi3VX8f5iZSTd3WZHfhTGV/2wZwwSbzPI/0tNw8NChBLm4lDjIaQeENBiEZ4EwLZK9Qty3Fs15ZK/yveDG13JPCq80q27Gr8r9aCGK8gJRlOne94oiu8cAryAUarpjjjuRZqkJJVYYUVqEgsF5xlNoztOU9znlQvB9pquR/WmhUFDoqqJGVVxM+4njx4vVEaJMdWai5MmZC//98686/8qVy2jZvIVqoZI65euKUGIr3jltjhob30Nzf+yffybbDcwk2tcKEYY2Wy3ItsykAvdZ5B51Ee1s3UW36mqQnHzFTxsHgz1qM2PblSlHHQgT2WBiyxKRk7Zyj3LE3KOMoqR1FaLZI5sgNWu7KFD//jNV5KKoigPSlUsrPSpmo+3ZvYeSHcZMYomDwW/GHjiUrlD+Avjzjz+UK4yKWrs2bcWKfxk1xXLhZv64wIQZjhveuHGjsppIAGwJ89vo0UrZe+3lV1CzWjXV5DLW/cyi5GrynUkcrLNZumSJep7y/XWnr5T3oYxYO7RYzBZzgr4Hm3H2321DmiUm5F1qxCzZt+I0OuS5MJEJH1GIG2yM3s9elvvB2GQPUZQ3XuYgvGcvvuIVhBJsjsC3u+1IJ0LADWu+aL4TREjq0tUi2vDzciM4EKeHaGQnDPfOtacvmAH0HGJV0Axmfn1ZsT7YUvvjpk1VY0fGRi7GBNHPnjmLalWqiFaWWpnPDerWu0koJKeOX3RQDfH42pAffhCLxuwNl+ypwB3O+Eok/jvhRH25N2l9DEglpJ97lRldRRvbe5VDvbS18tghl3j5aSeKivLFqabLhOhjrURWbvMezRTLpKHco9Q+0Y1Bq8nPS8655a1R2LdnN6pWrqys+C87dFCNHy9euqQ2Vm7ADFD3/b4vzpw+c5tc0e3LuMtnLVshICBAdd2uXrWailX+J5v9/eYSPQpoKVEu2fU4FiQVttMn0aVPk0Y1ury10zEJhJYTkwbYfy/Ww8DP+earrxUJFc5fUFk6Fy6cT9D3oGue8Sq6fxkfuV8/PDa8PWEMx6RjTny41qwsFd6PfGLt9xOrn9mVEc+QzHgFoQSFhqOtmIPphVAG7bXjhhAM61J2iRb2m9wIpuK9MjcMr4lwNPATjVhuakQ8QS5mdPj6+qJ923YokDcvcgqh0CdMtxXnXH/ZoeNtft79+/ar1gu0QO4kFGo41MBIKFyUnPTI4V7JHQ5XpPLPjz7kQOW19BUzcB9t/o854sBxL2jq+SyD++VUuc4ZFhqQT67/+kvuuzRd1qTsEflhJX3epdEbYMV1Zqy6FAGjwYRF8+aik8gCFaZfRo1SSSnsWdeta1eVbn/ixAmxXCJu+ZtROCZWAt1OnJL608iRGDliBAYNGKgsfwb7nzTMJhNG//ILihUugsYNGirrJNZ15RCr6p8pU1WN2Ftp06F2zZo3m12yuzItFLaMoRuPRERSvR+sYlGMOsy4lQEFxPJbdC7hxdfczwJE4frpgEN5YJ6bFYZU8jmNtlgwRfa4U2HxJ1IkJXgFoey56kbd9Wa8KYTCIrtbs4iYHREoAkMzMVNMx1xuXPuu3btOhcHGKu9/oDJWOKKURVvUVkg069etv2lp+G7ejErlK6hz7iQUNsX7ol37m4Tyw8CBSW7+/OMEA8PrL7jRdrsNhdjxVu5NOrEm2/hbMe9MjK9Y47GgvxDFi7Ip5Re5ORAWP4Fft0ZiohB/kZUm1eK+0joLVlyMgNsTifNnzyg5oWUyY/p0ZXEw4cR+j+FzfI1ywcD8yhUrcfLESRW7fJJgnIbFx8zUpCuLru2O7Tsot1hslhdlmCnBJAzW1jSoV1/+11XqtVhCYayIXgzOeOFso/vhUHA4mrEAWPahTqLYnjc8uOLkFJlZLhblJwFWFFxuxP+E6LPJ53UItGKRPH9RlOmkzCxeQShL5EK+I4yfXkzJeeddcRZonQ6LwA+7bSqz4lXRhjsLwZw0xD1vnsE4LvgWzZvjvQoVUPLdYipHnoFGLrBmTZqqVEKCaY4kFBLGnYSyfft21UAullAGDRigLZQ4wDYuc084VaCeQ73ooswqQtJDiMZPiN/oinroNHD6w+nuoDuF6d0cJ+COOZzyO19jijcfudm5XM6brz8rqdx3bUoRUWgi1/a56TfwgWi4Ifdpk2OU1/865ESRFdED1z4QUtl6NeLmLXnQefKx73laoIeBFhWtDhICCaVsqdIYPOgHHD9+PDo2evkyhg0dirw5cykPxecix4GB29X7GXshoVCJpMLJjLbY+Mq9MOuUC9kWGvE6p8medD58F4mo6FHnc447UE9k5i35vBdFZgoJwXy3wyb3xg3TI8jM04RXEMqwo068JNpWOiGUzcHh8d6EC6LxDhFSybQkOlWy504brt8xc56m97gxY1R+Oruf0sydPGky6taqrQiFi4+LjIVcbo9HTWFkVtitLq/Q69HmO1u2MLWS7jKazSQUbaHEDfqKg4wRmHDEiXKrTCqd8g0RvmJrzfhlvwMnbzycSU9tdM+ePWpuxfp161SB6s1Dnrv1d77Og91xqXGymM1bSYWbHt0zD7MxnxUttgqLgIUc+u2yq+aF972OzihMPOxAvqVGVSPxubz/uDFpasIkBE6MZKYWFUQWY2aVg0XI0/79TykfTMKJJRSSBlOHadUQHEnxoITC8oV+Bx14XvaptLJP+V73PPKGb5f7dlSsyzFyXyqtNiGl3Jc0i4wot86MPw6IzMhrj1JIfK+19bgUgqdOKMyT/2afQ81zLiIb0f6we28AZ+QidxZz8SUxFfOKxrVItAZnjEDR58u4R+OGDfF8ihSqWp6LiyTAcaUkDi4+ur+4oLjh8OD5md58U9WnMMvrRmh0LjtNaubXk4RIOD+PHPnEzfukBs5W2XLZjSH03TN4KQKYcYkJNUUTYzzsygO6wWh9sE0IR8x269IFtWvURL06dVStETOSONecXaA5xnbQwIFq0iA7GrD/Gq1QbyIUxvcYm+D/whRbHnNmz8ZWX1+VJJKQ78qNjZNMy2ywILMoVlMOOeBMYD1QqChfP8tGlZobl48Bow7ZVXZYUgOvI0mFdTMsTixfugzSpUqtCpPp0ma2Gi1W9iq7SSgi74dlHRGxhEKXF5XFKpUrq84Y9wI7O7cSq/DFedFxjzOWxLtuRsrMJTf67bGjmMgM3WBZKDO+FowVmblkinhg7jIZjap+aIdcI8oP+xiq4+hRlY3HnoRU1PbLz4cOHlQ1dZGJQDIPTSjUrijs3LDvbHnA33lD6aJgyiEtAaWNxbzvVnY0ycVsK1rWC3KjPpVNh9rX/bBHBKrGRoua/VxTHvdcj7ZqGKRjGiSzTjjetH2btjd9qsxS4WAhFkNlEYJo2riJqrqlRcOZJmxl/frLr95Wh8LCRmoxPJ/1KHNiJtVpJEBIRABnnXbh4wAbcnG2vSgMaRcb0X2XDavPuxM8LZKbLCcK0s3BtuqvvviSIn6SPDcPxgBYZLrVd6uKAbDQjkVvrDdibMAbCslsdrtqB/TrqFEqA5Fjo5nuShJk3ygGwvv07KU63B45cvie35kK2KozLhReY0ahlSYsDnLC8wB1QKxJaelrRQohlBKiFbNLblLGeSHiz1u1FjlNj7fSp1f1JiyA5D7D60tXN2W4xSefCmlsVu+JdXlxHfH1z+T990p55u04FOxBbSGSDMuMGLPfLiSQ+OuK2a5UkL8UhTmPUsYMeEtkhhmUqy64EWxNuHLEvZDdkxeJTLCeqFvnLupgRwHukfS+zJw+HaN//RW9Ze2xISgVaLadeRQl7KEJhRs1+1eR5ahhcW7I6lWrVeBr61ZfFdzjP+Tn56dyx5nHzhYO3MQZFIsF55s39bchrZh6PwqxhNoTwPyipY074VSaFutUfj3iEKGCWCJhKkOFRYoklC9kw7nVoliyaLEyb9OJtdG4QQNV6EjC4/euXvVDPCdWDQnFaDCq8yf/PUmdmzVjJnwtJjNbNGg8GOgrniQmfRUh/gyLTSobrLRYlsw+2hkSDusDdMhlJbQiE7EwqXkySeLcuXO3ncNu0ZMnT1YV3XPmzHnqM86pdC2Xdc8sJLaK5/yNSWJVseUHlRymprPlyTv58yN/7tzo3rWb0iz5f8QFuklmHnMgp1zDihvMaqjWg6Rqs2HhmotuvCuExBYhvYXgLUl4+iA3P26KLF4kcVD2ef0IKhism+HzdF0vXrRIPR+bNvzGK6+q11n8fK9O4XQ7rT/rQim5ZvmEhJcIoT/OwVq0SNh5vYKSGaNqOvmuEMwwITLWE5kSeL+4t5Fc2372mbLSYht4Thg3TnUQ4LgNWvjsKMKMN9YlDRn0g0puiHzIAS8PTSjUomgmsTKdrEdBYfC7qHwpmpfMD/9XNK7ff/tNVaV/VLs2KpYtp/Leqa3FYvdVt9psKCBzhCQcCewTdTyMqcYW1byw4SYLDoREIlIW155dO5VLhOTQqnmL21oxzJwxQ9WlMEjHpng0jaOLG6+o1MEXnnsOteXi0v0QFRWJsX+OwRspX1Oph3xvfEKucW+w6eTB0HD8JCRSUrTqlxcakUYE5UPZEJn+ymywhKxfavYkeMbCqFkOHjToZhcEIraDNN1KtACoyNgdT29QG8mEXagZl+P3puU0ZfIUpVDFCiytef4PdOexoJCZiB07dIS/KF5xwSAW/Yjd0QpY3W1W1Z7oQREm2vWPe+xILfeh/Hqz6s/m7Z1xKadUDuLa6KjQNmvcWHkfvhA5jiUHFiazxiy2sPHWOpTYwkbeE2a4me5RX0YLcMZRIfElRhTjaI2rngdqCfWwMkPPCzuwF5e98SW5V6nl71dca8bYQw5cEEUtIbeMSgstE7r3Yjsg8P8Nl72SSSxGg0GlfnOAIAmHKdjseUi34BMlFIIMSGFgwV9G0RrZ/uCl/z2vuvpekOcp2PTf0dc5fuxYNGnUCM0//VSZWwSXhs9JJwrIBSvEfPoLrnjrS+4E04mZmsrGbOmEwX89Gr3ZO6xmFYzLJhfovXLllZbCi7pPLKYO8r1IKB83baask9giKWo53HyYNUJSJHmQ2bt8/bVidC6+oJMnNTM8IkKskVh/yYOuO2zIuyQ6ZTL3MhPqycY4XdZBmO3epjYtlFsJhRbK2bP/P8N88+bNar1RUGgh0wpwPCVC4Zpi8Z+aWS6ywe/8dadOSnmJC0wwqPfRR3JeJmV9cT77qaC7+2JdkWvU2teK5+XatdppUx0MHnx3BgKEREqvt6hCu95yP0Id3m2l0BMy5s8/lWxSu74VtPIa12+oyIE1MbFpz1R4eR1p/VX7oKrq5UfQs0LvRapXU6JOrVq3tWuJj1D+FcXnbVGCSonyu+8J1llRZjaIRdl9lx1ZOLZ7tgHZRWaa+FsxTRTw6/dxg1Gh7tO7j2qKy4P7H+N2t7pV6aFpWL++ciPznE+afaxq+R4GiRKUp+83X+486sswU6qfmJB3gjeZbi8WT9EFoEhBDvojUy80oLhoq4FXPQ/k8z4umm11sU44u6P5divMzuj3HjqwH8OHDVOmHt0J9Bn+8dvv6NTxS/Tq3lNlBN2puZKx6Y+nL5GzUzgPhRox4yucraKD8YmHC4ZwzBRh+MzPioysLWI9hZj0DEpuuOhBqDVu4b6TUFi5HatJUescK0rLCtk0uIYYw+PxtFxe3LSYJEByoEywB9bfE/+Kt8X6ZSEartm8OXOrFHU2QOT5d250RwwRKC7KV4oZYfhCtNeHHT3LVOLOQki89hyotj3E47XlD2z6OnHiRFWozDYrbOy6ds0aUfKClKJHeW3UoKFqZnnrHBN6FNiynp2F+V72AOM6oeJBgmGGGC3Z+3W/cAuhTDzoUD0GSSh7rz/5NXXRGIGpx51oLUSSnjIzMwz5hFi67LJhpShptngUC1rDjJHcSiizZ826bZ89dvSYSnBhggKTlj6o/L5qu/Mw8cdHJhRutJMnTbpJKBT47/t8e/N1+uNiK9NDhS15bmyHU27RPXba8fzsMFTYYsFZy4MFg5jdQpdJluXRpvv2S/8vrGGhIQj024q5s2Zg0sTxmPnfv9iycQMunqNGG8+FiorApQvn4Cvncab01i2bEHL1imaAxwSOrB0v96+8KAWZRDgYE3t/tRmjDjhUp2PbHe7PWELJGkMo33/7rVpfdF1SafhWfo930t4TBq1wFsxRgDOlf1PFUNasXhMvoVisVtXIkFmFlCP6tGnpG+9IU/cNDkemVSakmmPA8GPOR/qOC0+51Iz0jELm/xx3JqgB69NARLgb8+fMxvsVyqNwvrwoX6oE2n3eGhPHjcWs6f/hu149MH7MHwgNudtN43bYsGjeHDSrXxdftWuLFYsXYvKEsWjRpBEGfdcHV86fvf/fl8vSSyyEF2Wfek/2qXOWp5c5GCp/+/ejDpQRYsvMZBexMNm0deJRpyI68x3xlbgIhVbcrWRBq55p1VTUeNCDk5BCz7jwWAil77ff3XydQZ/p06ff/J3DcOh+IphBWn2bFSmm3UAdYV5L7HCgBB5R4VHwE9Odfs03xcr5Xawdxy0us3CPbEpWG0xGE6wWy91Wxq2fdwtcTpfSbt2ue5z/FA6uAQYIw5P4ERXz/9Bvb3BEwfeyB30CrcixJLooko33PhKLddZJJ67ZIxF7S2MJJZtoUdT82bhzqhDJkB8Go1yp0mKqN8O2bVu9YhNkI0M2FaUbgVmCLZs3R2BgYLwZNLSkmEbMGArliGnqzEwiYd5cfpFRWHzBjUwrTSguJLDyjPvh15PgeEg4Pt1qVZXfnUX+zrErcdTTX+d3rXv5vy9dvITZs2djQP/+6NWjpwqks/XLrBkzEBgQiBu3tn65Q6aNZit8t/lhzJjxGDZ8JP74cyx8Fi7GiZOnlPVBwrjXeuWQrNox+1Q1eQwVa+BpyQwTMFj0GHjNg14iM5liZCb9UhOqi8z8e9yhGliGR8ZPKLNish95UMHhda1WperNmhwmOTATzmsIpf/3faNfky9LLYutr2NB81KNyo2KdlmVpMtKmL/lVouax8z0vD1XE3YcuubG6jMulNkQ3SK6mrD2lotuHBXzfX9wBA7doItArCRj9CN/Z/Ce7abj+jw+v19e53mHw6LP3x8SoZoe7nmKR+zfp997UZAT/4k2Mv1Y0j5myDHrhBMLhDRmi8b1606bcr2ogVGidb3gY0BB2Tg77rBhd2h0umzf3r1uEkq+mHHMAwcORIP69ZVm1ahBAwQE+D91MmFsjv5+xt8oE4yhfNGunSqsi8+NQKJhsDSWUJg40rh+A+WeCQ+PtmqsspGNl2uVQcikiFjlkw46VHPB/dcefD3tk2PbORe+8LdFdzYQbZcNWY+HeJ76eo9LLvm45WQYlu48DR//45i39QjmbjmMZbvPYvsF+01ZvVNmtl3yYPE5ejLsGLXxDPr67MHQlccwYVcoZp5wi9Liuec6nS2W2ySxokvTzTgnDIVoDRyWtRuzhp+03LC7sY/sAfOOOTBCZKO6fC82aKXM/G+BAflFZr6R5wOuRHeQNoRev0koVG6YTs+gO2Pfu3btxDRRYtg5hK6u7EI2VMqYnfuw6faJTihkua+/7CSWyDbVS6dQ/oIqy+tuAQLWXXAh92qzIpRcIiQfCiHU2mxBtU0JO2rLuR/K42sczDXbgBRyYSsJuXz0AJ+RFI7qMY+VxRJ7R64Tg4PZlzwbRw458i4zql5TKRdHD1hjexD1OP0GMsjryy5Ed9Ht3yeaUN7OmEkRSveuXbF48WKlcfX9/nt06dwZGzasf+qEYrXbVXYjhTdLTKCT2Ue0NuIT1DstlMxCKPVq1VaBZLcr2rXFolB2qH1B1jnn0hRdZVLDm2o8xHpSa2qjGTli2rHweueRz6u35f/XmzcdNTZb8ZGfCw22R6Dhjkh18Oe6AR7U8nXId7bGKTNsiMlYQ47lVhRY48I76z0ouNaFvCvtyLnMfN/1mUsO9tpiurtak3LdMy2Mfj7HU5SbPCIzBeXeZV4cTSbqHopSzdja27I+Zhx1q6Qn843/JxSWP9BqZpx44oSJaN2yJSpVrChWSzbVkZ2taxiMp3fmYZGohEIG5Jf+pGlTlYpG4Xj5+Rfw4+Ahd2txskGsFQ2prizgArJJ5pXFnHPlgx+55Mgv7y0oxJQ/5jNyrHy4z/Lmg4LPx0IiICWEeItveLaOEnKUlv+r7C1HGSHQtoE27DcwaQI3LZRb04Zjs6aY+TNmzBg1pvmpWygu100LJXOMZsheUsw8iy+b6E4Lha1+GtWrr1JiYy0Uth4audeutOX8K83IverR11XeGNnhkTtJyI45jiN+meE1KirrqOTG6DVWIubxQddn7Nos85Dvf1wyUyrmO92UGXmufQBHdUdbKMZbCUXkhqnVLP6lss+xzrHWcN3atVXS1MPWnzw2QuHBMZ2cR835I/yyA/sPuOt9DJewV83yMy5lxs0+4VSZPw9zsH5l7kl5PPnwn+Htx/Tj0Y8bxYTfG+rB7pBn59gVc+y57sG+W4498twxWSOOmPjRtz3vJpQLMXNtuCEvXbJUtTB/2qAVwiSB22IonzZXacQJjaEw04sV4LcW3LHod8sFN+afjJaXWYmwrmbHyM7ck48mg954TBOZmRvkxDa6+EIffm3uvh67NsOx93r077Fr9mnKzO4Ymdl7i8zw55OGcJhjwr/Xr98eQ6HV7DN/gUq3Z/1gwZj1xiy4jh2+UG1YvIZQYgWhV/ceamxoQGCg6p/FlLQ4NbmI6MpfmysKdn0k6IiKrWbywuDpYzticL86FPYqurNy/mmBaa3M8mIqZmyW19o1a+PN8rLabCqBJTbLK3vWrPi2T5/bUlo9ojwy803LQcIO7iuqz19kMpKZOxBXUH6Rz0Kl9FD5qlvnIxU/yfLWWyjx7rsY/MMPd9X5PFVCYc59bFCeGNCvn+pXdCtYO3DyxAlERni8Qvg1kgb69O59G6GwoDbWQiFYxOgt3QwY9ORAtrw5ciqZqFzxPdXKJ766mAsXLyhhZpYNK5prVa+uinKf1Rb8Gk8G96pDYW0gsxErliun1iiJhY1Vue4etiD4sdehrF69+ubsEYICxWIjdlx1PMW2GBpJC1wrHOP86gsvIu3rqVSsrmf37rel1XoTSATsY8dO1nT7qn5wnTrFq/2tWrUSNavXQOY331Jdc0cOH6GsfA2NRwE7rX8n+/GthDJ//v8XLV4PDVVjOfLnzhttGWfOghaffqqarT6Vwkaa8FMmT463DoX5zLeOB2URDYOP7AGme2Np3A8MErLFz+HDh1UKOjV++n3ZDJAbNOefGMLCvFKTZyfu+fPnq15etDpKFS+hOuCeP3dOrf0I+d+oJZ44flz1v+M57+QvoKaExtfLS0MjoaDyzrXGRpjcl3kwpkcDgApaLGGwEwhHQTO+wmQQhi3YVYTDyih7D0IsiUYoeXPlVpoYTSeaWHFlC5BchgwejK5duqhJiU+7E6yG94MDtthrid0VKAi/jx6t2uj8+ccfasYNmy+y2Sh7FnlDq/o7wdb7HPjF5oWZM2REyWLF0alDByxYMF81L6QbjBphDhFmkgmr/zliV1vvGo8CRSbnzyv3FWcHsZwj1lLu2rmLShCJHRbocrmxQBSfD96rpGq8OFumcIGCKobH+VIP0nbqkQmFaZvMtiHzsTMvZ4qwr8769etx8MABxXIcbLN86TLVZDFntuxo26aNyl7xxg1Aw7vAjZVxklNBQWoYGnsx0S8cIsrJZfmdvZwYmGexrLeuJ1ojFGDWpnAeSvGiRdVEURLJB5Uqo2Tx4mgnMsH+SSd1E1KNRJIbFtIy5MBkj59GjsTPI39SQ8cYNwnwD1B7d6ziz5/nzZ2H0b/8qs5l37MJEyaoMeixzTYTgocmFLoY6A9mo0USCs16zhyoU7OmGmz1hwgPC87mz52rHpn7XPPD6qhQtpzSLql5amgkNwSdOqViP7RIUqd8XSli5cuUEWGeqy+ORqKBSgw9QlS+uNdabValdPGgZULFjM/f6kmiVWOz21RfOZ4XFhamznuQ0ESKR/nCNIdWrVihGuExTfLOg8/HHhzAxapfDtnioCpt0mskV3A0AucCsfCRw5/oivi2d/R8HmqDdCNTYdMWvMaj4Gmsn0caAcygI7uhslSfBBN7kCzUeGCzWeXR85HnMMDD1ykwWlg0kiuoCbLNftOYoVCc5MjRtT179MC8efNUDIX1NJQvDY2khBT6EmhoPHkYjUZs2bxZ+arbfv45GtSrh08/+QS9evbEiBEjsGjRokcqMNPQeBrQhKKh8RRxLfiaamtPi4UzzxlL4UQ9Numj/1pDIylBE4qGhoaGRqJAE4qGhoaGRqJAE4qGhoaGRqJAE4qGhoaGRqJAE4qGhoaGRqJAE4qGhoaGRqJAE4qGhoaGRqJAE4qGhoaGRqJAE4qGhoaGRqJAE4qGhoaGRqJAE4qGhoaGRqJAE4qGhoaGRqJAE4qGhoaGRqJAE4qGhoaGRqJAE4rGM4vYgW6PgtjhcQSHwnF4HAfEaWho3A1NKBrPHKxWC7b6+mL16tW4cP78Q30GyWjnjh0Y/uOPmDJ5MoJDQhSR7N+3DxvWr8eFCxf0hdbQuAOaUDSeKXAo1ZLFizFi+AjMnTMHFx9y46dlwveXLVUKLZs3x8mgoJuE8t9//2HmjBk4dOiQtlY0NG6BJhSNZwZut1vNZO/WtRumT5uOa9euITIy8qE+i3Pf9+/fj4H9+2Pc2LE3pydGRETgyJEj+G30aPTv10/Nf+e5GhoamlA0nhGQODZv2oTvvv0Wv/zyC65cufLIn8nYybWrVxEaGqqIJBa0SgL8/dGje3f0/f577N27V98ADQ1oQtF4RnDp0iV80+krfNGuPfbt2/fY/x6D83SJVav6IUb9/DPMZrO+CRrJHppQNJI8GEBfsGABKpQth77ffXdbZpfValWur5CQEITduIGQ4GD1u8ViUVlbPPe6vHb58mUEy/NhYWE3rRG60C4LUfH8uGIlp0+fRqMGDdG4YSP4+fnpG6GR7KEJRSPJ49SpU/i6UydUKFcO//7zz22vXb16VWVlzZg+HVMnTVbB9C2bNyuXGImDlsXe3bvhI4Q0a+ZMbN++HQaDQZHI2rVrMXzYMGWJGI3Gu/4un/th0CC8V6ECfhk1CuE6QK+RzKEJRSPJY93adXivXHnUrVMHmzdvuu01uqY2C4F88/XXKF+mLNq3bYetvluV9UELhaQSdPKkCrwzHrJt2zaVGcZMrk+aNUOh/AVUYP6GWDd3gtbN3Lnz5G9XwGctW+HixYv6Zmgka2hC0UjSsNntmCyWR7HCRfBlhw44evTIXefQ3fXXxIl4R8ihWpWq2LTpdtJhUH3okCGYNm2aslzoDqOl0r9vP+TPnQddv+mM0DgIhdldmzdvQc1q1VG7eg0EBATojC+NZA1NKBpJGkznZVC8ZLFi6CcWxvl4ChlPnzqFJg0bKlIZN27czXRiWikL5s9Ht65dceLEiZvn8/lVK1bi/Yrv3ZNQ/MSiqf9RXVSuUBHz5XPsQnAaGskVmlA0kjQYSB85bIQiFLqm4nM7MTj/008/IU/OXPisVSsVIyEYhJ/099/KQgmNqTUhGOhfvHARKpWvgG6du8RJKHSXbQ8MFKJqpP4+iSquWIuGRnKBJhSNJA0Syohhw9WGPmjAgHgJJUqO3bt3o2H9+vigUiUVcGcMJFAIYdLfk+Dv76/iKrFg7GWRz8J7EgqtmMOHD6Plp81R5J1CKjBPgtLQSK7QhKKRpHEnobAeJT7QHTVArJiC+fKpADxTgseOGYMfxTq5s44koYRy8OBBtPjkUxQrUhR//vGHyhDT0Eiu0ISikaTBgPtPI0cqQhnQr999mzbOmzsXFcqVx4cfVME///wj7+mPcWPGKnK4FbcSSvcuXXEjDsuDLq8dO3agcYOGqFi2nEo7pmtNQyO5QhOKRpKG2WLBhPETUKLou+jyzTe3BdbjwskTJ9G9azfkypYdH1apKmT0Ew4dPHTXeXR/LV2yRAXbaaHERSgMyjPNuG7t2qhR9UNs3LhRN4vUSNbQhKKRpBEplsWypctQpkRJNGrYQMVC7gVaFTOmTUe2zFnU8d+//97WpysWtDSUNVO6LD5v3RrHjx+/q9EkyWPt2jWoVqWKslIYT9HQSM7QhKKR5HFg/wEVbC9Xpgzmz5t33/MDAwPwSbOP0ahBA/hu2XLX6ySKQ4cOqm7CBfPmQ4WyZTF58mQVn7nVNWa32VSGWPmyZdCtS1dYtLtLI5lDE4pGkkeYwaDayRcvWhTDhgy9b8t6Fi8uXrxY1Y3ENYCLwfs9e3YrsmBx46CBAzF79mycPHnyNpcWa2A6tP9CxWNozWhoJHdoQtFI8qDVwGFXnzRpig7t2iMoKOie55MUmI0VHBwMu8Nx1+usQQkJua5eJ2mEyMG6FbZfuZVQmOFVq3oNsU663DO7TEMjuUATisYzAdaUTPvvP3Tq+CX+mTpVTVx8WJCg7sz6in0+FiQbxl++aNcOixYujPN8DY3kBk0oGs8MaEGMHz8e3/burdJ5H1fGFfuHsQNxm88+U92Ljbr2RENDQROKxjMFziiZM3u22uj9/fxuju5NDNAKYd3LQrFI+vftiwlCXmyPr6GhEQ1NKBrPHBgf4TjgVStXxtss8mHA9GLWubAgkrPr9ZRGDY3boQlF45kECxPZV+tRYil3goRCi4cz5nUBo4bG3dCEovFMIzGD5fwsPe9EQyN+aELR0NDQ0EgUaELR0NDQ0EgUaELR0NDQ0EgUaELR0NDQ0EgUaELR0NDQ0EgUaELR0NDQ0EgU/B/TkQIJ4xmx8wAAAABJRU5ErkJggg==)
Answer:(i) From the figure:
∠A = ∠P = 60°
∠B = ∠Q = 80°
∠C = ∠R = 40°
Therefore, ΔABC
ΔPQR [By AAA similarity]
Now corresponding sides of triangles will be propotional,
![](data:image/png;base64,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)
(ii)
From the triangle,
![](data:image/png;base64,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)
Hence the corresponding sides are propotional
Thus the corresponding angles will be equal
The triangles ABC and QRP are similar to each other by SSS similarity
(iii) The given triangles are not similar because the corresponding sides are not proportional
(iv) In triangle MNL and QPR, we have
∠M = ∠Q = 70o
but
![](data:image/png;base64,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)
Therefore, MNL and QPR are not similar.
(v) In triangle ABC and DEF, we have
AB = 2.5, BC = 3
∠A = 80o
EF = 6
DF = 5
∠F = 80o
![](data:image/png;base64,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)
And, ![](data:image/png;base64,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)
∠B ≠ ∠F
Hence, triangle ABC and DEF are not similar
(vi) In triangle DEF, we have
∠D + ∠E + ∠F = 180o (Sum of angles of triangle)
70o + 80o + ∠F = 180o
∠F = 30o
In PQR, we have
∠P + ∠Q + ∠R = 180o
∠P + 80o + 30o = 180o
∠P = 70o
In triangle DEF and PQR, we have
∠D = ∠P = 70o
∠F = ∠Q = 80o
∠F = ∠R = 30o
Hence, ΔDEF ~ ΔPQR (AAA similarity)
Question 2.In Fig. 6.35, ΔODC ~ ΔOBA, ∠BOC = 125° and ∠CDO = 70°. Find ∠ DOC, ∠ DCO and ∠ OAB
![](data:image/png;base64,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)
Answer:From the figure,
![](data:image/png;base64,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)
We see, DOB is a straight line
∠ DOC + ∠ COB = 180° (angles on a straight line form a supplementary pair)
∠ DOC = 180° - 125°
∠ DOC = 55°
Now, In ΔDOC,
∠ DCO + ∠ CDO + ∠ DOC = 180°
(Sum of the measures of the angles of a triangle is 180°)
∠ DCO + 70° + 55° = 180°
∠ DCO = 55°
It is given that ΔODC
ΔOBA
∠ OAB = ∠ OCD (Corresponding angles are equal in similar triangles)
Thus, ∠ OAB = 55°
Question 3.Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O. Show that ![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
In ΔDOC and ΔBOA,
∠CDO = ∠ABO (Alternate interior angles as AB || CD)
∠DCO = ∠BAO (Alternate interior angles as AB || CD)
∠DOC = ∠BOA (Vertically opposite angles)
Therefore,
ΔDOC ∼ ΔBOA [ BY AAA similarity]
Now in similar triangles, the ratio of corresponding sides are proportional to each other. Therefore,
......... (Corresponding sides are proportional)
or,
![](data:image/png;base64,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)
Hence, Proved.
Question 4.In Fig. 6.36,
and ∠1 = ∠2. Show that Δ PQS ~ Δ TQR.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
To Prove: Δ PQS ∼ Δ TQR
Given: In ΔPQR,
∠PQR = ∠PRQ
Proof:
As∠PQR = ∠PRQ
PQ = PR [sides opposite to equal angles are equal] (i)
Given,
![](data:image/png;base64,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)
by (1)
In Δ PQS and Δ TQR, we get
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADoAAAAkCAMAAADvudnxAAAAAXNSR0IArs4c6QAAAHhQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OgBmOjo6OjpmOjqQOmZmOmaQOma2OpDbZgAAZjoAZmZmZrbbZrb/kDoAkLbbkNv/tmYAtpA6tpBmtrbbttv/tv//25A627aQ2////7Zm/9uQ/9u2/9vb//+2///bDqC5CAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABXklEQVRIS82UD2+CMBDFr44/m24TdHawTRHq6Pf/hrsDWuzoNY3LEi/GYHzv3h1pfwB/Kf2Zi6QC6EshRHLkW01ClaNOiAxAy/QIzcMJoElbXact5zXCLoMGPwVARy71iLE1/kI7ZzXCS6tlAarCUDQM1r48wDk/8KFGOAbRhiSmMNohsOoshG4cbejQl+OsUztv8CyEGl/RkFrARWIbmlzLjF3VCqHfTVupnRBbNDRiVeEXLeQvI4SalGMF3qrbZCnsy80mcBJmu0f4/cVu6MZGC/kjGf6nHg4qlX0nvw1WYR+YlgvhrUOFfBED/0fsHfc0cILz+iV/5g/WEmIWTurpBIq3uhCTdGctnIYHvlyI0XWf4aRl8s47PRC7Yg4uw990F2KrNwy5Yg4Oz7PUgdg4nGVOg8RBNnPlQGwSGeZ8rPf718CddyBmAmLh5NHFwsmni2VOrO6Or85to/0ASZ0iWdg4aM0AAAAASUVORK5CYII=)
∠Q = ∠Q
Therefore,
By SAS similarity Rule which states that Triangles are similar if two sides in one triangle are in the
same proportion to the corresponding sides in the other, and the included angle are equal.
Δ PQS ∼ Δ TQR
Hence, Proved.
Question 5.S and T are points on sides PR and QR of Δ PQR such that ∠P = ∠RTS. Show that Δ RPQ ~ Δ RTS
Answer:![](data:image/png;base64,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)
In ΔRPQ and ΔRST,
∠ RTS = ∠ QPS (Given)
∠ R = ∠ R (Common to both the triangles)
If two angles of two triangles are equal, third angle will also be equal. As the sum of interior angles of triangle is constant and is 180°
∴ ΔRPQ
ΔRTS (By AAA similarity)
Question 6.In Fig. 6.37, if Δ ABE ≅Δ ACD, show that
Δ ADE ~ Δ ABC.
![](data:image/png;base64,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)
Answer:To Prove: Δ ADE ∼ Δ ABC
Given: ΔABE ≅ ΔACD
Proof:
ΔABE ≅ ΔACD
∴ AB = AC (By CPCT) (i)
And,
AD = AE (By CPCT) (ii)
In ΔADE and ΔABC,
Dividing equation (ii) by (i)
![](data:image/png;base64,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)
∠A = ∠A (Common)
SAS Similarity: Triangles are similar if two sides in one triangle are in the same proportion to the corresponding sides in the other, and the included angle are equal.
Therefore,
ΔADE
ΔABC (By SAS similarity)
Hence, Proved.
Question 7.In Fig. 6.38, altitudes AD and CE of Δ ABCintersect each other at the point P. Showthat:
(i) Δ AEP ~ Δ CDP
(ii) Δ ABD ~ Δ CBE
(iii) Δ AEP ~ Δ ADB
(iv) Δ PDC ~ Δ BEC
![](data:image/png;base64,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)
Answer:(i) In ΔAEP and ΔCDP,
∠AEP = ∠CDP (Each 90°)
∠APE = ∠CPD (Vertically opposite angles)
Hence, by using AA similarity,
ΔAEP
ΔCDP
(ii) In ΔABD and ΔCBE,
∠ADB = ∠CEB (Each 90°)
∠ABD = ∠CBE (Common)
Hence, by using AA similarity,
ΔABD
ΔCBE
(iii) In ΔAEP and ΔADB,
∠AEP = ∠ADB (Each 90°)
∠PAE = ∠DAB (Common)
Hence, by using AA similarity,
ΔAEP
ΔADB
(iv) In ΔPDC and ΔBEC,
∠PDC = ∠BEC (Each 90°)
∠PCD = ∠BCE (Common angle)
Hence, by using AA similarity,
ΔPDC
ΔBEC
Question 8.E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that Δ ABE ~ Δ CFB
Answer:
![](data:image/png;base64,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)
To Prove: Δ ABE ∼ Δ CFB
Given: E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. As shown in the figure.
Proof:
In ΔABE and ΔCFB,
∠A = ∠C (Opposite angles of a parallelogram are equal)
∠AEB = ∠CBF (Alternate interior angles are equal because AE || BC)
Therefore,
ΔABE
ΔCFB (By AA similarity)
Hence, Proved.
Question 9.In Fig. 6.39, ABC and AMP are two right triangles, right angled at B and M respectively. Prove that:
(i) Δ ABC ~ Δ AMP
(ii) ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFYAAAA0CAYAAAAQas+mAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAQMSURBVHja7Vq9TuNAEN5cDdQHZOg4arLmDVAwCpSWzlhpXViRJX4kFxROuujEA5x0DVx1T4CQgPIK7gVOFLwA8Arkzmt7zdp4/Z9kIy3SSCjxbub7PDM7OzNoNBohKc2LJEESK4mVIomVxEpipRQk1vtrhfIpIa2cNbnPzQRguu6FdKuCvRCxZIOB3u1hgBvv/3+RADxu4L0fmmXhtB9xdXxIn8W6ezhPYocGPojpzggAvtGs8y9NYs8l1nHMZbWN7sMNJ568JYR8NsHG8CC59gijK/o9wkdXghDLwYCf+q672hT2TGKZjScI8INqHO/HlLXtz8eGuq8AXOP+sBezVre/6r3KJ4SNSwOjyzTF50EsdAenMT1tfVMFdOt7FUNQHey5xEauDOqtOR4vlQFC1xJlKah5hgMesUQGXThDCF5U291uAnsusYErwyv7g0UlWBtYaWS9naOfAhB7xh5AjqVtEd0AGxdNYc8kdjw2lzxXuKviwo7TX6NhgH4WhAN43bXOO6IdXgg6fzTL2aKHUB3sucRGVtZW78q6QuBa8ZjFWoyYh9e7bnWwT81i2XWa46xHLudo600p23SMJYcQIPRCXX+qFlvVfc+t3Y6n5CvX7eYUDrKIDb3slPWypkJXljITz8ruTcdZTkuEmVtJiwkDae5GZS7hIItY/xKQCF9VsBcm1neJMMcjAb6rD3qaaa5E7m2aa/RWQhSKXIiTojQZu5rKCkxTWxnoO3rgZe8pV1nspW9ePhmAHqIb1Ef39q2TJMk0DIBqn/D2m1d2kJkVhNiSepfBXqlWQN4evWXE3Hpj46+iqN90290kz9kqnHikPWflfsM+7pG1WeRPhdjwd9MEQLlO3qzKYpdlQ1mPlcRKWURicwrUQhTRF5LYIIvg5sRv8zgIZSgQkdgC7teITDsUzAoHD0uaQm+zkGmHglnh4GGRbitjrCRWyih/rqDKoSHqsEar7DN18md+dctWt9MK1+12+/eOPtB5m4s6rMHTJaYvUwasir8MsZO0PhGv8yrssEZYuGa/D2cI7igmDrGl8BcmNll5Z/tEydqqqMMaiqJ89ydXElYbWCu8KAr84hFbBn8tYonQPtGH6RJBhzV2DPur3xVgrDayVs8Ikn2vqvhrEZvWJ4qHAfGGNZgXHVkttVZSnC9DbBb+ssSe5fWJAgsQd1gj6stRq3XNVWqtrAVyiC2Ev3ZWQIN58jop8rBGsgOL9/AFIHikxGQRWxR/7ayA9Il02469KdGHNShhsQ4s41k5xObib+zwSorowxoxL/Kbi/HGZ9nDq9bNq8zGog9rZB0ywhK7CMMaC0nsIgxriEjsc97ptwjDGlkTK+8Y4s8VxS/LhrIeK4mVIomVxEpipWTLf7t6YzQ3dFptAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
Answer:(i)
To Prove: Δ ABC ∼ Δ AMP
Given: In ΔABC and ΔAMP,
∠ABC = ∠AMP (Each 90°)
Proof:
∠ABC = ∠AMP (Each 90°)
∠A = ∠A (Common)
∴ΔABC
ΔAMP (By AA similarity)
Hence, Proved.
(ii) Δ ABC ∼ Δ AMP
Now we get that,
Similarity Theorem - If the lengths of the corresponding sides of two triangles are proportional, then the triangles must be similar. And the converse is also true, so we have
![](data:image/png;base64,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)
Hence, Proved.
Question 10.CD and GH are respectively the bisectors of ∠ ACB and ∠ EGF in such a way that D and H lie on sides AB and FE of Δ ABC and Δ EFG respectively. If Δ ABC ~ Δ FEG, show that:
(i) ![](data:image/png;base64,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)
(ii) Δ DCB ~ Δ HGE
(iii) Δ DCA ~ Δ HGF
Answer:![](data:image/png;base64,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)
Given, Δ ABC ∼ Δ FEG …..eq(1)
⇒ corresponding angles of similar triangles
⇒ ∠ BAC = ∠ EFG ….eq(2)
And ∠ ABC = ∠ FEG …….eq(3)
⇒ ∠ ACB = ∠ FGE
⇒ ![](data:image/png;base64,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)
⇒ ∠ ACD = ∠ FGH and ∠ BCD = ∠ EGH ……eq(4)
Consider Δ ACD and Δ FGH
⇒ From eq(2) we have
⇒ ∠ DAC = ∠ HFG
⇒ From eq(4) we have
⇒ ∠ ACD = ∠ EGH
Also, ∠ ADC = ∠ FGH
⇒ If the 2 angle of triangle are equal to the 2 angle of another triangle, then by angle sum property of triangle 3rd angle will also be equal.
⇒ by AAA similarity we have in two triangles if the angles are equal, then sides opposite to the equal angles are in the same ratio (or proportional) and hence the triangles are similar.
∴ Δ ADC ∼ Δ FHG
⇒ By Converse proportionality theorem
⇒ ![](data:image/png;base64,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)
Consider Δ DCB and Δ HGE
From eq(3) we have
⇒ ∠ DBC = ∠ HEG
⇒ From eq(4) we have
⇒ ∠ BCD = ∠ FGH
Also, ∠ BDC = ∠ EHG
∴ Δ DCB ∼ ΔHGE
Hence proved.
Question 11.In Fig. 6.40, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC,prove that Δ ABD ~ Δ ECF
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKkAAAC8CAYAAAADzo4HAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAB/aSURBVHja7Z0JWJTntcdn5tqbpYleq7Eaq/VJbprkNnvSLNWkalqtto9pHhtvGmvMZqMmqVETNCqJ4kIi4K4EUdCIC2pccAOVJVACJSqCBC6KCBJ4FILgOJNxJuOce877frOwM8OscP7P8yqzfMt83+8773ve5RwVsFh+LhVfAhZDyvKo8k6fhlOnTjGkLP/Vww8+CAP79weLxcKQsvxPFy5cAJVKJUp6ejpDyvI/jRkzxgbpqJEjGVKWf+nq1augVqttkFK5cP48Q8ryH82YPh2CgoLgzp//3Abp1MlTGVKWf4icpPvuvReSk5Ph2LFjDaxpXV0dQ8ryvRYuWAgv/fWvUFlZCTqdrgGkSz/9lCFl+VZkRf/r9tuxmu8HYZ+FQWjokgZVPpXO1h3FkAaYtm3bBn8aPRqio6LgYEICJOzbBzt37GjgRO3A7zCkLJ+ILGSv7j1g3ty5TT57//33bZD27tmzU1lThjRAVFVVBX8cMUJA+NRjT0JFRYXts5rqGvhw5swG1nTiq69CbU0NQ8ryngoLC+HPo0bBow88BFMmvQ25ubnifbKXZaXn4NPQUHh+6FAY+uyz8NzgwfD2pElQWlrKkLJ8q9w6gPgygBud/HcypIF883abQRWmh7AihpTlh/rOiDdvnRFUwTroudPEkLL8T4vz8eaFG0AVogfVCgOUdd6ZegxpwN64/RZQLdCBaglC+pkeYsoYUpYf6QpaTdUmrOo/USDFMiSRIWX5kTaXgKjiRVUfimURlrUGuMaQsvxFQ9JAVvXLDKKqF5Bi+3RfFUPK8gP9QDdtq0lY0oHxZlCtNIA6ziQg/VsmQ8ryAyVUyKr+zoMWeCHJIv5+NUep/mNN0BmdfIY0wDQuG2/aPB28WwDwjwwQVf5K9OzVinX9RsuQsnx9w/aYRRs0Vwcw4wSIEadotK5Ts2W/6Xs5DCnLhzpVC8KLV2FblDQ5W0L6BTpMmfUgu6PiOt/oE0MaQJqcS1W9FoZlyddv4v/k3cddkq/VBPBaI5QZGVKWj9TtsEW0R6Mr5etXMyWksUrX09g02UaNKGBIWT7QZQMI710Va4RaswJphoQ0Wpn/vKsaX4foRLuVIWV5XfNplClYBw85RNOxQrpegbQaZBtVFW0U/akMKcurGkRV+YdaWFzSMqSkRw7LvtO4EoaU5UXVYe1NXjt59gXa1iENL5VV/rPJDCnLizpQJbuXbj7ccDypOUjzDfI9grqzOPkMaQBobC7eqFlamJQHbUJKun2nGVSrDZBezZCyvCCynWKUaYUeMmvaB+mkXFnlv5HNkLK8oKw6xWNH69i4Y6klSNO1ylS+3Z2jK4oh9XO9UyS9+l9nNP2sJUjJt1JTn2q0ES7oGFKWh3X3MQnitrL2Q0oamSWr/KA8hpTlQZ2jZcvoAJGnrjU7B2kU9QjM1oKmE6x9Ykj9WEsrZFX/82PNf94apGXUFbXWKBbsVQf4xCiG1I81JF1W2SH5zkNKuj+F+ld1sCXAQ0IxpH6qero5G9ESrjdCqc41SIOKZZU/JIMhZXlAiXWyG0m9t+VVS21BmkddUcv0oNpugh8ZUpa79VouQaqHqSfAZUhJ/7HXLJaVpAbw6BND6ociR16zXU4oya7pGKQTcmWVP+4kQ8pyo7J0yuTlL1p3y9sD6bFq6TypDgbuYmeG1A8VVAgiztNvUqDDkOopbhRZ5dVGOF3HkLLcpHsPyInLB8o7DinpkUzZ3zotQIPtMqR+pmKTMh90o7HNaCTthXR5iQwoMTBAJ0IzpH6myHLZHr3/cNttyPZCesmohIpcb4SLBoaU1UE9lywjkawrbPu77YWUdEeSnDi9sJwhZXVAZOTEhJLPjVDTDmfcGUjnFsgq/8kAHH1iSP1IRymMTqge1PHtm6zsDKSFFIYH4adurSsB1hvFkPqR/kbQheshOLd933cGUpKaeg2wvZtYy5CyXL0Z5NysMEB+O2fTOwvpWycpwIQWxgfYRGiG1E+Up5drmdQb2z/501lIs2pkVL5uu80BlUWPIfUTLcmXVf2krPZv4yykhL8IZb5ED1kBFGyXIfUTddsjZysdvOQ5SEn30UToOVqYe44hZTmhyxYl5v06o1NRR1yBdG+ZDA/5aBJDynJCWxRwnj7sXN+QK5CKvthNMlvJhQDpimJI/UAPUCQ8ijPqZOpFVyAl9Tggg/FGBUjeJ4bUxxJhdNYbhWfv7OR5VyENzZfbDU9jSFnt0JEq2R79qQvpwF2FtNygjD4FSLBdhtTHGp8uQfuk0PltXYWUREOvqkU6SK5nSFlt3YA4s0hkm+FCzKaOQDotR247OQDWPjGkPtSZejkCpP7CBK4EGekIpGL0SYTw8f/IewypDzU/Tw6FTnAxjmhHICXRECzNusrz84nQDKkvL/5us1hwt6fGN5AOT5bbL/fzJBAMqY9EQcTIu6ZRJldnznUU0oRK2bMw8IB/9+ozpD7SWorTFGaAx4+5vo+OQkpDsPSQ0OjTFYaU1VgDE+Woz9oK1/fRUUhJd+6xiHbxZj9e+8SQ+kDUgU7LOAiwog7ksXEHpMuL5BTB4cf8t8pnSH2g+DIJxi862BZ0B6SlZjm5hdrH/oopQ+oDieC4s7Uwvbhj+3EHpCQ1heFBUNPrGFKW9aJT11OIDtI6ODveXZAGnZRr/adm+c81Ykh9qG/ESI8RbnZDum93QZpRJ5dStxXFjyHtIhp3gpZv6GCsG8bM3QUptUXVNF1wpQG+1TOkXV4qmnD8iQ62u2HCsbsgJb2SLp25sHyGtEuLstOJUaZNJpEe3J8gTaBgu4tkesiWZLFY2iwMaYArolgGx33cTfGY3AmpSPWoxKFqbvQpOysL5syeDdOnT4dZs2bBBzNmwHvvvAPvYKH/33v3XfH+V6lfMaSBrLtpOfE8Lawtc8/+3Akp6XFaa7VMD7HNTDjR6XQQGbkOVCqVrURERMDOHTsgJiYGHn7oYVCr1fD++/9kSANVYkIJjTKtM8I5NyWldTekIjbqAh3c28Kq1fz8fBug3W+7DbRaex9aRUUFvPiXv8Drr09kSANVW5TguD3cmOvT3ZCWmO1dUc1hevLkSRukfXr3BpNJdlldvHgRjEYjfP311zBt2jSGNFA1mrqeZmphnBu9Z3dDSupNkVRWGuBQReuQ9uvb1+YsTXtvmrCynhJD6gWRvyxGmVYYINuNYRc9AenMQpnk7OXM1iHVYDl+7DgEzfhAvM7JzvbY9WNIvaDUWiVZw173rifyBKRJ9RJS6oqytAKpAFWjEc4S/Z170nMr+hhSL+jVApmi5lk3j417AlJqZYoJJ+jgFda3DGmfXr2guLgY1q1ZI0A9ceIEQxrI6nNQhtHZ6+aJxZ6AlDQmWzp5M/JagRQdJ2vn/crlKyEvz3OReRlSD+ucQU4oUcWZRHa6QIB0W7WcX6BqNN/VEdIBAwYIj55UWVkJNTU1HruGDKmHFVEub/j9Ke7ft6cgvYR1vvpzOXxb7bBy4Pz58w3apFZIPS2G1MN6giZuLNHDumL379tTkJL9/GOWrPKXKud97tw5+Psrr4j2p7W8PnGieJ8hDWBVmZWIeRuNUOaBKXDunKpH5Qb+8zVW9UFncL+0QG+2Fnonys8KCwsheO5cGI+gTsAy/uVX4OPgYPE+QxrAiq+Rob/V+z0zO6gjkAooFTATvwMY/2+AW45YZLS9T7A9+pFWDJGSl/91tU8vI0PqSY0/KcfC3/BQF6KzkDpazEMXAQZ/BaI/VMSECtaBOggfqPk60GwxwbNp2C6NNYmUOtN8PMeUIfWQqHYXeZk+N0BRne8gtUJpxrKvDGA0wqfaLoc+hcXEov5UD5pdZpiCMO64hN664g/R6gEayn0gnSHtlDquBWmdtntu3ZAV0uiK5sG8/CPAemwydqfVAGQVVxikpVysg58ilGL+KG4fWiznkzZWVLn8DapYI5z34bIShtRDmlYghxdHejDk90QF0phKO5jZVwDmnVKqcWpfLkMw0UvXoLX87wQzfIxAZuvkyNIEJU1kWAs9DwVaZe0TNlkifJhShyH1kLqLtp4RMi55Zv8EpbCkYXoYjdXx2HRlaQpW42oETx2KVXikAZ49DhBTIafhNVbKJRkY4pb4lq39g2lySHdkDkPaqUSpZwge6gx3N5hkLSvQLY9Ey0bVMPXBinSPEQjlUiybTfBGFsDBatkubktqEbBMDxdamPsSXKSMPmGzpdpHK54ZUg9oaQmIePS/SepY15PVG6fhVKqip50AuC3eJJZ4qMNke1KkHo8zwVJse55zAaKnE2XAstiypg9DKbZpR6TIwQg6zq5KhrTT6Em68ViNxrkQnNYKSBWWXZcB3shWqvEQhBGhVGN1rsHXf0J4esSbmnWcnNG2Mhm95L6DFriCx0y9CvD2N/aAauowWSgC4Ac+apcypG5WHSgTStBpqWqHZbNaSxP+k38drfB5QGCULiJ0WEQ1jlUy9V1SppI0h3kcryuO08YOWDiajUdx+4W1jJZOEj0MmjX4MGwywlvYdBiWJPt7n/BRVxRD6mbtq5bVY+89ljbBvIb/7PkeYGoeOlq0bINAoW4rspYbEMwvzbAYPyttoXE50U3Dog/tNwtnSxOJx9xmgilovfMc5pKW6pThXWwDX/ZBu5QhdbMmZMpunZC8pmBSNX7hB4ANaPlG/ktJ602d6fOxrDIIQB49aoFtpQDtWVDqrrH7vbj9ygJodRWrWqR61EL8Je9fU4bU3ReU+iax+rzqAGZOHUDQ/1F0Z+Vz9JbVC3WgiZLWciJarqMuVNmemgXVnMTo0xwtjMtlSANahUal6wlB3PWdXCGq2WuWQWpna+Xw42YT/OchhJYsVwez0XkT0nxap7UOf8dOk5iYwpAGkKzWshyr8RfTlAV3BCq2L8WEDXJ8dprhd9gM2IrVeLUb5wl7E1KSerdM9ZiqBa+KIXUFSgXM03UAs8jpSVImk4TJ/kTqIup+yAJj0ZIeq5JLmj0hb0MqIlRjlf9uIXhVDGl7wbTIcuAiwDN0s/bIsXH1x4rjs0x246g/N0BunXfOy9uQHiyXw6h3HfZudH2GtA0wK66jN34W4F6ylltlgAf1R1iNh+iFN05j2jvRWk7JlJ3io5K9d47ehpRqBMqDSqCWeTElKUPqAKVFsZb5dViN0xDkfotY+iHGxtFiasL10CfBDNOLAJLQkdA6GJQhSdJpiinz3jl7G1LS/ccsoi93rReP2aUhdZwQfAi98T/TOHWcDIxAnriY4hZpgGfw/QiEr6iFRLFigjN1LaGVrfXi+fsC0jVF8mEcnOK9Y3Y5SG0TgtH7WYUOwGMUuCFaAia6iAjMGCO8QdV4NXrj7Wh+JVbJHJ137vFuWm5fQFpuUEaf1nkv1WOnh9RxXc9pHcDSMw7LJ5YpYEYYYBBW48EFAFn69o32OOoPVAWiV7/Yy16vLyAlqWmu7AIdJNZ753idElIrlDTF7Ui1MlRJud3RsSEvnNqWmjVGeCbJAhvQY+3oSJ9YmrFID/lG7/7ONzMlpFurvHvcD07I47550jvH6zSQWsGkmUSrzgM8ZR2CpPmWyxFMKliNv4U3Nq1WLp9wh76hkZjVCP8m76c9/FOaDHo7Ay34WUsr5YbMZ+ouFWqVmVPo6f/IkLYOpXVCcMY1EMG1+tEQZKgy2kNQogN00y6zmOyR66FRkvdyJChTc71/DUSzhVZ8UtYQbEs3W2hmFX7nj26OJ6beJGuPf3thgV5AQWod7SnHx3cXVuMvZilVLU0IXqLMgYwxwbNHAaLPYTXuBT/GmoJxf433r4cVUnW0nG/aXFFHYm0ySwtD3Vw1v5giq/x5Be24bx1Mo+MSpM0dyBM5fBydnmy0lvMRvKfSlKpmjjJhI0rOgRxH1biXp5HRMl8x6oTerpeHs+XN2yodmD2t/O73S/F7M+rh+Vz3HvtIpezR6L/X0ionN27cgOTkZIhcsxZWLV8Bx48ehcuXL4v3L11q3w1zGtKiwkJxoNzcXBEnncIBpqamivfo/5ycHPH+1atXOwTmlRsyAdab6I33pE51WtMzG60GLTZDa9ktwSIStxb7gg5Fos8QrcnwNN8c3wrp1lam+U055xlIRbBd6opapofLLQB65NARePKxJ2xRoak89sgj8Ifnn4ehQ4dCrx49QK9ruy/FaUj37d0LI0aMaBA7fdTIkSKQ1fBhw2zhqVeuXOkUmGQtv0OnJ/YiwNCvlQnB1KaiKW40IXiHGe45DhCFYFR52YtuSf0OyxSMURW+Ob4V0rhWIJ3sIUhJjx+Ui/g2lDUFdH1UlI2R+371K2G8SNXV1bAwJEQAS5/V1LQ9/OFSdZ+YmNggTiW91uv1UFpSAm9PmiRA/XDmzDatpXUI8t1vAQYcU9qXtHwCi2YdgrnPAoOzAVJ9MBu8LeksyvmiJam0+OYcfA3pmmK5CuHJRhNOjhw6ZGPj9ptvFUF2G4tCmRMnl6ravrkuQZqdnd0AUqr6SdaTIVApTCDphmOhvssbcgjyrycAbqInca1RWsuP5UhPH7SWC9Fafm9oum1bLFgaH68d29lmODXarq1t9pXJG3T3QR8R6geQkq8oJnTjPbROhKbAunffdZeNjfXr17e4fcj8+e0KxOsSpJmZmQ0gpXjpZOKnTJ4MZaWlwqTn52SLkZv/war77q+wpAP0TcYDxpul4zNbWUKx0wRPZgCsLAGocOjOGH4a4L5/ye1EwW2DSls/rz/n4fdSHbZRtptU3PpNpO802Ab3MaqVm7q0UhkcwKo+tMxeM3i7CO8eIU2qtk8lbFzm0vS69+thdL6HzoF6N8INkF7bPBsFBQXQUbkFUjLd+xIS4MEHHoCyMnsDJbFWJnwVETDm6WTwqwXybzV6hTRS0txzJCZsUH/nbGU7KjO0oGojzqewyh9q7dtQmakVFqfFbehGz2i0De1jdctP+G3JMvQMneM4fMBWYHMlzIslAsuqb5XBCiWz8k1Hodkifh/9pr1miCx07zlEoFM7kCBF53G0MuFk3erVDdgoLy/3D0itzhLlm3QM8H/CoCynWCQ72G0FoR3dSucyTTai7g3q/7RtQxe6jZSHoo34ia7hsejBaGV5sWqvRe7bcRvax8aWx6QG0pi5so2YLeWrslDWRuq5WKjJ1FyhNv5C/O5iD50D7TdUB5OUXGMhwcEN2HA0Wj6F9PfDhwtvrRv+XesAKTm94ofM18sLZS148X6T0zqkNGLUYLuPtKA51Pp5aTaY8KZoGx5rLm63q2VINV9a5CRmx21wH5roliEdgJCqZ+uhfxpAMDZTJqGFegtrtbfyvVv+iced3s4yBc/vDTce+w2lvI0luNged2rH1q0N2Dh16pR/QFpQWAgncnJg8DPPQGmpbDhaO/eTsGF6SNuo1AO0VQkc1zfdprANHyXTIL/XeLvcVgbqc83Nb5PRaO6otWOaylks+y7fgGvKayqeGMwIRFH1bq1ZZbrxsBa/295r5jbHiURefUmJDIB09OhR0SXVGUSDEyN///smTRzrzejbqyfsit/hFVCrKivg2zN58G1BPhShU0L/f3vmDOSdPgVni4v84oGZHRRkuzY9u3dvmuOJgmRcuADLwpd5DtJstJqON6xxht7a2lq49557bF1TnUGUltDxN0evXw9pKSkNrMZHeHM8LUpJ8/RTTzU4l1EjR8CgX/5S/E1Nrri4OJ+CSsce+txztmvzMDrUZ8+eFanHr2m1kJqcCr/o1w8+mPmB5yBNQE/e8SLt2rULdDodXL9+HfJPn4YB/fuL97VaH45ZulnUnzewX3/bb7amhtm/f3+DawFegGPOnDm243W/9VYxBl5RUQF39Oxle3/C+PE+t6g06mgdDiVgaeTJ+jomJqbd+3EaUmp7vvLyy7aDUenVsye8NHaszYGiMuDOOzsNoKT6+nro36dvkwGMM9jUcWwCmLyQJS48PNx2zIFoEKyqRFAdLXtkZKTPr5vZbIaioiKI2RADmzdvhrS0NHEtnZHTkFJVTv2iVO1Q+5P+ppOwFuq8pf/pe50ZUppQc+3aNXhtwqs2QIO8UN2TPvvsM3uOT6w2TSb7g+FoZW/5yU86xbXnJc0uQvr8sGEwZPBg2+sXX3jRa9Vra5Du2bOnyUALQ9pFIaWZX5S+0Dqb56Zu3WALVme+hpS6Ax0hPenBPPQMqZ9Dah2Tbuz1f/fddz6FtPH5eCNBLUPqp5Ba50eKi+gARfC8YJ9Cumf3brsjp1J3imvPkLZT1J02oG+/JgMY1A7tptLYPeo1nveoW4N0VtAs22cjhg1nSLuSfvjhBzF6YgUgbssWAegs9Oit79120y1eOZdly5bZjnn3oEG2BW5XamvtKyawrVxWWsqQdhXRZO6FCxfCz3r0sPUDD/ntb+HdqVOhm/J68NNPi/VfnhbB+PrrrzdoYny5axck7NsHfe+4Q3SFDRrwS8hITw+AK8uQuk00mkY3PSMjQ1TztPgwJSUFDh06JOYxlHrJYpkRUDouzZF48vHH4dGHHhIPywfTp8P0adNgzJgxsHL58k410seQBqBoCJQmbNAwLY2FGwwGsRKCSmcVQ8piSFkshpTFkLJYDCmLxZCyGFIWiyFlMaQsFkPKYjGkLIaUxWJIWSyGlMWQslgMKYshZbEYUn9RczHlzY2KNcmDVRZL+5JKeFIWh/O44ervbmnfDr/bXyOsdhlIc0tBZM8Tudo/V8pGE2g224t6A+VxN4Eqx07H6O34Oh5gld7750zQXEe6jhQDPL8fz2+VCR4pQqic2YcOoF8s/q5saJK1r+YKwOSDZtBswn3vBFhS7dpDwJC6UVV4w57eKVM+quYZoH8BAC2ho0KR3VPxnzs3GECdLL9fewlEaHLVAiPcmu99QI/kWUC1Ug/qKBP0SQKIrpTn6YzCkvEh+1AHqhSZ0sa2/zqA7usN8JN0ADwMHKXsfviA/u6c/1nULtcmjcs0K1lQjPB8M5ns6hDkUQ7x/CftM4M6AbcztgyTtUCjvzsC6PI0JbHvFoBQFwMUnhJpJSmjih5UCKPjbmbsResaYoT/dXizH2V82QTwFUPqW33hAOkQB7N0thzAmrMrpUqC8s1VgOMIbTKWkmZAqkFwD2CVGU/f+wEgDcsB/PtIB0OUHs1RUoR/AbDHRei/R/iGUTUfThlYGkFaR+mE8L1QM4Q75BP4A723wghjqxhSn2qTA6SjKu1OyWtYnWY60KDHBlyfKIPMbxqKN/tkQ0DjT1NVjE2DDdiepe8tUVIBbcQ2XpY9G4ezMuED0WMZAWQQKYG+vAwQ8z0+ME44NvR7FmBtMOkEWsfVdktap3xeVYTnHo7vf9YQ0lc3UoogPG4GQ+ofkIbgzUgDmIXW9IUDWLXGAuxu9N2SMotMjraoIaTbMmUmOtVGtHRETj22XVfKG/xAB4PYpZ00SdhXG2HgcYC7tuCDQNVwnAXW1LUP1LhcgH+eo/hVCPyKppAmp+P5L8L3wxpBGks5rPC6HADwp/ASXRdSBEq9Ga0etjk1a/DGRMuq1VHllJ6RLOkSB0ixKu/9hUyYpkqSTpe8wbiPBfj+3oYOirP67KBBVvXRFohX3gs+jMefhe/FAcSaWt++ENslL2fIXFhUv9/WDKQpGa1BimW3zMHFkPoaUqzuRyttLz1S9TO8MYmNzFRZRTOQ4t2/eZMdUmuzdvImg7zB8R27wTZQtqLXrbxXiuAJqD4xwj1FLW/7Iz5A8zIBToPSjME2Rz+CdA7uL8tuhZPIkoY0hXQiHZsetINsSf0GUkfHKQWJaBxurFlIUR8lmUQWPdV2gFylI5y6ilQLDdCrg11VU+IUSHHf1tSxuiqQbch5BuiO59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)
To Prove: Δ ABD ∼ Δ ECF
Given: ABC is an isosceles triangle, AD is perpendicular to BC
BC is produced to E and EF is perpendicular to AC
Proof:
Given that ABC is an isosceles triangle
AB = AC
⇒ ∠ABD = ∠ECF
In ΔABD and ΔECF,
∠ADB = ∠EFC (Each 90°)
∠ABD = ∠ECF (Proved above)
Therefore,
ΔABD
ΔECF (By using AA similarity criterion)
AA Criterion: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
Hence, Proved.
Question 12.Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of
Δ PQR (see Fig. 6.41). Show that
Δ ABC ~ Δ PQR.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUsAAAC7CAYAAADsUrwzAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAACriSURBVHja7Z0JeBRV1ve7O8zgwggqo6OOji/IgOC4viLK4PA54jYqqIzjijq+zrgxjIOi7BhWJQGZQCSEJSxBZEtAtoQYZN8SthjWgEEMxEAINN003TR9vnPura7uLB06SS9V1ef3PJeE6kp11a1b/zr33HPPNQHDMAxzUUxcBQzDMBeHxZJhQsTJkyfhtNUKDocDzp49C6dPnxY/3W43XLhwATweD1eSjmGxZJgQ4HK5ICUlBa69ujmYTCZohOWm3/4WLBaL+H+He9vD+vXrWTB1DIslw4SI0qNH4Q9tbhXiSOXD3r1hbGKiKphUtmzZwhWlU1gsGSaEDB44UBXGVatWiW19PvxQ3db1yae5knQKiyXDhBB/sVy0aJHYNiMtTd3WvNlVYLPZuKJ0CIslw4SQgQMGqMKYnZ0tfJQf9+mjbvvLo49zJekUFkuGCSH+YklWZsLnCeJ38lvGxcXBxo0buZJ0Coslw4QQf7H0CiSVxMREMWLO6BcWS4YJIf5iuXDhQq4QA8FiyTAhxF8sly9fzhViIFgsGSaEDIuPV8Vy1syZXCEGgsWSYUIEjXw/3727KpYf9OrFM3YMBIslw4QAp9MJ06ZNgyaXXy4Gdqj8oV07WLZsGVeOQWCxZJgQQMkzpk6eDNOnT4fMzEzIyMiA1JQU8ZMxBiyWDMMwQcBiyTAhhryUF9hVaThYLBkmhJBGzikG6JkH4GbBNBQslgwTQvJt+FBNcIBpmA0afeOBigtcJ0aBxZJhQgQZktdkuMEUbxNiaRqMZaEHyi/Izxh9w2LJMCEiaT8+UKPtYB5pBxOVEViGYpnhglVlLJh6h8WSYULASVRC0xQnmMc54OWtIMUy2QlXoqVpHoIWZqoTVv7MgqlnDCOWNFOCZ0swUWl7WJ5Zgw/TMDvcn+0BB/7fnO4SArm5FOBP60AKZpIDUg/wSLleMYxYfvPNN7Bhwwa+o0zE2XoaHyS0KM1jHbDHIbc9TuI5xg5T98v/99gEYBmF1uZoByTsZsHUI4YQS7IoO7RvD1de0RROnqzgu8pEru1huWy+G0yf2qFXvm97wmEQAzx3rvRtG1DgFUw7vL+VBVNvGEIsN2zapCYvmPf113xXmYgxdrf0T1qmusDqt32rE7fHozBid9xfE2kQyDLegeJqg67rOBZTTxhCLP94//2qWHZ64AH2XTIRwXoBH6A0lxj9Tj9S+TPVbznJCYXWyp8txn0tySiYA21wz7d4HG6uukD3YllUVAQtf/c/YDabVcHcsWMH31kmrJC+PbFWdrVvz6pZ7R5fL63Ocburf7akBCAOhZYEs3GmRwgma6a20b1YvvTii9CnTx+45467VLF84fkX+M4yYWXDCRCj2zSokxdgZdupR3GfATb4fVbNnxfbUTDnuMHU3waWhR7YeYYFU8voWizLy8vhsUcegZycHMjPz1fFkkpxcTHfXSYskKA1oZk6/a3Qa3vg/Q44sSueaAfTLFdAETyEgnnlErewMClOc1sFC6ZW0bVY/vPNt+Dhzg+JXIJut7uSWA4ZPJjvLhMWvqBBnRF2sEx3QcVF9v0VieoEB6wrC7wPrfl4c7YHzINk8Dp10VkwtYduxfL8+fPQukULkZH6X++/D+9jubJZs0qCee7sOb7DTEgppVHuGS4wDbdVG9SpiW550q/54faL73vvarREaV55khOmHKCQOK5vLaFbsfx81Ch44L77YOnSpZCVlSVW0qPuuP9Az8wZM/gOMyGDtOvpjfjQ9LNCi+zglCwVrUTTJ1a4ekVw1mKvbQAWmk/+hQOS93IsppbQpVhSt7tTx45i2dGqfNS7dyXr0oXdc4YJBbllNCvHAebxDthyKri/OWAHMV/clO6GYPs5H+9CwfwcBfMzO/TYzIKpFXQnluSbfOKRR4QF+cZrr2FD8rUkl8sFE5KSxGfeQqPlDNNQKC3l1d94xKDOm3l1+9tLMt3CUlxTFvzfTC5GwUx0CN/oyxs4eF0L6E4sS0pK4O233hJLjvb9+GPY5hdTWVCwC8YmJsI/8PM3evSA1195Bfr27QtHjhzR22UyGmMcpV+Lt4FljrvOQeTPbZdd91476/Z3sw8DxI2zi9k+12E3/jwLZlQxTtYh8PqEuEUxoeXIOUq/5gITdo1n1iMibd5RKbRNVnjq3Do3Y3c/broTTINscM1SD5zl4PWoYQixJJ/ODGzEy8rYv8OEFpF+jfJT9rXCr7Pqd4wSirec7BRTI8ucdf97mi4ZR1MnKc3bLBcHr0cJQ4jlAOzemBJkduoX2CHOhJDckyAGWswpTth+qv7HaY5WJbXP+SX1+/sKbNO/WuwRFiaJbt5pFsxIo3ux3G+TGarFDIh4mcr/ORZMJgRQE7pykVtYdK9sbtixXtqO7bS3Fbpsr/8xKHj92iyPjMVMdsCCn1gwI4muxZIayl05MujXnCBDLUQ6f2xMbZdL/w7D1JekA75BHXsDj5VB8ZZDbdA0y9NggetOmddH2kQY05SDbBhECl2L5Vc/ye435RJ8PtsjEhtQ/kBLmlOMIF6d6YETvBQpUw9KKf3aRGxPiXaYF4I0AzTzx0w9IGybPzsbfrw3tiqJhNFA6L2DBTMS6FYsqXGY5soEBKOKAIqpOz7RCU1wW345QNxc2X0yfeWCAvbvMHVADOpslD2WZstD13IuW+YRL/FZR0NzvKGFKJhjHWLtn/e3cSxmuNGtWPYtAJHK/9IMj/DliIuh/IDYDUeDE8rdAC2XKg7xaU7YxYLJBMnaChrUsYE52SmyAoWK12gg8iMrdMkP3TGnoqFgGSczr7dfzYIZTnQploVnQCwzav7cDstLfdubfCPf3JOVEUdqN22WK9lcJjlhDjvEmYtA7aMprakzzAavbwrtsdeWSbfRLxZ5QtoOZxdjT2qyHORskQ3g5EYeFnQnltQOOq7CE//YCg+urvzZuO+pMTrgufW+bTQz/M/ebC5j7DDzRzl1jWFqYvx+Jf3abBeEOquA3aMsNZHsEHPGQ8kuCl6fKgWz6WI3HDjL9zLU6E4s02lUcYRNBPmWVHGU78AGY5rgFIG7VXl7KzbUoTbxZv+gkB3iTHVoGiP1QGimTkaYZsg2yaKpjzaYEIbjF1DweobMvG5CsT90lntSoURXYklZW0zz5MBNv8IAF5SKjX2kAw7WYBYMpmwuY+0iHvPv21gwGR8i/Rr2QKj7ff3y8DWMd7bLeeKP54fn+LTCReNMN5gHyuD1Rex6Chm6Esu+hXKE8vLMwB2kdivkIlHTAry5pxf7RhC7rGbBZCRraU2dMXaxpk6xI3zfs64Uv2ecAy5b5A6biFEP/+5ckL76CQ7IZMEMCboRy8KzspFRY15ay5Sx2UUg0mF1+TbwPkuOomB+6RTCe9sKDzi4JcU0YqbOQrd4gf4jL7zfRZ4j81duERMcar9lVZ7ZgN9F4XP43NB65WwYNAxdiCXd44dWyZXy7s+pfd9il1x1j3xPtbWN/FMg1lAhh/hNiz3V/J9M7DCG1tQZbQdLugtcEfi+xitk9vQvfwr/d72X70sk3L+ABbMh6EIs5/4M4q1vnuqE0iBas5niLbHx77xId2qHDSButktMQ6N1VXbbuLsSa4hBnWlOMA+3w+wIpT2NJ3GOt0OXDZH5vjF7FcEcaRcDnRyLWT80L5bnqDF/LYPNBxUE9zdP58p4trH7Lr4v9YSupWwuQ6RDfFMFC2asQPf50e9AxObekR257y08JWeb0eyySC2pl1qEhsF4GbzeYRULZn3QvFj22SmTGTSeF3zUW9ohuVZKxxXB7U/G6k1LPDK0CLvw83kp0pgg52fFD55oh122yH63+Wu3MAB22CP3nbSGkDd4vR2+HDjRTN3QtFj+4PQb1KnDfNpDLimW9PauS3t4kbK5DJcr6yX9wP4dI0O39ppFcsbXu9sj//2XZ8kQosTiyH7v6jIl8zoaII1QsMlXz808ODQrlnQD78mWvspOOXX/ezMtA4CCubOOb+4eGwAsCQ7x1v9gJwumURlRKGMqaaaOLQrfn7hbJhV+dH3kv7vCrQSvU2jRHDcUsK8+KDQrlkuOyXhJS4oTjtfj75/JldblF3vq/rfJ+5TkBCPs8C4HrxuOM+QHn+ESU2AnR2ktuz3kt0yWKQXPReH7T2EdNFrslqFFyU5Y+TML5sXQpFiK9GtfSZ/O8ML6HWPmYRkOcu+K+jUBcohbkmUsZoccFkyjQLfxVUq/NtAG9+RG91zMX9HApQ12RnEe959WKdOAKXj9GLfz2tCkWPbKk8kMGs2tfyoDSkZEMzJo+mN97z/5SS2pLjV4vYwzcOieTScVPziWPGt0z+WRXDkSP+pgdM/jsdVKIuEvHPD5XhbMQGhOLCmLNL3lKP1azvGGHetyGnHEh2Jdef2PkU/JCSh4fZANGuPxis9pq76Y4CENaLlcWpX/2hn980k/IF/oD6yMfhf4012+WMzhu1kwa0JTYikaM62CF2+DP69q+PH+uUX6LYdsb9hxjqCAX7ZAZmUn98BeXopUlyQelJacZY4LHBo4HxqJFvGWWGwaOJ9RBSiYiXYxqPrEZo7FrIqmxHJ5ibKmzngHlIbgRmWUye68aWHDMxOScXoVZXMZYhVd++XsENcVJ2lNHVqbabgNUg5r57xEfks0DjZqQS1BJpqJS5bB6x0583olNCOW6po62HA+3xOaYwq/ZYKcJ34+BMejKKQHvdlcsEEtYcHUBXSPemyl+dg2uDVbW3fs6e9kftahe7VzTlmlimBiO795qQfKzmvn3KKJZsSS5qyKuLd5oU1l0IwEeIID1hwP3TGfWqtkc/nCAfH7OfO61tlSId0x5i+dsP2Uts5tziGZJeuBLG2J+Gass7g5aPX2t0JT7FEdO8eGgSbEkjI6k/VHs2eyjof22G/lyRCi/iFOttrXzyE+mB3imoVuS6vl0g/eM19753fUrfgtk52gtbHDEpcimNSTmu6CNWWxLZhRF0uq/Jtops4Aa1iysCwok05908LQ3+ZRe2i2j0x/1XUNC6YWEYM6g2mmjluz50ip4ci3vlkjfkt/yjzyZWMeKH31607ErmBGXSwp7T2FT1Ay3kNhyClJhqrIb4k3+mQYzn/eERADUiTID69ih7iWKCc/+BSnGDRMK9buef59o+z9UMiOVvnfHF8i4fEHY9P1FFWxFOnXlDV1Ru4L3/fcusQj/ELfhGlqWy4qMk3LJMFsudgDJ1gwo46YqbNZWpUtlmr7hmQdlX7LGzPcmrba3sL6tIzEntRoByQdjL2eVFTF8u08GSD8S2wk4UxU/sH3Mtnqq2FMWrCVgtepO/WpzOZy7Dw7xKPJ9jMyDM2ML7HdVm2fK/W+zRMcYhBKgz3xSny0TfHVY92+nxdbghk1sfz+jFyJ0TzKBktLw/tdi8ulKIci3rI2yL8TN0eGP1GCBBqFZcGMPFTnN37jEcHVb2zSxzlfSj2sz+yQc0L75/rlfhTM/zpEO39+Y+y4nqIillS3bb7FL//YCn+OQGp9EjGR4WWaC06E2c9/HI//P4uVRMITHbD2JAtmpKEuIvUkaI0lrVtqXv61RcYEf5Knj/NdcBgNgxQl0Qw+y84YaORREUvKRE5vUctUJxRFKFN0mxXSL7Q4QrM3HiSHOFmYE5wwgzOvRwyxpg6tHT/aLjLm64WsMimWl87Xtt/SnxwKXk+Trqfr0ECweYzdziMulnZqzKKrGtnRv/cp2epAKzwXwWSrT65CwaRsLvjgJhzg4PVI8MI6mTD6hsX6emyF35K6tuMcoKeFRmmNdeGrH2SDpgvcwr1mVMGMqFhSJX64Uy4D2ijTHdFGIfyWA9DSy4hsvB0tsmZRBHNwIcdihpM9NmWmDorOTo0P6tTE9ZS9HM+f8g7oiUMomI0WeFAwrWCa4jKsYEZULGlRKJF+baxdzD+NJGXemRJpTjjhiux3j9yjOMQH26D7OhbMcEBVeukiObj2pk4Gdaoy9HvZFX9zvT7Pvw0Fr9Nsn1QnfGPAvAkRE0uquHu/lYs0Pbg2OhfbbqUM/p0VBV/W3BJf8HonrIcT3CcPKRP3K8uQTHWCDo1KwQarvAbTLP34Las+4/fnKpnX0UKeWWwswyBiYplxzNeYS6PklOldhOfwkRXar4nO9y+hlfVo8GGADZovdEM5C2ZIEIM6lH4N29dcDaVfqyuUY9NML1Tsfel5YgMlxbGQYH5hh+QDxhHMiIglrU9smuWSqagKonex2afkGuThjresjT12xSE+0CrWQt93lkfKGwLV3QvrZcaq65fovybvXSpnmy34Ud/X8eE2JW8CvsB65BkjFjMiYjm4QAaFW+ZFN5kBhTaYSbQnOWF/FAPwDqNlHTdXyeaS5oItp1kw68uOChDhWeQH36mXoMpaiFeWyH19rf6vZdJBFMyxMvP6cwYIXg+7WBae8y0Qtaos+hd8+3cyYDmlKLrnUYENp+1Sn0OclyKtO1RfjRZ5xMAZJfc1Autssn2a0vXpt6wKuUXiFF/9vTkecOj4osIqllQvnbJl1/fBVdq44Hf24fn0tkIHDYw4kp3d2esQx5fJlGIWzLqQvFfxg6c5odwg1yTiLWm22UQnnDBIhvJNFUrwOvYub13uEUt86JGwiqUY1BmNjXmyU0wD1AK0YiR1c0wZ2pGlt/PxAaFR0DF2GLufQ4uC4fh5xQ+OL+KZR4x1bQ/lyrSFUw4Y55oKbIpgUpq32S7YbdOfYRA2sXSLEUqXePNHc1CnKuS3pC4OzdvWUjaaXvkUvG4T6a8oFRYLZmCoal7cINOv3bzceBU1tlgOWHVaaaxrO4qX0zzTo/rqaekKPV1h2MTy4x1yZUVadlRrtFsjH7TxRdo6r3RKJIzdcaq31zdwIuFArD7hndzggDy9BlXWQr5TidpAy9loTYDU4HpKNCPyJjhEngi9XGNYxPLQOaUxJ9hhXYX2LjqhSAbH36XBmRIyeN0pHpbW2KhiIZtLXaDqaEzJnPtb4W86ydBTVyi3jDlNRm0cOGPMa3x2NYg1tyhMamaJPnpSIRdLuuYHsmUyg8dWafOiC04pS0187dbcIlHEBjy/uKmUed0ON2W64TQLpsr4/bJtWWa7xBRWo/Lwd3LqY7KGlsgNNa+sUxIJf2aHDwq0L5ghF0sKgaG3Ba2pU6rRxkz3xDzfLZzoGyu0eY4ieH06Whc0Uv6VC3Zz8Dr8TN3TGbJOJmt4TZ1QMLJYxia3/9bY1zmUVkkd6xATVv61U9uup5CKJb0ZGs2V6ddGanjxJeLu9TL58IB92j3HIygOLRfLNYpoOl+BDkcQQ4W6pk4/G7TKNn4trHMofsuvjRFvWRsTi5RYTLzeLqu0K5ghFcsPC5RBnbnaG9SpSsI++ea+fY22z5PmC/9+ieIQn+iEucdiUzBpuQXqsVD6tfxTxr9euu/kajCy39KfJUeVvAmDbXAXvgzParCRh0wsRRcJbyzFC66u0P7NKawAsbC96WsXnNX4uZI3g/y/3uD1tB9jSzDpWq+gNXUGWqH7lti57m6bpPHxWWFsXO9W4auXsbPXZXrgR40NKIRELEX6tRwQU5qe0dGcVvNCuUiUVv2WVXlzq7JURYIDhu2OnVhMWqeaLA4KQ7PG0FviyxLpdrhuRey8HClnwyUL3HKBQbSsfzinnWsPiVhmlcgM1ZYUB5Rovweucvca6bccpKOZEv3QyrAkSv9Or23GF8xymkQwBXsAo+yQqrG42HCzF/viFH5HA3yx1JOowHIpCqa5PwrmNCd8e0IbgtlgsaSHtTFZaINsMFLDgyU1Qck0aKbEPRr3W1Y772JFMIfZ4enVAOcM+iTRZf19q1wO5JasGFILv+u/jKysCQ7YqIEkNJGkAssfspVEM3j92WXRX8OqwWL5boHsflsy9Rf0dtShWC3p2vdbVmXmURTML1EwB1jhzuUA5w0omN9VyNwClFhiVwwM6tTEX7ZIF0TfnbF5/U+hMWAZJH31Iw9GtyfVILHcZ1MGdbCLlH1cnzfDTItEodhnVujv3LeRQ3yyU1j1Ny72wDGDZKkh6Jm4htKvxdvhb5tjUyiI5CP4jPW1wm9Wxm7YWM+tSvD6SDsM2Rs9way3WNL5dlgtHdBd1+n3Rjy5Xk59fHuPPs9/mxUFc44cQaQEIQedxniokg/KOENLemz566pCK1bSHHjTV25dLZEbaj7b65vt02NzdGIx6y2WS0qULtJkFxx26PcmzC2W08rartTvNVAuieYLlOD1GS7ILaufYHo8HrVE9XpoUIdi7rB9TY6xQZ2aaLrELbqh62PMb1mVaT+gYTBODm4+virygmnyf0CqlkBQ+FOThR7xcPbbpe8bcJTiQ6e5xMNZpmMThgSzzVIleD3ZAcvqkHmd7rXb7Yb8/HyYMmUKLF++HI4cOSK2XbhwAX744YeIXQedc4+NMlt4CwOsqRMKnt8uozae3M51kUWL/qU4heuswwqIaN4E0/ikJEgaNw7Gjx8PqZMmiZ9jEhJgwYIF4HDUbDK+XwhiYMGSYYxMBmYSfryexQZI90UuEZHNBd/AKUE4xEkMU1NSwWQygdlshri4OOh4//3ip8VigQ7t20PbNm3AZovMAjfrT5KlbxczdXYaMP1afZhDvbhBNmic5eFM+khOuS9vwqVfu+HYhci4nkz0kFC59BeNYdSokfDsM8+Ih4a2tWndGqzWyi2WfChkuZg+t8Ncg2SopkB6GnH8QKd+y6o8T9lcRtmF6PTfGVgwPSiUz3fvrgplj1degcNoUZIwHj58GEaNGCEEkz63O8Lva6HT/A2FoQ2zw1sGWVMnFByheEtyS8xwwUkdxTGHE0rS00jx1dO00IYkmgnW7aSKZVsURrvdLjY+8tDD4N3e49VXKzXmh9bIAZFbVhun4jMPy3nHtxsolm/8ISUWc7RDLEtak2AOGjBAvc+d7u9YY6MZOXy4EMxIWJZJ++WSH7SmjoGzr9WLpss8YjQ4o4TrwstxStwzz63mTVh38uKC+XNpKRQfOgQ//vijKHv27IFdO3bB999/D6XHjomeViDxVMXyf++6C7xfNWvmTPUhIovDy6Jjyvo1+Jbbc1I+gEYoh88oAwoTHVDsNM51jaBlVVEs6SF7KAfA5dcGfir5Sb3HVMhfWRNlpWXY4xgFFRUVQTVgamgul0v4PKmcO3dONMCL4RIzdVxips50g6dfqw9/zZcL7T0Zo/GWtfHHbCVvAj6/i44HDl4vKiqCF/7610rtngwBr8uJ/v/oww/Dxo0baxRMVSw7duggGjWVZ7p2VYVy0MCB8iHA0pxiEvvJAYTO34LItXevzgtdQ4eVcrlemo/aZJFHXJver+sBLJ2+VdZBGmwTDvGufvP2/a3K5s2a1SqGwXRTaJ9j+GYegZbos926wRNPPCFcOt3w94HYhg4dOhjwOLT16TUyqW+rxWxT1gS5vMhHd81K9lvWxMM5PtdTwoHaffWX/fKXatufNnWa2LZr1y5opAgmlby8vMBiacHSv29fePmFF9U/uOfuO9WuOS012gxNXkuyUyT2taBgWsYbpCTLZMWGvq5EO9zuFw/7586d1fv8l8cea1BDJRFctmyZerwnUSip8dGb3N8Hvigjo0bB3ORNvzbWAfm2qD93mqTUqSw1McUJx2I54LIWBu1SBHO0HYbsDhxadO1VzdW2OnvWbHV7n9691bba+U+dq7VVk393m8xRKt5tff7zHzhzxpdMj5LRri4FWFsqfxqprDXodXmvLacE4JDfGE3nP/5Rvc+dO3VqUCOlLrz3WFdecUW1zzt26Kh+nrWysmNYzNTJ8Airsq/Ow9DCzfW5Mgfr1J+4LgKRuB+EoUCp7Z5bV7Ng/rrZVWp7nDl9prqdwua8Ynndr68NLJYPduyIVqQNSktL4bZb21ayEqIdpMyEnpdfekm9x9dc3RxOnz5dr+NQ22jdqrV6rPRZ6dX2yczIrPRd552+eZmjChW/apIDCirkUsWnL3CpWmjhuseU7P4d1gBYL8jgfa4bX6H6IHHsjz1o82g5PbIr1tUZT2CxzFiQobofX3zxRdVwTEpKCiyWd99xh/rh8fLySk7QnTuN61WuWiFamMESCXJX5apvUSrr168NWD+1DdBQ2/BvKzSqWJUDBw5U2mdxZqb6mZnCP/pbRTecln6ldGSU2IRLlfK1W4z4illaXFe11JNSL2OwjijFGwrmnOLAYtn9uecgfsgQeLzLo6pQPtqlCzid1X0dqli2v/suMWPD+4D4N+61a3WU0bcOUDgMOXIpfIDCCQ5h2bVjB+Rt3Qp7CgvBgRUWzEiuXunc6UH1Ht971z3Vwibo9/lz50LXp54KeIzkCRMqtRXqmVSFfJf++/T+93/Uz97Ll3Pb47Chx810iWBjLgEK1RHV1Wyuq1rLTKWOsDRd4Ias0sBi2a5dO3UkXDwH99xz8dChtq3bqOZo8vjxlYbWjQrNUJozZw7cfMON6vU+27UbfNKnD7T83e/gF3jtXZ98Eo6VlBjS2ixCi+9mvE6vhfnqyy8LS5FemhT2k5iYCDffeCP0eq9nwGPQoKC/EJaUlFzUsvxb979W+rwc39HH8UV+3MXFv1C9UGY6tWATLK/HPrFayqjUEFzhL5apqanQr1+/Sr2s3btrXn/YRDt5y1/RJO3erZv4nUSyySWXQXZ2tmHF0ms9+T/IH/buLSxMEgrvG+fqpk1he/52Q15/WVkZvP2Pf6ixZt7S+pZb4LFHH4UF8+bV+vdTJ0+uVH9Hjx69qGVJAssEx9nTJ/Dl5cRyvsZejndev/jcZYdz1gqutIvgL5be9n1nuz+o236HBoK3l+2P6cP//Af+3bMXvPnGG/Dp4MFA/6ffybo8ciQ2pgu0vPlmtaJmpKWp21NSUnwDE1deXSkywGgcxe4z5QP4fORIGB4/FOZh97sm4asKWY2V38rV10Cmbf5imZOdw09sEJAQpqVNhd80l6Euf+rYqdo9WbpsGVx5RVMZK/3AA7BlSwyt6FZPagodKsGelH8k0D/+7/+qvZxMsVhZVbnphht8ZvmkSep2ervE+QkBzWRhqnNb61t99ZeSWu3zmX4zwlq1aMUVVge+++67Si+jj/v0UT8jMW13q6/ub7zuuhoHJhhffZEANr38crXOJk2cpIri9OnTK/kvJ02cqH4meqBchYHFknijx2vqZy1uuokrqwb27t2rvpWbNmkiuvbeqAIaRGvVoqXq/96+fTtXWB0g9899992nCib5kL3ZwMi//P6776rt848dO3KF1UJBQQE8/+yz1VxO/3zrLXVMotvTT1f6fMigQeKzL8aMYbEkahPLnu+8U6kLydQMzdj5FQql9808ZPAQYVFe1rix2HYJ/tyyibuIdYUsy57vvQdvYbdQDaSeMUM8wM916wYL589Xt9+PosrUzsGiIijAtvo9Cmchlh07tokMW16oXklUqT1v2rBJje44fvw4iyVRm1i+9/bb6mfNLv8VV1YtUBdwdno63Pib6yu9YEYMG8GVU09yc3PhHXxhb1y/HiyKddnl4YdFQuZ3cTsNRnqtThbL8MJiCbWL5T/ffFP9jKIFmItD3XJ/30+vnr2E/5dngtUdEsvXevQQv7/4/PNqnba/917IyMgQ21ksIwOLJQQWS3LuNr/yat/IWXo6V1aQpGNdeX0/Zqy72267DaZNmwb79+/nyqkDJJavvPSS+J3m4HuFkX7uUSIPWCwjA4slQgM3XkGkXJ7ewYklSxar2ylwnakb5O9JTEiAO9q1g8YonG+hlZ7pN9WRuTgbNm6EN7HevFb5XbffLtrjC2hlevGKZaeOHdl6DyMxL5YnTpyo5F97Hbs8NAUybepUdQT3hmuvDSrmkGFCTQK+bFq2aAHbtm0T/6f4Z2qT3oQlFHngFcsrmzatcQYVExpiXiwnT54M1za/Rk1P1/qWViIHY/OrroKrsPFNTk3lVsJEBZpy+tSTT8Elv2gM8fHxYj0sGkSjeMDSo6Ui12xqSooI16K2e+NvfyvaM2WqZ0JPzItleXm5aHQut1s0MvqdsoZzcC+jBU6dOiXiKulnTVBbpc9dbl/bZcID+ywZhmGCgMWSYRgmCFgsGYZhgoDFkmEYJghYLBmGYYKAxZJhGCYIWCwZhmGCgMWSYRgmCFgsGYZhgoDFkmEYJghYLBmGYYKAxZJhGCYIWCwZhmGCgMWSYRgmCFgsGYZhgoDFkmEYJghYLBmGYYKAxZJhGCYIWCwZhmGCgMWSYRgmCFgsGYZhgoDFkmEYJghYLBmGYYKAxZJhGCYIWCwZhmGCgMWSYRgmCFgsGYZhgoDF0mB4giw1/Z1Wzr0hf88w4YLF0kCcsAEklwCknAD46iRAOpbxxwA+L/GVMT8DpJUBFPgpy94zAKvPRk9sPPjFbiwry+T5/liPYxTiNWy9EOD4WC7gPwedAGXcTJh6wmJpIHK3AcSlO8A8zA6mwTYwjbCDZbob4ub5lS8dYOqL++yUf2M9jI0gAfcd54Gx9sieL4nYaRTpQVsBWmW4wJLshLi5KPJ1VO2fD+I1jMZrXgvgrHL8Ujz+3GKA5xa7wDTXA5/auJ0w9YPF0oC8NMUhxXKCC0ZUFQf8f8t0N9ypiGXRLjdY4q1gHuqCnuWRO0cSsl1oQlqS7GBOQJHMBZh9tO7Wrec8wN3TUChRBU2b0EL1+2zXIYBnMp1g6oefDcCS5oEJEX4hMMaBxdKADJvvkOKR5IJPKnzbSYjI8rKhNTkPhcQKsns6ZzfAv4sAKmo4FnWRL9RUGniOW/Zj4/vMBub/uuFvxfU7Bp3bqCwUwxHSijZtqSyWq/cC/HcfwK8mKZb2DBZLpv6wWBqQwXNrFsutRwC+U34nI3LfcYCX8wC6o1j+HcuqKmadGxVxPFqgbbF72xatts47ALpgV//ONQCflNb//C6cALh0HJ7fp0548Efpr6RSV6tyMZ7bg3NRLL9AMRxWXSy9fJTlkJYliyXTAFgsDYgqltgNTzgnhegAWnKvrgRY47ffKVTMW1JRZD62YlfVAY+V+D4rPwlw3VcoRNRFXgUQNxuP+RHuN8IJ5gyAQQ0Qy0/JGhyAx5rohg54Tm2wC94KRTvrfPCCWYZd9pfXASzdg414Il5DfGCxfGcZiyXTcFgsDYgQS7K0RuPP+QDmJW60vuTv31fZd+cm/GwYCskwJ/zNTwBfnIF/PwDLImVDBR6HBoJGuuChQw04OQeKsPfYSwDi0aLtjNahmcRuFsDUIEblPTYUXFT9OXgsQOvYlMRiyYQfFksDIsQyHsVhjBMab0ALrADgF6lOsKBY7qyy78aNbunz8xdLO/kTSYDwOCuVbS6A9mm43ye4Pbdm/2Yw2NF6NVEXfKADrsj3bW9LfsV+UpwP1PL3JKQJmwD+VaRsKK0sljUJLYslEwpYLA2Ifzd8jENus2G3dehGgNwq+66vSSydAFck+sRSCBAep22qFEvLGqGn9aIERc40Eo8z2Anti3zbJy5yynP+wg1ptfz9VlTSnthlP6L4Od0/+4llntxWFRZLJhSwWBqQQAM8+8oBNlXZt0axRFJy0BIlAUrHrjsK0D6KZRxiA8tUDww/Vf9zsx3B44yRlmWr3b7tX61wKtawG4Y5Av/9g/Nxv3EuMM3B807HMsUpYyxpNDwZf8+vbl2yWDKhgMXSgHwaQCxrIpBYEhO2eMCS7ADLdBTONBc0ywFY4qy8j3f2jTvYkRkUq2vSZJe7cZ4I+xQsy3VJ3+k4D6T77V5ppNwF0GaOA+IGo3WLwirKUDzWSEUsh+P/s4QRXIn3/MQymcWSqScslgbEXywHWGvfd+smn1i+7DcXsKIC4NUlAEknATLw98VnAIoV4fKPsVyIgmqa6IIrNgD8FOT5TV7nBnN/qxhwylVEdvoypxiUsiz3TUksLKaRbtyeDbBB2UZGbaHbVzbtIx+o0g3/DmB7le+iw7+7xCeWKWe5fTD1g8XSQJCVdxBF7QYSDxKHBCd03C/9e4EMv3Er0KIbSD5EO7QsADinbB+WgQIzwiHFapJSJjiF4Lx+QMZpErfNVEKKxnpgvCvIE8X9nkQL0TLSCa0LAQ6geXlfGv4/xQP/9TMLh5LIfYLHHuOC/3c4wLFogOcLm7yGLZU/cuBFbz8G0ITqY6Ac8OpcWHt9MEwgWCwNxNINboib6oS4L5WSQj9dEIfWWn4N+xeh6MWlOnz7T/XAKKWb+qWYGaOIjH8ZLMOH7lEGZzI3eyAu2QWXrAM4XJeTRaswcRWdL57fZBf8fi1AdpW4nwL8jjiaL45d67WBjnMc95mJ+4x3wk27Kotgzww6tl9dpCi/5wKs5+bC1BEWS4MRKovphx8BrktzSjHzljQsKQ4ZI7m+um+wvrjDWB/hPDYTW7BYMtVBhblrokPEPDo8lfNgnikGMCc64OrvuZqY2ILFkqmRrrNdYJnngXd3A8SjlRmPIpn0E8Bnaz3w0Lrq8ZoMY3RYLJmALNgLcMMCN8QtUHJhZgEMOeIL92GYWILFkmEYJghYLBmGYYKAxZJhGCYIWCwZhmGCgMWSYRgmCFgsGYZhgoDFkmEYJghYLBmGYYKAxZJhGCYIWCwZhmGCgMWSYRgmCFgsGYZhgoDFkmEYJghYLBmGYYKAxZJhGCYIWCwZhmGCgMWSYRgmCFgsGYZhgoDFkmEYJgj+PwTMFOlKH3frAAAAAElFTkSuQmCC)
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)
To Prove: Δ ABC ∼ Δ PQR
Given:
![](data:image/png;base64,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)
Proof:
Median divides the opposite side
BD =
and,
QM = ![](data:image/png;base64,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)
Now,
![](data:image/png;base64,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)
Multiplying and dividing by 2, we get,
= ![](data:image/png;base64,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)
![](data:image/png;base64,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)
In Δ ABD and Δ PQM,
![](data:image/png;base64,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)
Side-Side-Side (SSS) Similarity Theorem - If the lengths of the corresponding sides of two triangles are proportional, then the triangles must be similar.
ΔABD
ΔPQM (By SSS similarity)
∠ABD = ∠PQM (Corresponding angles of similar triangles)
In ΔABC and ΔPQR,
∠ABD = ∠PQM (Proved above)
![](data:image/png;base64,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)
The SAS Similarity Theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.
ΔABC
ΔPQR (By SAS similarity)
Hence, Proved.
Question 13.D is a point on the side BC of a triangle ABC such that ∠ ADC = ∠ BAC. Show that CA2 = CB.CD
Answer:In ΔADC and ΔBAC,
![](data:image/png;base64,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)
To Prove : CA2 = CB . CD
Given: ∠ADC = ∠BAC
Proof: Now In ΔADC and ΔBAC,
∠ADC = ∠BAC
∠ACD = ∠BCA (Common angle)
According to AA similarity, if two corresponding angles of two triangles are equal then the triangles are similar
ΔADC
ΔBAC (By AA similarity)
We know that corresponding sides of similar triangles are in proportion
Hence in ΔADC and ΔBAC,
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOgAAAAhCAYAAADTTucEAAAIUElEQVR4Xu2cBch0RRSGn9/ubsUCu7sVuxsbu7sQu7u7FbtQsbvAwO7EQMXu7uSRuXBd7u7e3Tv3c9edgY//5/tuzLwz75lz3nPmDiO1hEBCoGcRGNazPUsdSwgkBOgXgo4LzAT8DLwM/JLmLiEwCAj0OkGHA7YDRgWeBhYBNgVOAs4F/hqESUpjHFwEep2gkvFt4MHcFK0NXAdsAlw2uFOXRj4ICPQyQYcHbgIeA44FfgsTMlrYTX8EFsz9fhDmK41xwBDoZYKODDwDTAVMB3yUm5v7gRmBWYEvB2zO0nAHCIFeJqjTMBswNvBwbk5GCTvo78B8wK8DNF9pqAOGQK8TtGg65gceAfYFThiw+UrDHTAEeoGgKrVjAV+XwH5E4Abge2DjFH+WQCxd0tcIlCWoMeB6gLuX7fNAqPOBV8PvtgbuBN7rEJEdgUWBDUrct3u4VgX3hxLX/x8uqYL9CMBqgMJaq2Yc/yTw2f8BsNwYqmA3ErBqSPG1guXTgN1XdWDXjqAKNMcA0wInArcAP4WOjAnsCTwB+P89gMU6jAknD0LQS8DSbQa4Tnj+XgNSqBADewm6PDAhcEj49yDgkwasZwC2BW4DdgO+qWOxDeEzY2AnQVcAJgCOAMYDDgA+zo1D7292YH3gVmDv2Ni1IuhawDnA2aGDWZojj7MdPCMUD1wNbNnBJPjuk0MhwivAAi1cVonvj+mWP8I75gFe7NAgdNC9//TS2NiPATwbFG+LPRTYGptE1gO6GNiij4tAYmPn5vM88G3wIItEyUmDcTP0Whn4LtbqaUbQ7UO1jjvkWW1eNndQVTcEruqgYwsDkky31aYlcoCNTSV38WAo/sz9cVfgzCaLrYNu9NyldWA/B/BcMIh6OkXNHUJPxvSWKax+dHfrwM41+hRwIbBVi9Uyb8g2HAocHWtVFRF0FeDaUKVjmV2eFEXvNQ1iGZ7uwJslO2aqRLdBt8sqIWMFf/Lug4+aJgDjNVlZn312R/AZO5V8X79cVhf2uq96Qz5fN7aoTQK8FmJ7jWK3+WWNgeT+sAToemBLhDWQeUYlbiu8pC7sdgZOC27sNS06p0tsuKeQKVmzULDb8fxzXyNB3aq1FpJBy9EYqxS9zDrZK4PIYzF7mbZ5EJesEroPWAowDno9d7MDvSdMYNEzjQeOLPOyPrmmTuxVvpcJO+MHTfCwrFL39rwQj3YLmzu0z1qxDUkl58HBJZSkVUS/OrFTd1kWmAV4qw0oFtAsCUwPvNEtgPn7GglqPKmqqpBweMkXqBDuEsSkMrcIprGq5NIQaJXWDeqs+c1BbXVhn8WfKu+q5UU7lQvKxeWiWrNkyqvZPGXEW6MFSctc08k6qAu7MvFnvp8ZQc12qIpXbnmCShyPchmDzBnLAhT00J1Pfz4r3TsFMJ50YdxYeUSdPcCFMgXgv902Q4D3S4QCrZ5fJ/at4k+9FLWD/QBFPkU4a5yrtlYEjE3OOrErG3+Kl7zR+7T8VD1FAbNyyxN0I+By4NGgmFaNCYo6p2XRVbgo90dlfdXcHYIQVHlQHTxAMK8HLMzvtklQT9hUmZA6sc/iT6uuFIqyZgzvLufYNZrWPcdsRUSMTU77Wyd2ZeNP+2HK0BhelTeayJYnqOcrtwHc0TJlNeaEGUQfFoShfKxqgYIxrNZ7n5gv7KNn1Ym98ac5ZhdNkXAzM3A3cHPwZIrSad1CmRHSYgnTDxqLVq5vN++pEzsxWa5k/GlRg9c/EOL9duJqqbHmCWqiVRA3Ay4pdXdnFykcjBPcgPydFry7g0pSreEgtrqwHz3sjF+08Yo0jKYGDDVULGO2jKR6SIYCikeNan2V99WFXafx56Wh/FQBVLEtSssTVPZrBTqJBacEzIO2ix0nCqKQE9TYJgbMX90VUjVRBtZnD6kLe9MlL7TJfwqVu5o77b1BsYwJn2vswFBp5uH72AStC7ssv98u/ylWk4UcsobHM8oWNURpeYK6ixkPWlLnFwvKNF1iAWpnEfcPcWeRi6XvrnxttYbFC3XEvmXG8l9eUxf2Jtatl26V/3TczqOuonO5ekQgMnK6pjT+7qKmLGKStC7szLGfXiL/KVzHhUyGm9sdEfH7Vx7UPJl5RwsItHjtmvW55i8vaHOhSpiqsJaoqFnokJXsqX7FUBHb9T37u4KVZ011vbttWksrnTQw3ba6sFcAM4Yy/myW/8znmyWRLmOMlifnSuEQhe6utd0xSVoXdmXjT0tQJaUaityJ+p2s/A6qiGMtphUlqq1FZXfZxFkWptX1412tDkz7zKOCStisiCGTp3V1JcxQlpi5YNzBq6i47vgu/iqiQB3YZ/GnFUHN8p/Op4UFHoSw5tpdo8o4svVRRM7sb7FJWgd2ZePPhULVncUdkjMGdv8yjo2FCpbWWVanqqc7UvR5S31zLaJqbysSW2HkxHvO0zxbsybAj4ddtrGaKIYl75dnxMTeMWc5vGaqvEbWUkuPCZ4ailNifJ3CNWVIY37VAvyi44eS9PjggcVwd2NjZ6hl0Uyz+NOY03DQ8lYFttvrWmRFtbgm7t0Zpw5xox114nQ/VVwVHa5oYS10WY175go7kwKRMa11vfld1G/d6uNbtyiZPWFhuZe5Ol3sd+sadA8/tyr2Hi8zleVcKVaMH8onzW1nrpfegu9xh9W9N0TJzvTGgMZKNH8kXqs5zEjq6RrTQFVK/ex3Vex09d0F9eIy7N4BHsrpIn5YwLVqGOaaVlir9RvN7c6Dxpiw9IyEQEKgSwQSQbsELt2WEBgKBBJBhwLl9I6EQJcIJIJ2CVy6LSEwFAgkgg4FyukdCYEuEUgE7RK4dFtCYCgQ+Bt3ABdAoXUz8gAAAABJRU5ErkJggg==)
Hence Proved
Question 14.Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR.
Show that Δ ABC ~ Δ PQR
Answer:To Prove: Δ ABC ∼ Δ PQR
Given:
![](data:image/png;base64,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)
Proof:
![](data:image/png;base64,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)
Let us extend AD and PM up to point E and L respectively, such that AD = DE and PM = ML.
Then, join B to E, C to
E, Q to L, and R to L
We know that medians divide opposite sides.
Hence, BD = DC and QM = MR
Also, AD = DE (By construction)
And, PM = ML (By construction)
In quadrilateral ABEC,
Diagonals AE and BC bisect each other at point D.
Therefore,
Quadrilateral ABEC is a parallelogram.
AC = BE and AB = EC (Opposite sides of a parallelogram are equal)
Similarly, we can prove that quadrilateral PQLR is a parallelogram and PR = QL, PQ = LR
It was given in the question that,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHYAAAAvCAMAAAAB+M4cAAAAAXNSR0IArs4c6QAAAIRQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgBmOjqQOmaQOma2OpDbZgAAZgBmZjoAZjpmZpC2ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kJA6kLbbkNv/tmYAtmY6tpA6ttv/tv//25A625Bm27Zm27aQ2////7Zm/9uQ/9u2//+2///b5+i6SAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACaklEQVRYR+2X21LCQAyGtxW1CuIRBKWIlUPpvv/7uUmWbrZMk3a84MLmwslMv/7ZJFtMjLmk2fnN3sU/JGDpGPw24wz5SYIvCxbJM7zwbxbpyphdditpcAZ9Oxd5pxXJB7x6/qADF1ffICOenjPom3wmJxvLB3w9o/dNDueupuLpOYO+arF8jZf3ewpbTR+MOT6JyXIGfLtQcjWRfMDt+8pgk0yZwY16E4/PGfSpTu3WkK/xg0vxgGEhZ/uFbqtxBnyXixw2lq/xaopfDcTKobxaaxmDvGJN+RNeuGTdF+s6RFdbDssZ/cuBCjbkfdjyDnpTZi4s/nEnALDNOEN+9Sg190yecH/iH4iFDd5mYuU4g/5R/LE4k/f4Mkndkd2vXLoqscmjF6lfnCE/kYpjz+RFXLsnw/OhAkMFOlQg91OL/83W3uiO17oNpyVCT9y08Nr5L/O8e9XwfD3xy+T0n6LSaD/6xJyPS/etvCrpBwje1QZHph/hMDXahR8dbzZmK44XMIQEqFBYSIDpcxxnZBymaIxStoII8mO9WJ6gT1sHGUXBsDnNqrk4+kZQh9mR6dNoSoZjPoYq/c4lho0gZbht6EdDKeRp1zjC0fWQixxBNDvKFvT9aEp4ARf5Gi6yz7LMpIk1gmiHkS3o+5WH8LrepywL6ZuIoQ6t5f2MWntaFr1iNZUG5Qjqshaw9nOctYfqpxSOQ35FmEhVZvocz0NJYQ2xa2XR5BCuBcq14voBdw0P12Lr9tXxRrkiAfJrgXitmL6A+89D/yS0+9vvOdynnfavoBPUL+4hSybqrtwJ6hd3oIcK/KkCv2IAQ8vUVI1AAAAAAElFTkSuQmCC)
ΔABE
ΔPQL (By SSS similarity criterion)
We know that corresponding angles of similar triangles are equal.
∠BAE = ∠QPL ..... (i)
Similarly, it can be proved that
ΔAEC
ΔPLR and
∠CAE = ∠RPL ..... (ii)
Adding equation (i) and (ii), we obtain
∠BAE + ∠CAE = ∠QPL + ∠RPL
⇒∠CAB = ∠RPQ .... (iii)
In ΔABC and ΔPQR,
(Given)
∠CAB = ∠RPQ [Using equation (iii)]
ΔABC
ΔPQR (By SAS similarity criterion)
Hence, Proved.
Question 15.A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower
Answer:Let AB and CD be a tower and a pole respectively
And, the shadow of BE and DF be the shadow of AB and CD respectively
![](data:image/png;base64,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)
To find: AB
At the same time, the light rays from the sun will fall on the tower and the pole at the same angle
Therefore,
∠DCF = ∠BAE
And,
∠DFC = ∠BEA
∠CDF = ∠ABE (Tower and pole are vertical to the ground)
ΔABE
ΔCDF (AAA similarity)
Hence, By the properties of similar triangles that if two triangles are similar, their corresponding sides will be proportional.
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEMAAAAsCAMAAAAJtvXOAAAAAXNSR0IArs4c6QAAAJBQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OgBmOjoAOjqQOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjpmZmZmZpC2ZpDbZrbbZrb/kDoAkDo6kGY6kJA6kLaQkLbbkNv/tmYAtmY6tpA6tv//25A625Bm27Zm27aQ29v/2////7Zm/9uQ/9u2//+2///bmSM9cQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABxElEQVRIS+1Wa1PCMBBMikhURCo+AB80aG1tQvP//513lxRbSJviODjjcF+gzWZvb5PmwtivhVmeF0CmOEZ0jf9bwuQzzocJjmZXgH3c4lJOHCyNYDQXo3YOyedsEw/eETsHHj512PLuxXHgoBPl55HIn/IFoCiTtBMZWy9SnAxv8H0Zd+ggvKpxOKweF5ajjEHZZlZRt1YkEa2gKpZh8RDmKbFGMC3QUhjqDi0WCMgB7SiYguSKHlCNeavetxGZJUzAhPCDzlABtKDIQQaF7HBmWued/ymyokvO6hCHHNFKOBhZoy/RTSrR1qm2S+4tJsX0UL5TgNKdsg+cSKZkonNZ9AVgjCQrbgq7x555BMlhk0eJJmPOHjp2OlhGnwNJxb0+XIUW8TT+jx1wu6H6nloqtVtmPw6AH8HDfrUcQchfpDDr7qOjqcme4juhxOSzv3QtPBxKBHtCLUMZ3+9zhE7iHYVyartJI+hg7x1qXHg45OAVLgWTzrN0m6K8TVxXq2c1Szylc2xd4aBGBzrSpvRatwhz2KsOhJfDXSHCNFWHbiCp533fSMIsHk+1gDaaHbA4vn2q8a7Wv2tRZwyrPSF+5sAXv/Ak8ser0psAAAAASUVORK5CYII=)
AB = 42 m
Height of the Tower = 42 m
Question 16.If AD and PM are medians of triangles ABC and PQR, respectively where Δ ABC ~ Δ PQR, prove that ![](data:image/png;base64,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)
Answer:It is given that ΔABC is similar to ΔPQR
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Given: Δ ABC ~ Δ PQR
AD and PM are medians
We know that the corresponding sides of similar triangles are in proportion
..........eq(i)
And also the corresponding angles are equal
∠A = ∠P
∠B = ∠Q
∠C = ∠R ..........eq(ii)
Since AD and PM are medians, they divide their opposite sides in two equal parts
BD =
and,
QM =
.......eq(iii)
From (i) and (iii), we get
(iv)
In ΔABD and ΔPQM,
∠B = ∠Q [Using (ii)]
[Using (iv)]
ΔABD
ΔPQM (Since two sides are proportional and one angle is equal then by SAS similarity)
![](data:image/png;base64,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)
Hence, Proved
State which pairs of triangles in Fig. are similar.Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form:
Answer:
(i) From the figure:
∠A = ∠P = 60°
∠B = ∠Q = 80°
∠C = ∠R = 40°
Therefore, ΔABC ΔPQR [By AAA similarity]
Now corresponding sides of triangles will be propotional,
(ii)
From the triangle,
Hence the corresponding sides are propotional
Thus the corresponding angles will be equal
The triangles ABC and QRP are similar to each other by SSS similarity
(iii) The given triangles are not similar because the corresponding sides are not proportional
(iv) In triangle MNL and QPR, we have
∠M = ∠Q = 70o
butTherefore, MNL and QPR are not similar.
(v) In triangle ABC and DEF, we have
AB = 2.5, BC = 3
∠A = 80o
EF = 6
DF = 5
∠F = 80o
And,
∠B ≠ ∠F
Hence, triangle ABC and DEF are not similar
(vi) In triangle DEF, we have
∠D + ∠E + ∠F = 180o (Sum of angles of triangle)
70o + 80o + ∠F = 180o
∠F = 30o
In PQR, we have
∠P + ∠Q + ∠R = 180o
∠P + 80o + 30o = 180o
∠P = 70o
In triangle DEF and PQR, we have
∠D = ∠P = 70o
∠F = ∠Q = 80o
∠F = ∠R = 30o
Hence, ΔDEF ~ ΔPQR (AAA similarity)
Question 2.
In Fig. 6.35, ΔODC ~ ΔOBA, ∠BOC = 125° and ∠CDO = 70°. Find ∠ DOC, ∠ DCO and ∠ OAB
Answer:
From the figure,
We see, DOB is a straight line
∠ DOC + ∠ COB = 180° (angles on a straight line form a supplementary pair)
∠ DOC = 180° - 125°
∠ DOC = 55°
Now, In ΔDOC,
∠ DCO + ∠ CDO + ∠ DOC = 180°
(Sum of the measures of the angles of a triangle is 180°)
∠ DCO + 70° + 55° = 180°
∠ DCO = 55°
It is given that ΔODC ΔOBA
∠ OAB = ∠ OCD (Corresponding angles are equal in similar triangles)
Thus, ∠ OAB = 55°
Question 3.
Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O. Show that
Answer:
In ΔDOC and ΔBOA,
∠CDO = ∠ABO (Alternate interior angles as AB || CD)
∠DCO = ∠BAO (Alternate interior angles as AB || CD)
∠DOC = ∠BOA (Vertically opposite angles)
Therefore,
ΔDOC ∼ ΔBOA [ BY AAA similarity]
Now in similar triangles, the ratio of corresponding sides are proportional to each other. Therefore,
......... (Corresponding sides are proportional)
or,
Hence, Proved.
Question 4.
In Fig. 6.36, and ∠1 = ∠2. Show that Δ PQS ~ Δ TQR.
Answer:
To Prove: Δ PQS ∼ Δ TQR
Given: In ΔPQR,
∠PQR = ∠PRQ
Proof:As∠PQR = ∠PRQ
PQ = PR [sides opposite to equal angles are equal] (i)
Given,
by (1)
In Δ PQS and Δ TQR, we get
∠Q = ∠Q
Therefore,
By SAS similarity Rule which states that Triangles are similar if two sides in one triangle are in thesame proportion to the corresponding sides in the other, and the included angle are equal.
Δ PQS ∼ Δ TQR
Hence, Proved.
Question 5.
S and T are points on sides PR and QR of Δ PQR such that ∠P = ∠RTS. Show that Δ RPQ ~ Δ RTS
Answer:
In ΔRPQ and ΔRST,
∠ RTS = ∠ QPS (Given)
∠ R = ∠ R (Common to both the triangles)
If two angles of two triangles are equal, third angle will also be equal. As the sum of interior angles of triangle is constant and is 180°
∴ ΔRPQ ΔRTS (By AAA similarity)
Question 6.
In Fig. 6.37, if Δ ABE ≅Δ ACD, show that
Δ ADE ~ Δ ABC.
Answer:
To Prove: Δ ADE ∼ Δ ABC
Given: ΔABE ≅ ΔACD
Proof:
ΔABE ≅ ΔACD
∴ AB = AC (By CPCT) (i)
And,
AD = AE (By CPCT) (ii)
In ΔADE and ΔABC,
Dividing equation (ii) by (i)
∠A = ∠A (Common)
SAS Similarity: Triangles are similar if two sides in one triangle are in the same proportion to the corresponding sides in the other, and the included angle are equal.
Therefore,
ΔADEΔABC (By SAS similarity)
Hence, Proved.
Question 7.
In Fig. 6.38, altitudes AD and CE of Δ ABCintersect each other at the point P. Showthat:
(i) Δ AEP ~ Δ CDP
(ii) Δ ABD ~ Δ CBE
(iii) Δ AEP ~ Δ ADB
(iv) Δ PDC ~ Δ BEC
Answer:
(i) In ΔAEP and ΔCDP,
∠AEP = ∠CDP (Each 90°)
∠APE = ∠CPD (Vertically opposite angles)
Hence, by using AA similarity,
ΔAEP ΔCDP
(ii) In ΔABD and ΔCBE,
∠ADB = ∠CEB (Each 90°)
∠ABD = ∠CBE (Common)
Hence, by using AA similarity,
ΔABD ΔCBE
(iii) In ΔAEP and ΔADB,
∠AEP = ∠ADB (Each 90°)
∠PAE = ∠DAB (Common)
Hence, by using AA similarity,
ΔAEP ΔADB
(iv) In ΔPDC and ΔBEC,
∠PDC = ∠BEC (Each 90°)
∠PCD = ∠BCE (Common angle)
Hence, by using AA similarity,
ΔPDC ΔBEC
Question 8.
E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that Δ ABE ~ Δ CFB
Answer:
To Prove: Δ ABE ∼ Δ CFB
Given: E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. As shown in the figure.
Proof:
In ΔABE and ΔCFB,
∠A = ∠C (Opposite angles of a parallelogram are equal)
∠AEB = ∠CBF (Alternate interior angles are equal because AE || BC)
Therefore,
ΔABE ΔCFB (By AA similarity)
Question 9.
In Fig. 6.39, ABC and AMP are two right triangles, right angled at B and M respectively. Prove that:
(i) Δ ABC ~ Δ AMP
(ii)
Answer:
(i)
To Prove: Δ ABC ∼ Δ AMP
Given: In ΔABC and ΔAMP,
∠ABC = ∠AMP (Each 90°)
Proof:∠ABC = ∠AMP (Each 90°)
∠A = ∠A (Common)
∴ΔABC ΔAMP (By AA similarity)
Hence, Proved.
(ii) Δ ABC ∼ Δ AMP
Now we get that,
Similarity Theorem - If the lengths of the corresponding sides of two triangles are proportional, then the triangles must be similar. And the converse is also true, so we have
Question 10.
CD and GH are respectively the bisectors of ∠ ACB and ∠ EGF in such a way that D and H lie on sides AB and FE of Δ ABC and Δ EFG respectively. If Δ ABC ~ Δ FEG, show that:
(i)
(ii) Δ DCB ~ Δ HGE
(iii) Δ DCA ~ Δ HGF
Answer:
Given, Δ ABC ∼ Δ FEG …..eq(1)
⇒ corresponding angles of similar triangles
⇒ ∠ BAC = ∠ EFG ….eq(2)
And ∠ ABC = ∠ FEG …….eq(3)
⇒ ∠ ACB = ∠ FGE
⇒
⇒ ∠ ACD = ∠ FGH and ∠ BCD = ∠ EGH ……eq(4)
Consider Δ ACD and Δ FGH
⇒ From eq(2) we have
⇒ ∠ DAC = ∠ HFG
⇒ From eq(4) we have
⇒ ∠ ACD = ∠ EGH
Also, ∠ ADC = ∠ FGH
⇒ If the 2 angle of triangle are equal to the 2 angle of another triangle, then by angle sum property of triangle 3rd angle will also be equal.
⇒ by AAA similarity we have in two triangles if the angles are equal, then sides opposite to the equal angles are in the same ratio (or proportional) and hence the triangles are similar.
∴ Δ ADC ∼ Δ FHG
⇒ By Converse proportionality theorem
⇒
Consider Δ DCB and Δ HGE
From eq(3) we have
⇒ ∠ DBC = ∠ HEG
⇒ From eq(4) we have
⇒ ∠ BCD = ∠ FGH
Also, ∠ BDC = ∠ EHG
∴ Δ DCB ∼ ΔHGE
Hence proved.
Question 11.
In Fig. 6.40, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC,prove that Δ ABD ~ Δ ECF
Answer:
To Prove: Δ ABD ∼ Δ ECF
Given: ABC is an isosceles triangle, AD is perpendicular to BC
BC is produced to E and EF is perpendicular to AC
Proof:
Given that ABC is an isosceles triangle
AB = AC
⇒ ∠ABD = ∠ECF
In ΔABD and ΔECF,
∠ADB = ∠EFC (Each 90°)
∠ABD = ∠ECF (Proved above)
Therefore,ΔABD ΔECF (By using AA similarity criterion)
AA Criterion: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
Hence, Proved.
Question 12.
Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of
Δ PQR (see Fig. 6.41). Show that
Δ ABC ~ Δ PQR.
Answer:
To Prove: Δ ABC ∼ Δ PQR
Given:
Proof:
Median divides the opposite side
BD = and,
QM =
Now,
=
In Δ ABD and Δ PQM,
ΔABD ΔPQM (By SSS similarity)
∠ABD = ∠PQM (Corresponding angles of similar triangles)
In ΔABC and ΔPQR,
∠ABD = ∠PQM (Proved above)
ΔABC ΔPQR (By SAS similarity)
Question 13.
D is a point on the side BC of a triangle ABC such that ∠ ADC = ∠ BAC. Show that CA2 = CB.CD
Answer:
In ΔADC and ΔBAC,
Given: ∠ADC = ∠BAC
Proof: Now In ΔADC and ΔBAC,
∠ADC = ∠BAC
∠ACD = ∠BCA (Common angle)
According to AA similarity, if two corresponding angles of two triangles are equal then the triangles are similar
ΔADC ΔBAC (By AA similarity)
We know that corresponding sides of similar triangles are in proportion
Hence in ΔADC and ΔBAC,
Hence Proved
Question 14.
Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR.
Show that Δ ABC ~ Δ PQR
Answer:
To Prove: Δ ABC ∼ Δ PQR
Given:
Let us extend AD and PM up to point E and L respectively, such that AD = DE and PM = ML.
Then, join B to E, C to
E, Q to L, and R to L
We know that medians divide opposite sides.
Hence, BD = DC and QM = MR
Also, AD = DE (By construction)
And, PM = ML (By construction)
In quadrilateral ABEC,
Diagonals AE and BC bisect each other at point D.
Therefore,
Quadrilateral ABEC is a parallelogram.
AC = BE and AB = EC (Opposite sides of a parallelogram are equal)
Similarly, we can prove that quadrilateral PQLR is a parallelogram and PR = QL, PQ = LR
It was given in the question that,
ΔABE ΔPQL (By SSS similarity criterion)
We know that corresponding angles of similar triangles are equal.
∠BAE = ∠QPL ..... (i)
Similarly, it can be proved that
ΔAEC ΔPLR and
∠CAE = ∠RPL ..... (ii)
Adding equation (i) and (ii), we obtain
∠BAE + ∠CAE = ∠QPL + ∠RPL
⇒∠CAB = ∠RPQ .... (iii)
In ΔABC and ΔPQR,
(Given)
∠CAB = ∠RPQ [Using equation (iii)]
ΔABC ΔPQR (By SAS similarity criterion)
Hence, Proved.
Question 15.
A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower
Answer:
Let AB and CD be a tower and a pole respectively
And, the shadow of BE and DF be the shadow of AB and CD respectively
At the same time, the light rays from the sun will fall on the tower and the pole at the same angle
Therefore,
∠DCF = ∠BAE
And,
∠DFC = ∠BEA
∠CDF = ∠ABE (Tower and pole are vertical to the ground)
ΔABE ΔCDF (AAA similarity)
Hence, By the properties of similar triangles that if two triangles are similar, their corresponding sides will be proportional.
AB = 42 m
Height of the Tower = 42 m
Question 16.
If AD and PM are medians of triangles ABC and PQR, respectively where Δ ABC ~ Δ PQR, prove that
Answer:
It is given that ΔABC is similar to ΔPQR
Given: Δ ABC ~ Δ PQR
AD and PM are medians
We know that the corresponding sides of similar triangles are in proportion
..........eq(i)
∠A = ∠P
∠B = ∠Q
∠C = ∠R ..........eq(ii)
Since AD and PM are medians, they divide their opposite sides in two equal parts
BD = and,
QM = .......eq(iii)
From (i) and (iii), we get
(iv)
In ΔABD and ΔPQM,
∠B = ∠Q [Using (ii)]
[Using (iv)]
ΔABD ΔPQM (Since two sides are proportional and one angle is equal then by SAS similarity)
Hence, Proved
Exercise 6.4
Question 1.Let Δ ABC ~ Δ DEF and their areas be, respectively, 64 cm2 and 121 cm2. If EF = 15.4 cm, find BC
Answer:It is given that,
Δ ABC ~ Δ DEF
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)
Therefore,
![](data:image/png;base64,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)
Given:
EF = 15.4 cm
ar (ΔABC) = 64cm2
ar (ΔDEF) = 121 cm2
Hence,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Taking square root on both of the sides
![](data:image/png;base64,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)
BC = (8 × 15.4) / 11
BC = 8 × 1.4 = 11.2 cm
Question 2.Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2 CD, find the ratio of the areas of triangles AOB and COD
Answer:Since AB || CD,
∴∠OAB = ∠OCD and ∠OBA = ∠ODC (Alternate interior angles)
![](data:image/png;base64,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)
In ΔAOB and ΔCOD,
∠AOB = ∠COD (Vertically opposite angles)
∠OAB = ∠OCD (Alternate interior angles)
∠OBA = ∠ODC (Alternate interior angles)
ΔAOB ~ΔCOD (By AAA similarity)
When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles. If two similar triangles have a scale factor of a : b, then the ratio of their areas is a2 : b2.
![](data:image/png;base64,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)
Since, AB = 2 CD (Given)
Therefore,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Therefore, the ratio of the areas of triangles AOB and COD is 4:1
Question 3.In Fig. 6.44, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPUAAACnCAAAAADsnEVFAAAABGdBTUEAALGOfPtRkwAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAABDvSURBVHja7d1pUFNbngDwE+yaqv7Qr7ump6unp6u63+zVH2aqeqqr34d5b2acfu3r5zx9KiiKkpB9I4CsYYvIoiCRRWQTEQQEEVkFBXEDZBPZQWQJgoDs+yJics4kBDDBhCSX3OTi4/+F5G7cX86995x7lnsB+iEG2FXvqnfVu+pdtWp0LuG5m1AmHZDJAxJL3fdVFI5oWemXpH/8/X+6854TS50OfjSMH9oRkCxjLnNIoJRQ6oW9ANzE7fC2B0Cg+GD102JCqatIAHwxj5O6FoDPVz+Mez4lkvp9/B/l7Dyc1I4AfK38NLJIJHUR94UvAIff46P+BQBM427ROGr7z99kAQCe4qP+EQBkAqq7/rDH9msLABzxUf8FgP8lnhoK941MjmcA8MsuXNQpAPzDavEEQuKoYdOX7vLdgT8HgA3xUM/8lgQiZRDK7kcNEUb9+Mekn99CKMeCRCKF45LY7V+RSA63bpL3ZRGnRNp7zjmmRb5rcX6+fmX4nNmTjv920MnNOZtAR/jGkY5joPH2hlYpoa5ma4dhWfnj0hIc4kF5ec2ycY8do6nf0P70lyMcPsvowWMc3PfNLYKqM+iOFGZKu6Szw6jR2dsQac2kefYSUv1KkDRZwnEqN3rWJS2k2zfVO8RAIqpT2RL5qS2ips0bdffgyCV66CBCidxOAqp7nOIVfyaunPRsNiIb1jmTMxVXsk6uPySeOp/WqNzNMmfO7XdGO7oz6F4Nyo8pJxsJpx71Dlj/KImgn+kwSrrAvhBK5Hq11KC7n4xo6nxa9cbnpSKafZER9hA+5dvlfcinCywfE0w9IgxQ/dp67lTY0HaTezqZ7fVM5fukl3CBWOpsZqXa94VUqrBqW2z4MsgudkptUg2lmFDqGZ8zm4nPXemp09jd74tdBPc2TVsOcBkmkvoxL/+jaWOxdmdbsLInY48FfVxBUUfPJJBaFug9pWHyEz6jEFP1IWzzpSW/1TAj0rGXOOoKruYq4f5gaqjE8OSG99mCSo1zOjjxUqKoZf4+Y5rnLBc4uT40kA1Hw2yCX2mZmcJvIor6+UntTT3tQbTIUUPcsM6DdkNrDjVsHw0Jog7hS7TPnLpFdazWf09lmVTX2i3mX6eUEUPdcyp1y/lVrvS0Bf3csDfUOrRvqyVmeKL3hFCH20u2XmA4khKk130YLHdhZuq4c8mnFhFB3XNCZwOurNCBl6e7WW4h5ZSPzovVvMhtkgDqKG6/7oX6gk+E926d3FASejJsXPemyvlZ5ldLbNP1WexdNpf/ZCs2LHNi3NVnSytipzGzq7MY7fot+MLD7or2PGw2mebdrN+GqqkJ5lYPueidgU6n0YWNmheGXSHs1Bk9tyO9zO83szqL8UL/hWtdKOmaSpSwgO/yWP/NdPCvQLOq+90iDDoyIuW3Upv3GE5dIod2GLKZa8xWs6pz6c0GLb+Sz3MoVGfD5+6MjDmDttLnGgbNqJ7w9jN0lfYQVmi3yj5L8xj8SkM3kk+pN6P6Hv2Rwess3KI5buRhsF9MDpEY/mu7iubNpp4+I1rBsFqzj13CuLLDRY0DJeMthk08tHpoNnUR8wGm9aaiyWfr5eylbKoDtn6h74U+Y2ZSz4nOYG1VrnZjZS+9DqdGYN33KmqWmdSP6LmY1x2JsvPiUQuw7/ZF91dmUcPz7tuoqO1yPXwkYhs9ylvYydAc6mc87P0HoCSIe+kCN24E+55f3FZRBasanvfE3PcLPmQxHizP3uQJnmBmd3G3U4WGVV3Puo3VPB7LDFgt0zW42SVNYt33JHqt6dWhThgvJ7BVREtaK4IOX7H1asTIfm0fKDO1epCciG3Ft9kOzipFjBIBJw/jRS2HVWFqdTzrJaaEHoo6GqzWbNMfbBfWgym5J0TY60uxqV+TkzGh64SsDOWurnYYVIQ0l+NYiqkhp5iaZ1p1IrMbw1or+UyXZ2tpXpFa0jSjdHeIbK6MY0juxRD+vCnVvdQkDAk9cN4mQlmwWRED0l/9C+l3BUrr0nWGRw0GdtXJLFOqMykdhqOrnFi5yns0aAdIxzv7XQGIXLPWinjpcwa730XwB02nHnG7aHCmIU2zFa5XvPgDcEhB/A0AhWuThuOpIsMb+Ts4adBk6gKaoQ2qsDPQOurN2pfZnwCw2m4TCMB3G+f8YwdajsG/ZQK3x1TqN57BhqJLHHgFGzUQFQCA1SqgdAD+7s3GQl3BFLGheZjEPgqaSJ3LaDRshZn4E2fbPnzNkatXt5ABwGcq05eyuY4lBiJuMepNo57w9jUsoV/4U+JUO648AmDP6imeCcDfqjXctpylxQ8b5J50CFwwifqhfg1SGyfsPXuOek3TCAmA1TuHZAD+Q718spB8SlhnEDvX9qEp1POBXgb8unA8ge6/OZv7AoAQxbxDgCTcvMJTN7s0QyoQ33kFTptAXcosNADdepZ76yNEw08BGIAwF5D2flxxNi62CW43ILkfsO7gr17099G/pWIli+VapWF6xR6LX6dk/NLi3zW205U68Ir0Z78TuQ3hri5l6P3TwtEwcoTmbibDUeyQkNO3tZwqkuCToQN6u2sZhhdVDFTDYBd9C4GwWsDWfu/8dnpSexeU+Vyu01O9KUEMCc7qVl6avkd3Jt2pDmGNRm9Gor69b1u5lyG+6jC3Pv0SujvANnIAYY+RqxyvSj0xibxuXNXtzAz90I851LwVtK2oOE27qd/9c5dTBMRTHa5fk8NMGsWtGW03BiPJ5zr14tyk1eColtjp0+MItgfYxUwhI0QOy/mePgOGRj0DIX7qVHqb7oWkpXymUToAKn7mYGrEaz1ARbTHuKmHGHG674BnEshBr5CxYuk2ja9H79tpP+E8XuoM3RVHsM2bft14Y3Hk0eZGvqa7920ltRgn9QAnVif6LpNl7OH24wm0M6262G8DOUP4qDNO6nhEBhyJpIuN/xgN2UNX6g1d7AbrTIiHetw9SAe6QUjPWEQ4RP+FE6FdOlCX+BI81CW0rRsRF1LYQpwejoOW8jnc4q3ZPccNGKKtt3pcdHbLTr+94uNhrxFu0exHi+3fkhXLaDK++i69ait0hTM3V4ZwjMVkpkvFVuwxQTg0tnpMJNoCNXeTIWxCOEejkJG6VZEvnVlhbPV96j3tCd0dYBM9iXCPiVgb/y0K5hMegYvGVb8Lcdf6M8NH9rwSZJIotefmay+Y32GWGFddpr0byuLVE75dyETxKpwd0actuefOeI4aUy0NFmoZiQJ7zlhfmUYmi7d5HIf72tgV/FvGVFewsrWgCwROpRCZMtoDbGLGNP9LWajLtPHUsiAvjYcOnLh87Fw3MnFMXqNrG8lfRU2ARlO3aK44go0+tKRZZPqo8GAka2zkh+G2A0ZTR7to6nG0lMMRlCGzxFAMNaBNE/slR6+mXX3UPewUDT/rYBT9Qg8yV5Sw2UWaKtvT7JqMpI47/XHOBOt8eHlSZL7oCiaL33ycroPCUGgU9Sv6x2ONF29zhPXIrCHNoHho6H1baFdnFHWq7eZRiXAgmBI3iswdLSL61anN7gkX73kjqMc5EZvq82E5h10MzY5GaOYaxa1+847cpz4ygjr/5KYK/bcpdGELAcyKqPZgbB6o/k4kGtu2ekSg3rkMvvAmx08QBC3Pw8Ip5zc9nqSGnr1tde4JtbMa3mMw70sJg5aXGoqdebnqOyR2e71N9YhjoNq1IsHWt4NAZkV0+dtGDaom9wtmKtyeuvhYtUpCt/naXZshGFqe3Bl09cqlCG7rttRTQT4fhqot3+HwSglnVkSlO+e6ykj+XroYbkddwtzIBuBoDDmkj5BoRR7G8FbJw67YVW9DPR3gvZ4vwHpXnU8zMWtyn7bN2ti9Pqeg99jVJez1mqjlXCavlrhmeYxdtAne6H2bx32CWQ0vuijLnfC1mBozQGi04mk0HMGDNfa4r+gtVnUt54YSXevC3m43E1PEywsU8dpFrfBUPkY1vOi82jw6n8kT1RPfLI+5VFuhsufSXJDbAjZ1HUtRcQQ7zzGi3+wItDyqPMlJq5VLtdR0TGoY6jaoGEoqsC/aAUf3egxF2wU+h4pxRKxBvdXww9slWugZ8kz6Gt23beeYFVFympm1hFA79zrURz3Y1tVZU9W03rYQze+Drb42CcQrguqIwYtkcTdE1zk9GykJ1V8VoqJeTPzqs1/sO/z5r/xXKyMGBUlzpSynJzvNLA9ZDt3+CewTRCiKKrKOJzXVxYXNi1BzWs8dAiD9ze8BYCu+pfALr1n7E7UIqiO6zlKT+rIojYoT9UsAgMUesFflcZlq57U/AHdQCQB/I79fHbTnCujpRLqTNihm0+0DMyhiReXxExIARX3/CkAe1KgOBSAHlgHwG/nnG8csHcugzODA/koPI0etL93ymOJpQ31/DcAo6rIAFo80qs8D4JL9M/BreeF7inng++OeASJfA8P7YhGmuFPZ2Y0p+uekKxrivWylMdDqQMisvMT2EwA6EWIA8DuoRf3FH0hAsKJ4fHdsXHTYBUNDHCQ6hylCXBlcDpawd/fx1hh+fqyDBw7lINSpVEfLT+85LWr31O/lVzP56SxbxhSLw52YQlJVcAdTZF6NjdcYcfHJN25cq9lQJ8nVvZrUIQDcRegzAG6hTyjWjvA0ufqtlrS+g+BvAQj9BNW+APyzxvOaCUD4QjYAP+78lNTdPwPgFYL/BEjXNV3Du/5sYXEo9u8t9pz/lNDoueI9iK8CAOm/kAb1THZUWPjlOHHq0CeFXo60IJEc91rs8ZNqUn+i0XRB5OEZW/BEtQLsB/D+a0WHw00l6923fu+qd9W76l31rnpXvaveVX/yarVKQF01gerzP3yDO0w9fiMq4WpMWFhYREw3Gkwv25L86ma0Sre4ubz1njSdj2Z3lnr2ruc3BxxSUlIuWBeih/u8t0C3RgddSP7QqARTrNZeFjPk69y9s9QI1ZNtVnv45dSjheKGD0f9ZnTFaUGuSk9FmHnqqHKg/lDw9+59O039jGqToTgz56f6WySKbh5wqK6upblp02C3GpbbiNqP4Hvs2Kp6Nof3vdeOU9dS5WkNm2UIFVp/6yb/81RoLzhyWKg+2HPc3/LK4NCH7kIN+aXOVgr1YnF9krXHDlQfjxutTV6QAyK/9UDohYPj62FX5jP1pR5TmOEe5I0HbvSWwm4HqxKEZLUtKM/Kc3DHqRmWFD7Tf1EuuLbfE6F0qwgoizq66R08id+I3w34WkcpqzoG017LnvOtciCqz5mXpVi6vtxxaurxhNHyJHlaSxMV6lTLK0h6+cgltYWkEfsSEco/TFYm6oMTHD7t2GFqyXL0KT7f9sgRP8mOUyuu4S2ydXUz231qRrj5GTZx++IQqrA8qhxNU3hw//6DRw4fvrEYfGD//sOW/8dt2mFq+TV8Ld9VqlGdv4fXGcUTCFSzr8xvxQhVHmWMrE5daG9ty6IfiZlBw21tLWIr3kPZzlLD5xTr9LWHRl/d7wURrKyorJpQTKlP/ZCCL/ksCbx3JFZ+bKQox1lIHNbfYJJr6Y3bgBp81HPFXt9+x85afZZyFW3fsTzUIIguK39QIS+EXfxvlZO7yvNM0rnLw0h67n9iVic02H23Nn4h+c/2kp2lHkuLTEiIil9tOK2JSojPQfUu+/709d4DkVOoLrFBZcmXiWH5igrr6kTlETCWlbh25W66emduZ6k/jpmM8+eDL3hy7iIihKnUD64qunP1BpX8oNTZ554vLMw9uDzyg1LPlwfweKKiYUKgTViDNDs8PEkM82692a56V/0pxv8DqKS6GYcK6WUAAAAASUVORK5CYII=)
Answer:![](data:image/png;base64,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)
Construction: Draw two perpendiculars AP and DM on line BC and AB
![](data:image/png;base64,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)
Proof:
Area of a triangle = 1/2 x Base x Height
Therefore,
![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
In ΔAPO and ΔDMO,
∠APO = ∠DMO (Each = 90°)
∠AOP = ∠DOM (Vertically opposite angles)
∴ ΔAPO
ΔDMO (By AA similarity)
As we know in similar triangles the sides are proportional to each other.
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIQAAAAwCAMAAADnwSL2AAAAAXNSR0IArs4c6QAAAKVQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OgBmOjo6OjpmOjqQOmaQOma2OpC2OpDbZgAAZgBmZjoAZjpmZma2ZpCQZpC2ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kJA6kJBmkLaQkLbbkNv/tmYAtmY6tmZmtpA6tpBmttv/tv//25A625Bm27Zm27aQ2////7Zm/9uQ/9u2/9vb//+2///bTQpgeAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADUklEQVRYR+1YaXPaMBC1SApuG3K4Z8Bt0ganTeJQbGr//5/WvXSBbGINnaEd9CEYo316+3Yt6yVJDni0D9On4fTK88fhQZ0RbX65ioGr385jwoIxbX5l7tepvYabbT5GepXCMTpnquubVKnTGVzVrxc7WAgABgHAdffs6sTWolATd2KpiERSjmC1Xyn9Vqfjx2SpSISSf+4eGkCCvAzdqDa361bjry6J5sOtkECenFWT0d93RHyXFBqgyRDWyJIsU/Xq+3TV3kPOyxQyrFNT2SabF25u9/OSVSoQg5EKFEUPt5IhOTSABBWieTmaQYknyY9FefJtVr95SiqLWk4Sl0Q9XTGJJgMd1+9ZCK9exK5zaICaC5kICWo8zr1UXCFLAsWV1PGH9gt8JYY1dKIC9jibm0EPT7hNMgZAgnQ5iAtXUsfbZQtg5ZCo4CszxJvtT7rUisqCvSQMgFGABOEmpIVMOY0S9JRw6jiajJ5Lw5cKYXuLJ/WRMAA6qGQVqbjMxPSjJgFd6RWnxGqRkBwQJtHTEwZASPBzJSS4GYwAmg0/86bm2LNClWdUFMbKYuEMnii3+eEAcJAIgTmtlp+yq/qjLb7sE8JFU5K7z7gy8V2mQvJatwdy7N4yPQBAgT2BOhvTSWHvLNTFytmiqBfanLZmGJRke6NGkD7s16NFTc1x+pm0TJ5xz5YNvGfHdAEwA6XOel93u3acDrn7hegO6vjlEN6iIP4BnCcGS3cMOCrwAgUKvc3w26ZvmJl7vOhYr3OFF2T0T08ZUI7DzjNiz9yvAcOXZowH26cBIw5bHoxN19kdvf/jDJgLASgxHgwPm+ucTxeRBsyF0MZtmAeT0zAfzOIMmAux4cG2LFjYg/E5mg/fkQbMg+CNVA7/2xYs6MHoXC6H00gD5kL4HixgwYIeTA68pESkAXMhfA8WsGCO67IeTDthMkRxBsyF8DxYyIJZJRwPxvUUI26c8BADJu7M80xsPUIWzJBwPJg4AgqKNGA+hOQkH2h6fQtmng7Hg3E9uZ3iDJiESUd6HixkwSRVzYXWRNP1+yG9wJpEGTAfgjyk9WAhC5ZseTA2XbxpRxkwHcYQMP6aB9v1H6uBB4dDeItGebC9nycGCnec/v8o8AcvDYec7o9bTgAAAABJRU5ErkJggg==)
Hence, proved.
Question 4.If the areas of two similar triangles are equal, prove that they are congruent
Answer:![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/4RDuRXhpZgAATU0AKgAAAAgABAE7AAIAAAAMAAAISodpAAQAAAABAAAIVpydAAEAAAAYAAAQzuocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAGFobWFkIGF2YWlzAAAFkAMAAgAAABQAABCkkAQAAgAAABQAABC4kpEAAgAAAAMwMQAAkpIAAgAAAAMwMQAA6hwABwAACAwAAAiYAAAAABzqAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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)
Let us consider two similar triangles as ΔABC
ΔPQR (Given)
When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles.
If two similar triangles have a scale factor of a : b, then the ratio of their areas is a2 : b2.
![](data:image/png;base64,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)
Given that,
ar(Δ ABC) = ar(Δ PQR)
Therefore putting in equation (i) we get,
![](data:image/png;base64,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)
AB = PQ
BC = QR
And,
AC = PR
Therefore,
ΔABC
ΔPQR (By SSS rule)
Hence, Proved.
Question 5.D, E and F are respectively the mid-points of sides AB, BC and CA of Δ ABC. Find the ratio of the areas of ΔDEF and Δ ABC
Answer:![](data:image/png;base64,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)
Given: D, E and F are the mid points of sides AB, BC and CA respectively.
Because D, E and F are respectively the mid-points of sides AB, BC and CA of Δ ABC,
Midpoint Theorem: The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.
Therefore, From mid-point theorem,
DE || AC and DE =
AC [1]
DF || BC and DF =
BC [2]
EF || AB and EF =
AB [3]
From [1], [2] and [3]
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMgAAAAsCAYAAAAgjfcKAAAI5klEQVR4Xu2deeh2RRXHP1K2YGqSbS5pabQvlpptmkWlhdqCkUmk/ZO2o1mhFYVGueQfLqG0ImgUhRIuiZpaqQlaqW1SZmU7peZSkSufmIHhcu995j7Pve/c+3QHXnx9f+fOnGW+M3POzDm/jZjbrIFZA40a2GjWzayBWQPNGpgBMs+OWQMtGmgDyLeAN9V8eydwPfBT4LPAbxOa44GXZ2j8NOCrGXRDkQwp2zuAG4diPKPfrjbIpS8tVyr6I4D3AV8D/pChk6VJ2gDyFGAz4Meh91cAt4a/vwQ4DHgi8EbgkvDvfuO//SD8/2uBP4e/PxbYFTgK+BLwwaW5Xv3DvmXbBngLcBDwGuCi1VlcuoeuNmijH5NcKuQjwI7Aq4HtgNcBFyytqYwPc45YD4R+Hg/8LelzC+CHARC7VFbNpm/8XIA8Gzggg7+hSfqW7Tzgu8DnhmY8o/+uNmijH4tcAuQxwHMBF99RA0QbvRn4Zvizf2K0qrLdiT4DvAfYOUygPTKMPDRJ26TIlc2F4jnA94APA6667x+a8Yz+u9qgSj9WuRT9VODdUwCIk+GWYCwVenv4e1XZTwJ+B7hjCZYjgI9nGHlokjaA5Mr2fECfarewM7qbfmVoxjP672qDKv1Y5ZoUQB4C3BuM5cS4pgIQJ8q/w5b4sgCQDNtuMJI2gCyS7a3AP4F3hWOmABlTi7Ll2iDSj12uSQFEZqNiU+e0apznAS+dGEAWyXYu8FDAheHXYQcZM0AW2SDabOxyTQogHpdcRW1PTxz1tu1d2g+E3eaKwjOqbQfJlU1f6tgRAyQGV9Jjbp0NqroYq1yTAojRhOuCf7EDcF+DD5I66ZIY6dGhjUeyUjhpA0iubIZJdRg/VEqIhnHbnPQ6G1TpxyrXpAByJvA24L0hshBt1TbxDNP9HUid+lJzq43PZWQrJUfduF1t0EY/JrkmAZBNwg7wCeDrwIHJ7pGe3at3J+4kpwCvDOHQ0oqvmxTLylZalur4TRO+yQYzQGos2HZR6BOEPYEXhu+uTSJWzwT+G+4zTgDuCTRt30jyokCnI7hPwRnVh2y/DP6XR0XvQMbSutqgSj9WudRvfBbjbbonEZ+Z/BH4YvjTuw3aAGJ0ZsuGEWXsV8B/Kj9v+yYl/VPwXXoXKLPDZWTTJ4mrbBzm4YCy+GcsrasNpiKX+t0pWaSjvg3H3xUiib3bIOepSe+Dzh3OGpiKBsYOEP2Bs8Pte65O/wrsl0tciG5d5VKdayVbCpBPFpos6bBVHjYGPtZy1Ktj+Tc1jwVLy7aucqn/scrWi83HDpC+MNuLslZgZqjxh+q3i6hD8bBqv6t+/z8djP2IJY+PBtxJcpuBA5O6xt7WVa61stnYAeIk+j2waYfZ/pfweLDDJxucdF3liuBYG5uNHSAq3EeOXm7lNp30H+USF6RbV7nWymZTAEjBOTwP/f+uga4AcSX37ZUJQrntCYD56D5kNMKkj2A/Jt6nKby5/Y2FbipyLWOzsei4OB9dAWIliZNC5tzPFnBvRppVT8wd9vmC7VEhm9CkHJ8ImIJborVVNfk5cAPw6UrFlsjnmOWq0+Uim62iixK2s/CH9Qy8QfdVuPny8alT7/x0BciVwIuBT9XEv1PmDga+HJ6TWC7GJ/G23YGzgK2BzxcESFtVk2cE3lT63sBPEsHGLlfdBFlks2V10ftkzOjQog2HAoLaHdzTjBV09gVuy/i+M0kXgKjIm8IITngfMcb8j3RgV1hLBZmD7tuZKuM6pwpVEiCR36YXrB8NRSbOB14fiKckV5Qv12bSd9FF54nWwwcm5P0iLLLfD/0dF04k/lfw9N66AMRCCxaFc4vzGfsLkppZKWMXhtpQVvY4uYFjVzVBVOqItQggFsxzlbo6yRScklxRvlybtQGkThe9T8SMDuNR0cXZxcrm63BLT1nI0JTi3lsXgHjUsBKJK6qFCszrkOm0WTQuvmw1w1CnvK5ZN8rLv9LlcepWTfn6NrBXkPeYcK8yJbmiznNs1rZY1Omi90mY2aGguBj4RsjgTAGij+vRuPeWC5BnAZeHJCePTe4AHqHSNFuZMxEqVlncHLijgWMjWDpZd/cuUbcOI0DMM/hXuJC0+oq75NHB1/IYOTW51EKuzaoAWaSLbhoeltpcpMOB4kcsnfLtAR1uJ7a+iKUfPXLFMqOqQqfWc7vtYUNGF3rSexUgduutvXIq4zsBo3VTk0s5cm3WBJAmXfSk+pW7cXH2mG5pW3NgmhbjlQbK2UEEhMWYzSA0BBq3NgurnQ4cknBgpmEM/26V1OWtMvlk4GnAd1bifvWPmxxTQ9Py5i7pSuxiMCW5utisCpBqmnRVF6V3ffm1noFZnI8MWa+xeOHqM6LSQw5APFJZIDi9HHSVtXi1754sJxPj0J5ZzTR0QnmG17Gta94xmDdQsoC1fDUBJC0a9yrAqMmU5Opis0UAqerCu4eSzeO5PuLjAjjMJjTC5d1V7y0HIEainPjpTiEjOoBGDsxbvyzhzMiUDnxT3rkK10/R+dXpKtnaChvEel/e+xgpmZJcXW3Wtlik9cGiLkrZzLnzhbCDeFnoqwzz0404FolimRhvWO3twKUVrXjGtarJGeHMHn+sEBa0fkOo5G5RtfS+5MhQdNjCZHX3KBtS+U1RrBNDKaOrAPl0h5yKXMvYrAkgLox1utiQNkrH8mWG9x2xnKo/2zYEewb5bQGLqpp4c6zC/wF4eWb1CJug8Hc0eJtp874grSzhNmg0xHpZTjIjYPeHOwW3RsvWD3ZuzLBerI4Rq6ykFVs8HirXOWHXSAsyTEGurjbTFzTY0lUXGWrulUQA+AqjrmlPq8v03toAklaQsHqHldutQWtTmYZF012jrrKEN7kKZsTBItYeqTx6DfZ2JlNDbZU/jIb4W7N8K9bUxirXMjbT4W2qXpOji0yVr0zmUeqpDb14D3LzyiPUdJDjgwwx7tznrIFJaGAGyCTMNDNZSgMzQEppfh53EhqYATIJM81MltLADJBSmp/HnYQGZoBMwkwzk6U08CAfRcRLCafc+gAAAABJRU5ErkJggg==)
By SSS Similarity Criterion, we can see that
ΔDEF ∼ ΔABC
Theorem: The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
![](data:image/png;base64,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)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAhCAMAAAAieUHKAAAAAXNSR0IArs4c6QAAAFdQTFRFAAAAAAAAAABmADqQAGaQAGa2OgAAOjoAOmZmOma2OpDbZjoAZjpmZrbbZrb/kDoAkDo6kGaQtmYAtmY6tv//25A625Bm29uQ2////7Zm/9uQ//+2///bTz76BgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAWUlEQVQoU2NggAMZYVYQW4yDG0wzMIjip2WEWCRAqhiBgAthDAEWSDUQEK0eSaEUGx+IJyPADqZFeflBtCSnDIiW5hGR4ecVhDiHkRmsECzPwCDOxiRCyD4Am1IDVcQqJDwAAAAASUVORK5CYII=)
Question 6.Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians
Answer:![](data:image/png;base64,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)
Let us assume two similar triangles as ΔABC ~ ΔPQR.
Let AD and PS be the medians of these triangles
Then, because ΔABC ~ΔPQR
.....(i)
∠A = ∠P, ∠B = ∠Q, ∠C = ∠R .......(ii)
Since AD and PS are medians,
BD = DC =BC/2
And, QS = SR =QR/2
Equation (i) becomes,
.......(iii)
In ΔABD and ΔPQS,
∠B = ∠Q [From (ii)]
And,
[From (iii)]
ΔABD ~ ΔPQS (SAS similarity)
Therefore, it can be said that
.......(iv)
![](data:image/png;base64,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)
From (i) and (iv), we get
![](data:image/png;base64,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)
And hence,
![](data:image/png;base64,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)
Question 7.Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals
Answer:Let ABCD be a square of side a
![](data:image/png;base64,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)
To Prove = Area of ΔABE = 1/2 Area of ΔADB
Proof:
Let the side of square = a
To find the length of the diagonal of the square,
Pythagoras Theorem : It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Applying pythagoras theorem in ΔADB
AD2 + AB2 = BD2
a2 + a2 = BD2
BD = √2 a
Two desired equilateral triangles are formed as ΔABE and ΔDBF
Side of an equilateral triangle, ΔABE, described on one of its sides = a
Side of an equilateral triangle, ΔDBF, described on one of its diagonals = ![](data:image/png;base64,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)
![](data:image/png;base64,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)
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)
Therefore, Area of equilateral triangle on one of the side of the square is half of the area of equilateral triangle on diagonal.
Question 8.ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is
A. 2 : 1 B. 1 : 2
C. 4 : 1 D. 1 : 4
Answer:![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/4RDuRXhpZgAATU0AKgAAAAgABAE7AAIAAAAMAAAISodpAAQAAAABAAAIVpydAAEAAAAYAAAQzuocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAGFobWFkIGF2YWlzAAAFkAMAAgAAABQAABCkkAQAAgAAABQAABC4kpEAAgAAAAMzNQAAkpIAAgAAAAMzNQAA6hwABwAACAwAAAiYAAAAABzqAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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)
Given: D is mid point of BC
We know:
Equilateral triangles have all its angles as 60° and all its sides are of the same length. Therefore, all equilateral triangles are similar to each other.
Hence, the ratio between the areas of these triangles will be equal to the square of the ratio between the sides of these triangles.
Let side of ΔABC = x
Therefore,
Side of ΔBDE = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAgAAAAgCAMAAAAYLsniAAAAAXNSR0IArs4c6QAAAGxQTFRFAAAAAAAAAAA6ADpmADqQAGa2OgAAOgA6OgBmOma2OpDbZgAAZgA6ZjoAZjpmZma2Zrb/kDoAkJC2kLbbkNv/tmYAtpC2trZmttuQttu2tv//25A625Bm27Zm29u22//b/7Zm/9uQ//+2///b3ex8CwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAa0lEQVQoU5VPSQ6AMBCi7lvdd63W+v8/2tFGLx6UCyQwGQBuSM+F9CLs7Rb0mci1sRfuZSseEc1D2jlrCTT2qLhdP8efFDP4FH4JLZyxkNokFYRlvm++EdNZERAU0ZgMS81Sr1ExvadZP3AAJ18EgnbbqGMAAAAASUVORK5CYII=)
Therefore,
![](data:image/png;base64,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)
Hence, the correct answer is C
Question 9.Sides of two similar triangles are in the ratio 4: 9. Areas of these triangles are in the ratio
A. 2 : 3 B. 4 : 9
C. 81 : 16 D. 16 : 81
Answer:If two triangles are similar to each other, then the ratio of the areas of these triangles will be equal to the square of theratio of the corresponding sides of these triangles.
It is given that the sides are in the ratio 4:9
Therefore,
Ratio between areas of these triangles =
2
= ![](data:image/png;base64,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)
Hence, the correct answer is (D)
Let Δ ABC ~ Δ DEF and their areas be, respectively, 64 cm2 and 121 cm2. If EF = 15.4 cm, find BC
Answer:
It is given that,
Δ ABC ~ Δ DEF
Therefore,
Given:
EF = 15.4 cm
ar (ΔABC) = 64cm2
ar (ΔDEF) = 121 cm2
Hence,
Taking square root on both of the sides
BC = (8 × 15.4) / 11
BC = 8 × 1.4 = 11.2 cm
Question 2.
Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2 CD, find the ratio of the areas of triangles AOB and COD
Answer:
Since AB || CD,
∴∠OAB = ∠OCD and ∠OBA = ∠ODC (Alternate interior angles)
In ΔAOB and ΔCOD,
∠AOB = ∠COD (Vertically opposite angles)
∠OAB = ∠OCD (Alternate interior angles)
∠OBA = ∠ODC (Alternate interior angles)
ΔAOB ~ΔCOD (By AAA similarity)
When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles. If two similar triangles have a scale factor of a : b, then the ratio of their areas is a2 : b2.
Since, AB = 2 CD (Given)
Therefore,
Therefore, the ratio of the areas of triangles AOB and COD is 4:1
Question 3.
In Fig. 6.44, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that
Answer:
Construction: Draw two perpendiculars AP and DM on line BC and AB
Proof:
Area of a triangle = 1/2 x Base x Height
Therefore,
=
In ΔAPO and ΔDMO,
∠APO = ∠DMO (Each = 90°)
∠AOP = ∠DOM (Vertically opposite angles)
∴ ΔAPO ΔDMO (By AA similarity)
As we know in similar triangles the sides are proportional to each other.
Hence, proved.
Question 4.
If the areas of two similar triangles are equal, prove that they are congruent
Answer:
Let us consider two similar triangles as ΔABC ΔPQR (Given)
When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles.
If two similar triangles have a scale factor of a : b, then the ratio of their areas is a2 : b2.
Given that,
ar(Δ ABC) = ar(Δ PQR)
Therefore putting in equation (i) we get,
AB = PQ
BC = QR
And,
AC = PR
Therefore,
ΔABC ΔPQR (By SSS rule)
Hence, Proved.
Question 5.
D, E and F are respectively the mid-points of sides AB, BC and CA of Δ ABC. Find the ratio of the areas of ΔDEF and Δ ABC
Answer:
Given: D, E and F are the mid points of sides AB, BC and CA respectively.
Because D, E and F are respectively the mid-points of sides AB, BC and CA of Δ ABC,
Midpoint Theorem: The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.
Therefore, From mid-point theorem,
DE || AC and DE = AC [1]
DF || BC and DF = BC [2]
EF || AB and EF = AB [3]
From [1], [2] and [3]
By SSS Similarity Criterion, we can see that
ΔDEF ∼ ΔABC
Theorem: The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
=
Question 6.
Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians
Answer:
Let us assume two similar triangles as ΔABC ~ ΔPQR.
Let AD and PS be the medians of these triangles
Then, because ΔABC ~ΔPQR
.....(i)
∠A = ∠P, ∠B = ∠Q, ∠C = ∠R .......(ii)
Since AD and PS are medians,
BD = DC =BC/2
And, QS = SR =QR/2
Equation (i) becomes,
.......(iii)
In ΔABD and ΔPQS,
∠B = ∠Q [From (ii)]
And,
[From (iii)]
ΔABD ~ ΔPQS (SAS similarity)
Therefore, it can be said that
.......(iv)
From (i) and (iv), we get
And hence,
Question 7.
Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals
Answer:
Let ABCD be a square of side a
Proof:
Let the side of square = a
To find the length of the diagonal of the square,
Pythagoras Theorem : It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Applying pythagoras theorem in ΔADB
AD2 + AB2 = BD2
a2 + a2 = BD2
BD = √2 a
Two desired equilateral triangles are formed as ΔABE and ΔDBF
Side of an equilateral triangle, ΔABE, described on one of its sides = a
Side of an equilateral triangle, ΔDBF, described on one of its diagonals =
Therefore, Area of equilateral triangle on one of the side of the square is half of the area of equilateral triangle on diagonal.
Question 8.
ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is
A. 2 : 1 B. 1 : 2
C. 4 : 1 D. 1 : 4
Answer:
Given: D is mid point of BC
We know:
Equilateral triangles have all its angles as 60° and all its sides are of the same length. Therefore, all equilateral triangles are similar to each other.
Hence, the ratio between the areas of these triangles will be equal to the square of the ratio between the sides of these triangles.
Let side of ΔABC = x
Therefore,
Side of ΔBDE =
Therefore,
Hence, the correct answer is C
Question 9.
Sides of two similar triangles are in the ratio 4: 9. Areas of these triangles are in the ratio
A. 2 : 3 B. 4 : 9
C. 81 : 16 D. 16 : 81
Answer:
If two triangles are similar to each other, then the ratio of the areas of these triangles will be equal to the square of theratio of the corresponding sides of these triangles.
It is given that the sides are in the ratio 4:9
Therefore,
Ratio between areas of these triangles =2
=
Hence, the correct answer is (D)
Exercise 6.5
Question 1.Sides of triangles are given below. Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse.
(i) 7 cm, 24 cm, 25 cm
(ii) 3 cm, 8 cm, 6 cm
(iii) 50 cm, 80 cm, 100 cm
(iv) 13 cm, 12 cm, 5 cm
Answer:(i) Given: sides of the triangle are 7 cm, 24 cm, and 25 cm
Squaring the lengths of these sides, we get: 49, 576, and 625.
49 + 576 = 625
Or, 72 + 242 = 252
The sides of the given triangle satisfy Pythagoras theorem
Hence, it is a right triangle
We know that the longest side of a right triangle is the hypotenuse
Therefore, the length of the hypotenuse of this triangle is 25 cm
(ii) It is given that the sides of the triangle are 3 cm, 8 cm, and 6 cm
Squaring the lengths of these sides, we will obtain 9, 64, and 36
However, 9 + 36 ≠ 64
Or, 32 + 62 ≠ 82
Clearly, the sum of the squares of the lengths of two sides is not equal to the square of the length of the third side
Therefore, the given triangle is not satisfying Pythagoras theorem
Hence, it is not a right triangle
(iii)Given that sides are 50 cm, 80 cm, and 100 cm.
Squaring the lengths of these sides, we will obtain 2500, 6400, and 10000.
And, 2500 + 6400 ≠ 10000
Or, 502 + 802 ≠ 1002
Now, the sum of the squares of the lengths of two sides is not equal to the square of the length of the third side
Therefore, the given triangle is not satisfying Pythagoras theorem
Hence, it is not a right triangle
(iv)Given: Sides are 13 cm, 12 cm, and 5 cm
Squaring the lengths of these sides, we get 169, 144, and 25.
Clearly, 144 +25 = 169
Or, 122 + 52 = 132
The sides of the given triangle are satisfying Pythagoras theorem
Therefore, it is a right triangle
We know that the longest side of a right triangle is the hypotenuse
Therefore, the length of the hypotenuse of this triangle is 13 cm
Question 2.PQR is a triangle right angled at P and M is a point on QR such that PM ⊥ QR. Show that PM2 = QM×MR
Answer:
![](data:image/png;base64,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)
⇒ Let ∠MPR = x
⇒ In Δ MPR, ∠MRP = 180-90-x
⇒ ∠MRP = 90-x
Similarly in Δ MPQ,
∠MPQ = 90-∠MPR = 90-x
⇒ ∠MQP = 180-90-(90-x)
⇒ ∠MQP = x
In Δ QMP and Δ PMR
⇒ ∠MPQ = ∠MRP
⇒ ∠PMQ = ∠RMP
⇒ ∠MQP = ∠MPR
⇒ Δ QMP ∼ Δ PMR
⇒
= ![](data:image/png;base64,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)
⇒ PM2 = MR × QM
Hence proved
Question 3.In Fig. 6.53, ABD is a triangle right angled at Aand AC ⊥ BD. Show that:
(i) AB2 = BC . BD
(ii) AC2 = BC . DC
(iii) AD2 = BD . CD
![](data:image/png;base64,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)
Answer:(i) In ΔADB and ΔCAB, we have
∠DAB = ∠ACB (Each of 90o)
∠ABD = ∠CBA (Common angle)
Therefore,
ΔADB
ΔCAB (AA similarity)
![](data:image/png;base64,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)
AB2 = CB x BD
(ii) Let ∠CAB = x
In ΔCBA,
∠CBA + ∠CAB + ∠ACB = 180o
As, ∠ACB = 90o, we have
∠CBA = 180o – 90o – x
∠CBA = 90o – x
Similarly, in ΔCAD
∠CAD = 90o - ∠CBA
= 90o – x
∠CDA = 180o – 90o – (90o – x)
∠CDA = x
In triangle CBA and CAD, we have
∠CBA = ∠CAD
∠CAB = ∠CDA
∠ACB = ∠DCA (Each 90o)
Therefore,
ΔCBA
ΔCAD (By AAA similarity)
![](data:image/png;base64,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)
AC2 = DC * BC
(iii) In ΔDCA and ΔDAB, we have
∠DCA = ∠DAB (Each 90o)
∠CDA = ∠ADB (Common angle)
Therefore,
ΔDCA
ΔDAB (By AA similarity)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKIAAAA1CAYAAADCkTDgAAAIW0lEQVR4Xu2ddcg1RRTGf5/d3YoFBnZ3YIsd2IjdrX8odhe2YotdqCh2CwZ2JwYodncnD56F5bIxszuzd++9u/Dxfrzv7OycZ587c86ZM88dQ3d1CLQAgTEtGEM3hA4BOiJ2JMhDYCxgMuC7JiDyIeJ4wPrAhCUD+wJ4FvjWw4C5gC2ApeyerwyAS4A37Xe7APcCH3r0O0xNY+KfhdNewArAVk2A6EvEtYFpgOOBqYDDgc9SA9WnaCFgS+BO4GDg+wJDZgNOBuYETgfuAH619pMCBwHPAPr/gcCKwB9NANPCZ4iIofHPM3Nm4AXgNWC1JrDwIWIyHpHiZeAHm8GyiDEjcBfwE7Au8GOGMZsAFwIXGLH/zGgjYp8HbAfcAOzUBCgtf0Yo/PPMFCfOBHYH3gCWBrLeTVCYqhBxceA54DJg54LRLAE8DhwDnNTTbg/gDJvxzi+xaDHgeWBr4Pqg1g9mZyHwL7J8OUDPOMAaaYXThBL1qkLEfYBzbPm9sWB0Wkq0rI4LiJTJkrsecBNwtX3q/imxcHIjopald6OiMRid18W/yMoJbHU6GngUkO+uf2n3KwpKVYgoP24NYH7gvZJRPQysAswNvANoydZs+q996j53sErB0XXmNP/m0H7Ym9TBvwybHSw4fAp4CFgVmAd4u+zGun/3JaKLf5IeU0JERcOKpOXvKRo7EjjOcfATAftaUON4y9A2q4t/ETCaJOSDn2AThVa7zS1yfiI2or5EdPVPNO7xbfZbwCJppWRet98vYjNkbPuGrf86+L9aAoYyIPL7P7V2ZwH7ARsDt8UG0peIrv6Jxq0UwFuWbpkXWBO4BnjS0jB/xzZuCPuvg/+XBXhoxZKrdXmqzf4WPe9pmY2ocPoS8XYjlIt/qOS32j8CrG7G7Arok5ZEZFGNG8LO6+CfFxQqqDwWUICS9sGVyJZvfgpwSGwsfYjo659cBWwLyAG+whLcyiluD1wZ27Ah7L8u/nmQKEc7hblR6TZL2owoMm4TG08fIib5vLL8ocY8k2XlFfYvY8lvfZo1S/r4HLMCem50HyU20AH6r4t/1hCms+Dko4w/Tg8o33uf7egEMCG/Cx8i7g2c65A/1NNOtUhXpLvHHq9svfyOzYCbHa3SUi4CR89jOY6nn83q4p819sPML/wk44/y8ZWe0y6aktxRfXofIrr6J9oPFvnkW2hPWjlDXfITH7DfHeHwRrX/rDzWpQ5tR6FJXfx7MVIEruyFVrisSxsJirS1havdlV9iguxKRFf/ZFnbNbnYCJd2kOUUq3pmBtujLto2UkGFZkNtA45qkUP6vYfAP92f3sWJVrSSt0mQpN+0RCs4LYq6a3PUlYiampXUzPMP5RNq2dU2nCKsu3NGNodtHd0PKC3we0Y7+ULrWHQdfY+zNoLNdBAKf41WO1WqdFKd4aEFwxdZn7ZZM/ruShERtUespVWfBgUcUwPvA4+l/AUVTsowTdvy+27NIVfa3llsppvd/BMRPJn+Fam9AlwLlO1BN0OB/j0lNP5aalXfuSgwNqBARe9MVTbpWXFKiwVUH6B3+xfwM/ASIJfqgxiQuM6IMZ6tiFj70CKkSspEcNXAjToBY2Dd+j77ScQ2gKN6R83Q+ln10gdH6Y/uA1QVQRj5MyvaB7/FlqqqMIqAm1qEWbWPkb8vPSMeNaBoqPB20K9BxV64B8G/I2I7KNwRsR3voRvFqCMw6sHKqL//1tg/6kRUjlQHvFR9UvVS6mkl25Ot2sfI3zfqRFTaRpv7SvBWvVQM8HGXvqkK3//3tZmIjUpe1IMx+t3jABsAOr9TdH1jZ4OK9oWbVoxwAseHiE0b0KjkhRNa/WskIq4FTGuV1PqpA2i9pyC1J7ybiRto7z9LZaNJxQhnxHyJOLSSF86I9bfhJMCLgGa+5W0fuHdEIqyqnFQVv2OqDK+3nUtFj4tiRxBEfIiYPDC2AX2RvAiCZvxOFrbiAxUZSwso61IJnTRrVMalQ2t5y7TricAixY5gFlchYmwD+iJ5EQzRuB1p2ZVekNQypC2UdaneU6cnVTGzoM2eWe1cTwTmKXYEtbQKEWMa0DfJi6CoxutMZXaqdNdMp0g969JhKC3LKk4WcfOumIoR3ghUIWJMA/omeeGNXPM3JP6hhAqkW5h1hkTSLlLXkLyLzgvliWy6uFdpC3sVO4Jb70vEmAb0VfIiOLLhOyzyD1VEK7U0VVxLvk/nhYrOmLi6V7KiV7GjTDGikuW+RIxpQF8lLyqh1+xNiX94mgUsydPlzmxkSXlhqOLissvVvVI/vYodUc6u+BIxlgF9l7woe3Mt+Lv8Q6m3yj/MOv45H6CzQDrtJ82aInFN1xOBMrtXsSNKAbAvEWMY0ArJixYQrWgIE9tM93WJbpAOrkkUVUSUhmXW5ete9Sp2RIHKh4ixDGiF5EUUdMN1qjSMDpUV5Q/1NC3RmjkfNA3LrBHEUIyobakPEWMY0BrJi9pIxu1AEtE6gVeUP9QIdBb8IlueN8wZUgzFiNrW+xAxhgGtkbyojWTcDnSuRrJ+RflDRc5S0ljZ/Dp9q0PW5epe5Sl2RLHUh4ihDWiV5EUUdMN0mviH2l/Oyx/qSdry08F5fUuDJo2soMLVvSpS7AhjVU8vrkQMbUDrJC+ioBum0yRllqcrqb1laRvqC5HOtqqcPJmWkIoRYayzXlyJGNKAVkpeBEW1fmcq+5J4psSPEpUNCapLbTcRtVIxr85ka8ZUlbnEqpJv6UqPILRiRH3rMnpoUnKk1ZIXUdDtOnVGwHVGdO6wa9ghUAWBjohVUOvuCY5AR8TgkHYdVkGgI2IV1Lp7giPQETE4pF2HVRDoiFgFte6e4Aj8B6zkZ1Qwsa+qAAAAAElFTkSuQmCC)
AD2 = BD x CD
Question 4.ABC is an isosceles triangle right angled at C. Prove that ![](data:image/png;base64,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)
Answer:![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/4RDuRXhpZgAATU0AKgAAAAgABAE7AAIAAAAMAAAISodpAAQAAAABAAAIVpydAAEAAAAYAAAQzuocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAGFobWFkIGF2YWlzAAAFkAMAAgAAABQAABCkkAQAAgAAABQAABC4kpEAAgAAAAMzMQAAkpIAAgAAAAMzMQAA6hwABwAACAwAAAiYAAAAABzqAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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)
To Prove: 2 AC2 = AB2
Given: ΔABC is an isosceles triangle
Proof:
AC = CB ( Two sides of an isosceles triangle are equal, as the side opposite to right angle is largest, rest of the two sides are equal)
Pythagoras Theorem: It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Using Pythagoras theorem in ΔABC (i.e., right-angled at point C), we get
AC2 + CB2 = AB2
AC2 + AC2 = AB2 (AC = CB)
So,
2AC2 = AB2
Hence, Proved.
Question 5.ABC is an isosceles triangle with AC = BC. If AB2 = 2AC2, prove that ABC is a right triangle.
Answer:To Prove: ABC is a right angled triangle
Given: AB2 = 2AC2
Now 2 AC2 can be split into two parts
AB2 = AC2 + AC2
in an isosceles triangle ABC two sides are equal, and it is given that AC = BC. So,
AB2 = AC2 + BC2 (As, AC = BC)
Now According to pythagoras theorem, in a right angled triangle, square of one side equals to the sum of squares of other two sides
And clearly above equation satisfies it. Thus, the equation satisfies pythagoras theorem and the triangle should be right angled for that.
Therefore, the given triangle is a right-angled triangle
Hence, Proved.
Question 6.ABC is an equilateral triangle of side 2a. Find each of its altitudes
Answer:Let AD be the altitude of the given equilateral triangle, ΔABC
We know that altitude bisects the opposite side
BD = DC = a
![](data:image/png;base64,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)
In triangle ADB,
∠ADB = 90O
Using Pythagoras theorem, we get
AD2 + DB2 = AB2
AD2 + a2 = (2a)2
AD2 + a2 = 4a2
AD2 = 3a2
AD = a![](data:image/png;base64,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)
In an equilateral triangle, all the altitudes are equal in length.
Hence, the length of each altitude will be ![](data:image/png;base64,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)
Question 7.Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.
Answer:In Rhombus ABCD,
AB, BC, CD and AD are the sides of the rhombus.
BD and AC are the diagonals.
To prove: AB2 + BC2 + CD2 +AD2 = AC2 + BD2
Proof:
The figure is shownbelow:
![](data:image/png;base64,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)
In ΔAOB, ΔBOC, ΔCOD, ΔAOD,
Applying Pythagoras theorem, we obtain
AB2 = AO2 + OB2 .....................eq(i)
BC2 = BO2 + OC2 .......................eq (ii)
CD2 = CO2 + OD2 ....................eq(iii)
AD2 = AO2 + OD2.....................eq (iv)
Now after adding all equations, we get,
AB2 + BC2 + CD2 + AD2 = 2 (AO2 + OB2 + OC2 + OD2)
Diagonals of a rhombus bisect each other,
Thus AO = AC/2, OB = BD/2, OC=AC/2, and OD= BD/2
![](data:image/png;base64,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)
![](data:image/png;base64,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)
=(AC)2 + (BD)2
Hence Sum of squares of sides of a rhombus equals to sum of squares of diagonals of rhombus.
Question 8.In Fig. 6.54, O is a point in the interior of a triangle ABC, OD ⊥ BC, OE ⊥ AC and OF ⊥ AB. Show that
![](data:image/png;base64,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)
(i) ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUYAAAAcCAMAAAAqa+bnAAAAAXNSR0ICQMB9xQAAAIFQTFRFgYGBiIhmZoiIgG5ubm6Af39dXX9/f25ZWW5/f25IWW5uSG5/bltISFtugFszM1uAbls1W0g1bEYdHUZsMzNbMzNIWjMdHTNaRzMeHjNHWjMAADNaHR1INB0dHR00SBwAABxIMh0AAB0yMgAdHR0AAB0dMwAAAAAzHQAAAAAdAAAA2WMGTgAAACp0Uk5TAAwMGBgZGSUlMTExSkpMTFhxc3N/i42Nmpqhoam3t7y8ysrK2dnd3ezsXqIXJwAAAjlJREFUeNrtl+tSwjAQhbdFBARaKSqSihVUKPv+D+iQNL3ltqnjDIM5v7jMN9mc7GY3AEFBQUFBQUFB/1tRgXie3xw1BBoWntD4CSD5iG+NGgJRmGj1hXje3FVfE8S0/m/2FhOoBLnep14UACx2iPi9ffCgZiW2GBulCxFP997bQuGfZaEmriZpGWJen8LnnEJ1Y6RSvFSEUjolv+Amtq9lCdFzW9xGy0I8jiNupwCT18qE8TFnlR2QyA8OKsE1AEwKkcZUKirwsASA0WKX0qlZeVlrtCr5YZspJcSmxOjbojBCmcw9xr24sBJnOZESNkLGz9CDat02ZErYyHec2ihlsdR7KRpT9SBZzLOS74qd7sfHvEnw5kAgWRuoKhuPGy+KtXqfQhkjlDZCgrmFUkNMvZciMTKNZUpExSVvuYVM39wbQ3pUdYkcpj6UWI/QJbtr1TY2v1Ow3vXtw1C6et/G7OJ5VaS+NqIWM1EOG5w2Oo7hL21kyn57pExJ7Q4tNvJ/FqUui68lG1PvpUiM4ebpTj/qAeTGu7FKZTLFTO+C7mFb7kYPzGDJEIbQnDJaeeo7tWqjg6JVtaFT7x2bNHbd3zNqUXdHpagQO9MXTLK2zo3Ro6OodXNjLOdG6mTbnRvJGM3GIYxmcK8rhjkM0Y/7rhzu3RnjffsVQ3xn9V4xVIzUYhTGw0aIXvgzMq4HaDD06rYhbap+Uy8BPCiASLypn6f0CJU3NREj2thjfGwMCgoKCgoKukr9AL2Wlr/3Rh+TAAAAAElFTkSuQmCC)
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(ii) ![](data:image/png;base64,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)
Answer:(i)
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)
To Prove : OA2 + OB2 + OC2 – OD2 – OE2 – OF2 = AF2 + BD2 + EC2
Given: OD, OE and OF are perpendiculars on sides BC, AC and AB respectively
Construction : Join OA, OB and OC
Now according to pythagoras theorem, In a right angled triangle,
(hypotenuse)2 = (altitude)2 + (base)2
Applying Pythagoras theorem in ΔAOF, we obtain
OA2 = OF2 + AF2 ..................eq(i)
Similarly, in ΔBOD,
OB2 = OD2 + BD2 ..................eq(ii)
Similarly, in ΔCOE,
OC2 = OE2 + EC2 .................eq(iii)
Adding these equations, we get
OA2 + OB2 + OC2 = OF2 + AF2 + OD2 + BD2 + OE2 + EC2
Rearranging the equations we get,
OA2 + OB2 + OC2 – OD2 – OE2 – OF2 = AF2 + BD2 + EC2
Hence, Proved
(ii)
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To Prove: AF2 + BD2 + EC2 = AE2 + CD2 + BF2
From the above given result from (i),
AF2 + BD2 + EC2 = (AO2 – OE2) + (OC2 – OD2) + (OB2 – OF2)
and from eq(i), (ii) and (iii)
AO2 - OE2 = AE2 , OC2 - OD2 = CD2 , OB2 - OF2 - BF2
Putting these values in above equation we get,
AF2 + BD2 + EC2 = AE2 + CD2 + BF2
Hence, Proved
Question 9.A ladder 10 m long reaches a window 8 m above theground. Find the distance of the foot of the ladder from base of the wall
Answer:Let OA be the wall and AB be the ladder
![](data:image/png;base64,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)
By Pythagoras theorem,
AB2 = OA2 + BO2
(10)2 = (8)2 + OB2
100 = 64 + OB2
OB2 = 36
OB = 6 cm
Therefore, the distance of the foot of the ladder from the base of the wall is 6 m
Question 10.A wire attached to a vertical pole of height 18 m is 24 m long and has a stack attached to the other end. How far from the base of the pole should the stack be driven so that the wire will be taut?
Answer:To find: OA
Let OB be the pole and AB be the wire
By Pythagoras theorem,
Pythagoras Theorem : the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
![](data:image/png;base64,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)
AB2 = OB2 + OA2
(24)2 = (18)2 + OA2
OA2 = (576 – 324)
OA2 = 252
OA = 6√7 m
Question 11.An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after
hours?
Answer:![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/4RDuRXhpZgAATU0AKgAAAAgABAE7AAIAAAAMAAAISodpAAQAAAABAAAIVpydAAEAAAAYAAAQzuocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAGFobWFkIGF2YWlzAAAFkAMAAgAAABQAABCkkAQAAgAAABQAABC4kpEAAgAAAAM0NAAAkpIAAgAAAAM0NAAA6hwABwAACAwAAAiYAAAAABzqAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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we know,
Distance = speed × time
Distance traveled by the plane flying towards north in
= 1,000 x![](data:image/png;base64,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)
= 1,500 km
Similarly, distance traveled by the plane flying towards west in
= 1,200 x![](data:image/png;base64,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)
= 1,800 km
Let these distances be represented by OA and OB respectively.
Pythagoras Theorem : It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Applying Pythagoras theorem,
![](data:image/png;base64,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)
Distances between planes is 300√61 km
Question 12.Two poles of heights 6 m and 11 m stand on aplane ground. If the distance between the feetof the poles is 12 m, find the distance between their tops
Answer:Let CD and AB be the poles of height 11 m and 6 m
Therefore, CP = 11 - 6 = 5 m
From the figure, it can be observed that AP = 12m
Applying Pythagoras theorem for ΔAPC, we obtain
![](data:image/png;base64,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)
AP2 + PC2 = AC2
(12)2 + (5)2 = AC2
AC2 = (144 + 25)
AC2 = 169
AC = 13 m
Therefore, the distance between their tops is 13 m
Question 13.D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that AE2 + BD2 = AB2 + DE2
Answer:To Prove: AE2 + BD2 = AB2 + DE2
Given: D and E are midpoints of AD and CB and ABC is right angled at C
Applying Pythagoras theorem in ΔACE, we obtain
![](data:image/png;base64,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)
Pythagoras theorem: It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
AC2 + CE2 = AE2 ..........eqn(i)
Applying Pythagoras theorem in triangle BCD, we get
BC2 + CD2 = BD2 .........eqn(ii)
Adding equations (i) and (ii), we get
AC2 + CE2 + BC2 + CD2 = AE2 + BD2 .................eqn (iii)
Applying Pythagoras theorem in triangle CDE, we get
DE2 = CD2 + CE2
Applying Pythagoras in triangle ABC, we get
AB2 = AC2 + CB2
Putting these values in eqn(iii), we get
DE2 + AB2 = AE2 + BD2
Hence, Proved.
Question 14.The perpendicular from A on side BC of aΔABC intersects BC at D such that DB = 3 CD(see Fig. 6.55). Prove that 2AB2 = 2AC2 + BC2
![](data:image/png;base64,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)
Answer:We have two right angled triangles now ΔACD and ΔABD
Applying Pythagoras theorem for ΔACD, we obtain
AC2 = AD2 + DC2
AD2 = AC2 – DC2 ......................eq(i)
Applying Pythagoras theorem in ΔABD, we obtain
AB2 = AD2 + DB2
AD2 = AB2 – DB2 ........................eq(ii)
Now we can see from equation i and equation ii that LHS is same. Thus,
From (i) and (ii), we get
AC2 – DC2 = AB2 – DB2 (iii)
It is given that 3DC = DB
Therefore,
DC + DB = BC
DC + 3DC = BC
4 DC = BC ........................eq(iv)
and also,
DC = DB/3
putting this in eq (iii)
DB = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABgAAAAiCAMAAABySOkBAAAAAXNSR0IArs4c6QAAAIpQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OgBmOjoAOjpmOma2OpDbZgAAZgA6ZjoAZjpmZpDbZrbbZrb/kDoAkDo6kGY6kGaQkLbbkNv/tmYAtmY6tpA6tpBmttv/tv//25A625Bm27Zm27aQ29uQ2////7Zm/7aQ/9uQ/9u2//+2///bZtWh3AAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAxElEQVQ4T7WSyxaCMAxEE3xVUfCBoFIVCgpi+/+/Z1KUjWXFYRacKdPeJFCAXhU+egdKdYjYOnMXiGCSC5ReSms1r6Cc5AByloGyoGbJgQzA3BYANYdW71P0QwUEiulhJXHKQbPK4UVHdXjs+nkI8ooo/LLlkt+m0FDABHMlvA7JSNpZCNukomZxnTFz9zX9I46ecDMujV54cAH+yC6ZxHcHKoqdQb0xzkDvcxNH5+qviP2DSFfLITeKNj5Fd9UGjz4M8AHKXA1mHX7g8AAAAABJRU5ErkJggg==)
So,
DC =
and DB = ![](data:image/png;base64,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)
Putting these values in (iii), we get
AC2 –
= AB2 – ![](data:image/png;base64,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)
![](data:image/png;base64,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)
16AC2 – BC2 = 16AB2 – 9BC2
16AB2 – 16AC2 = 8BC2
2AB2 = 2AC2 + BC2
Question 15.In an equilateral triangle ABC, D is a point on side BC such that
Prove that 9 AD2 = 7 AB2
Answer:The figure is given below:
![](data:image/png;base64,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)
Given: BD = BC/3
To Prove: 9 AD2 = 7 AB2
Proof:
Let the side of the equilateral triangle be a, and AM be the altitude of ΔABC
BM = MC = BC/2 = a/2 [ Altitude of an equilateral triangle bisect the side]
And, then, in ΔABM, by pythagoras theorem we write,
Pythagoras Theorem : Square of the Hypotenuse equals to the sum of the squares of other two sides.
AM2 = AB2 - BM2
or AM2 = a2 - a2/4
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKsAAAA4CAYAAACCGgj0AAAJgUlEQVR4Xu2dB6wtVRWGPzpIV5EikY6gQBAQUEApgrTQ0UgXjaJAaImC0jQgoSjSVDqho1RLQELvAipYEKmidAMxCCidfLAmmYxzzpkzc8445769kpv38u7sMmv/s/a/yt5vOpIkDUyIBqabkHmmaSYNkMCaQKAGrgP+Djw6AnV8ZwR9lHaRwDouzU5Ov8sANwELA692edoJrF1enXbmdhzwCvCNdoarP0oCa33dTYWWswFPAKsAj3T9hRJYu75C453frsA2wMY9hpke+DzwYWBGYC7gA8BpwDXjndr/9p7A2rbGuzXeb4HvAleUTEts7A3cDNyd+/2WwE+BQ4Dvtfk6CaxtartbY30cuARYFHizZGpaU4F6IbAv8Ho8MysgyD8ELA/8ra3XSmBtS9PdG+f04KmH95ja6sDtwD+AFYB/xXPSAf9dnrsmcGtbr5bA2pamuzXOPMBjwNLAMz2mJih3DAfs6twzcwD3Au8HPhK/b+XtElhbUXPtQWYANgGWBJ4Hzo8t+y3gjdq9vstFPxHO07Dd2O424NigB8O2r/18Amtt1Y294eLAKeF569AsAGwHbBYZp0MbzOCvwFeBG4bsQ4v8C+BBYHfgP0O2b/R4Amsj9Y2t8WLA9cD+4eBkA+0MnBWgvaDm6OsCPwLMXFURrfsu4Yh9DjgbODLncFXpYyTPJLCORI0j7WQm4FJAK7ZOARRbB1j0wusG8X8W6dUTasxavnpEUIgvBXet0U29Jgms9fQ2zlYbAL8GBMMZhYF+AqwKrAa8VvjdpwCD+P229vmBB4BFct79sO/yHuBOYD7gk8DDw3ZQ9/kE1rqaG1+7i4DNI1wksDLR4v4mfr5WGH7tsMb/jpDSP3tM78DYzr/ccPo6Vzpphr+a9lV5Kk3A6lds+i2Lv1UeND3YUwOzRMBdT9+gfb4KSofrj8AXI4OUdSIH1QGTT64MrAdsBBgxyIvrZbhKB+33FdZgLUArfzLweOF5PxZ57z1h6YtWvkL3wz/SBKx6gwaFvzBgWON1KsjtI5M/V1SYzxsLdOvL5L+RHmxFQcOrtFELC0v+APwJMK2ZF3P00oKMr64BPB1bskC9Ft6pT74SuDG4Zb79FsC3CrrsNVk/GlOsy/UIUbn2J8bYziPLbjV6+UGN64L1g8DvQql+yf1EsPqlvxfwi1wW+CWw/aDJAXOGQ6GidTouj3ijC1KWIqzQZacfybZ6LZ+cNRPX6VzgowE2Le/XAZ2kJQq80WC96dAdIl2a9XEVIMU4s4IGjADcEmA1AqHu8yJ3NvR1FPDNCv2N5JE6YLWNnGU34L4eZL9sclpWayY/G9ubPKu4VRXbbQu4zbn1mfLLc7iRKKCDnRwAqJsNc/px95IjvgCsH5kjaYEffZm4hZ8TtOC5ALROkQXWVWOjWuvZS8Dtx+DH9DKgU9crAzZy1dYBqx6g3GifmI0gerHCzLQKKwa3WgpYCXBL7yX2q6Vxu1FpUoF+z1eYwkQ84ketMTBwb1rTHLzleBZInxrVTubttWr99CHopWmbxrNaSwtSqorY0Eh8DPh58GXBbi3BzIDlhaM4BlN1PkOfwbLi5jDA7IlHIQSdP3KnQeJ2YgHEV2IL6dfOcdz6rfq5H7g4FDdojKn0e4EhDXI3yVKrAlmLKpAHcXYdKkNg8letskamzs6koXA3lCtrlOxPmjFoVxz5WgxrWf3S/gLcEYTeLdpSsipKODi+cB0FszBaZ3lvmehcaE3cZtzq5F/njfztp36HFkrrsUvXPjPprzsMWBcM0u824FclWZfXVCkT0yK4BWmVdcgEotvTr0oUaNGGSrZY4gfhSEwrfHUceJL/vi9qV8fRf2t9DgNWA8oGgZ+K2f0Q2CtCLHrp/STjq1pHt38tsZzXPvIiR9Xy+pzbmB7pOPiqfbvN+mddMRph/HEqRiXq6mSs7aqCVedGwOXDHvIgHQFDKD8eMMuMrwpSc94Gt62RzIdn7MIQl56mHNjw2Lj4qvFDq+R1OuqKIDVX77skaUEDVcCq5+c5HZ2qvPdpOMX6SitwrA7qJxlftb3W0zDKs0Hcs3YLRVwvK/S1jlO+ulOEYVpQR+tDeI5pWpCRXHxRBaxaRa1h/tCYCjYdqGUVsP0C/Hm+mi2MXNUzPIZlDMm4HWdOVOb5ylf3DADr/U5FSWAdYlUHgVVHR4eqmBt2CCt4zEgZHjGA3UvyfDV7xosVBLjZLIsuPh1nfbKytyyDYuhGQE8L8dUhlm3afHQQWL8dPPXJEvXIKS0PM3BtDK/XMYs8X826keeeFGA1A6LHellujIyvekRYi5skaaBvUsA4qBknIwBlMnc4F1YGGVoy/VYmeb6a/d4gs7lqHSrDKhYE5yuMxs1XtfZGGqQ3dcXUp3FgP9YkLWigl2XVqfICA8NVvbbgrDJHOuDil9VQlvFVX8sjFSYXDFEdXbLg4+arcmStd5NogDuJV++k0FULQHWIMrBapvb9qFO1pKyXCGiLgbW+ZVks+za1appuj0InVpkLVmsitbx5sV/Pogt0rXviqy2BoevD5MHqtm6hhIULWhydK3PyVlflATNvlKbp+AhsaxlfirTeQWFtBLupWAHnz0MROchKzQSknNVYrW0V71zyR4tntswQl3FWQa2Fr1Is03V9/z/m5y7iqVidWE/IWqqZrYep2ImRQQ7WxLxImmipBgSqu6O82pi1aXINhYf+dHI1Fp4EmAhJYJ2IZao9SeswPBxYPHgoYK2eMpNnuaEnNzovCaydX6JGE/RqSi9es7b1rkJP+wHHhIPb+YuEnXsCayMsdL6xt6dY3ebNLh5DyYv1wsa29SOscei8JLB2fokaTdBoikeljw9HNd9ZdruLN6z4985LAmvnl2hsEzQRY/Rlq0L2cGwDNu04gbWpBiezvcfb5bAeTRKsg47IdOItE1g7sQytTsIYupVyAtYCpNZOpzZ9ywTWphqcvPae0PCSYP/TiyoHPTvzhgmsnVmKVibizTg6XF5h6eXEEyUJrBO1XI0m68FOz7d5g0q+Qs7060QAN4G10fpPTGOLiTyG5MmEvDNlJst7qzzx0XlJYO38EjWeoBks72HwZpui1++xdwvfzXR1XhJYO79EjSZoKabn3fyz7CSHxefeJ+aV8J2XBNbOL1GjCXrzYL/DnJZ3GsJq9c6qum+UwFpXc6ld6xpIYG1d5WnAuhpIYK2rudSudQ0ksLau8jRgXQ0ksNbVXGrXugYSWFtXeRqwrgbeBk8wl0hsW672AAAAAElFTkSuQmCC)
BD = a/3 [ BC = a]
DM = BM – BD
= a/2 – a/3
= a/6
According to pythagoras theorem in a right angled triangle,
(hypotenuse)2 = (altitude)2 + (base)2
Applying Pythagoras theorem in ΔADM, we obtain
AD2 = AM2 + DM2
![](data:image/gif;base64,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)
![](data:image/gif;base64,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)
![](data:image/gif;base64,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)
![](data:image/gif;base64,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)
Now, a = AB or a2 = AB2
![](data:image/png;base64,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)
36 AD2 = 28 AB2
9 AD2 = 7 AB2
Hence, Proved
Question 16.In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes
Answer:Let the side of the equilateral triangle be a, and AE be the altitude of ΔABC
![](data:image/png;base64,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)
To Prove : 4 × (Square of altitude) = 3 × (Square of one side)
Proof:
Altitude of equilateral triangle divides the side in two equal parts. Therefore,
![](data:image/png;base64,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)
Pythagoras Theorem : It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Applying Pythagoras theorem in ΔABE, we obtain
AB2 = AE2 + BE2
![](data:image/png;base64,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)
![](data:image/png;base64,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)
4 × (Square of altitude) = 3 × (Square of one side)
Question 17.Tick the correct answer and justify:
In ΔABC, AB = 6√3 cm, AC = 12 cm and BC = 6 cm, the angle B is:
A. 120° B. 60°
C. 90° D. 45°
Answer:![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/4RDuRXhpZgAATU0AKgAAAAgABAE7AAIAAAAMAAAISodpAAQAAAABAAAIVpydAAEAAAAYAAAQzuocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAGFobWFkIGF2YWlzAAAFkAMAAgAAABQAABCkkAQAAgAAABQAABC4kpEAAgAAAAM1MQAAkpIAAgAAAAM1MQAA6hwABwAACAwAAAiYAAAAABzqAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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Given that, AB = 6
cm,
AC = 12 cm,
And BC = 6 cm
It can be observed that
AB2 = 108
AC2 = 144
And, BC2 = 36
AB2 +BC2 = AC2
Pythagoras Theorem : It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
ΔABC, is satisfying Pythagoras theorem.
Therefore, the triangle is a right triangle, right-angled at B
∠B = 90°
Hence, the correct answer is (C)
Sides of triangles are given below. Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse.
(i) 7 cm, 24 cm, 25 cm
(ii) 3 cm, 8 cm, 6 cm
(iii) 50 cm, 80 cm, 100 cm
(iv) 13 cm, 12 cm, 5 cm
Answer:
(i) Given: sides of the triangle are 7 cm, 24 cm, and 25 cm
Squaring the lengths of these sides, we get: 49, 576, and 625.
49 + 576 = 625
Or, 72 + 242 = 252
The sides of the given triangle satisfy Pythagoras theorem
Hence, it is a right triangle
We know that the longest side of a right triangle is the hypotenuse
Therefore, the length of the hypotenuse of this triangle is 25 cm
(ii) It is given that the sides of the triangle are 3 cm, 8 cm, and 6 cm
Squaring the lengths of these sides, we will obtain 9, 64, and 36
However, 9 + 36 ≠ 64
Or, 32 + 62 ≠ 82
Clearly, the sum of the squares of the lengths of two sides is not equal to the square of the length of the third side
Therefore, the given triangle is not satisfying Pythagoras theorem
Hence, it is not a right triangle
(iii)Given that sides are 50 cm, 80 cm, and 100 cm.
Squaring the lengths of these sides, we will obtain 2500, 6400, and 10000.
And, 2500 + 6400 ≠ 10000
Or, 502 + 802 ≠ 1002
Now, the sum of the squares of the lengths of two sides is not equal to the square of the length of the third side
Therefore, the given triangle is not satisfying Pythagoras theorem
Hence, it is not a right triangle
(iv)Given: Sides are 13 cm, 12 cm, and 5 cm
Squaring the lengths of these sides, we get 169, 144, and 25.
Clearly, 144 +25 = 169
Or, 122 + 52 = 132
The sides of the given triangle are satisfying Pythagoras theorem
Therefore, it is a right triangle
We know that the longest side of a right triangle is the hypotenuse
Therefore, the length of the hypotenuse of this triangle is 13 cm
Question 2.
PQR is a triangle right angled at P and M is a point on QR such that PM ⊥ QR. Show that PM2 = QM×MR
Answer:
⇒ Let ∠MPR = x
⇒ In Δ MPR, ∠MRP = 180-90-x
⇒ ∠MRP = 90-x
Similarly in Δ MPQ,
∠MPQ = 90-∠MPR = 90-x
⇒ ∠MQP = 180-90-(90-x)
⇒ ∠MQP = x
In Δ QMP and Δ PMR
⇒ ∠MPQ = ∠MRP
⇒ ∠PMQ = ∠RMP
⇒ ∠MQP = ∠MPR
⇒ Δ QMP ∼ Δ PMR
⇒ =
⇒ PM2 = MR × QM
Hence proved
Question 3.
In Fig. 6.53, ABD is a triangle right angled at Aand AC ⊥ BD. Show that:
(i) AB2 = BC . BD
(ii) AC2 = BC . DC
(iii) AD2 = BD . CD
Answer:
(i) In ΔADB and ΔCAB, we have
∠DAB = ∠ACB (Each of 90o)
∠ABD = ∠CBA (Common angle)
Therefore,
ΔADB ΔCAB (AA similarity)
AB2 = CB x BD
(ii) Let ∠CAB = x
In ΔCBA,
∠CBA + ∠CAB + ∠ACB = 180oAs, ∠ACB = 90o, we have
∠CBA = 180o – 90o – x
∠CBA = 90o – x
Similarly, in ΔCAD
∠CAD = 90o - ∠CBA
= 90o – x
∠CDA = 180o – 90o – (90o – x)
∠CDA = x
In triangle CBA and CAD, we have
∠CBA = ∠CAD
∠CAB = ∠CDA
∠ACB = ∠DCA (Each 90o)
Therefore,
ΔCBA ΔCAD (By AAA similarity)
AC2 = DC * BC
(iii) In ΔDCA and ΔDAB, we have
∠DCA = ∠DAB (Each 90o)
∠CDA = ∠ADB (Common angle)
Therefore,
ΔDCA ΔDAB (By AA similarity)
AD2 = BD x CD
Question 4.
ABC is an isosceles triangle right angled at C. Prove that
Answer:
To Prove: 2 AC2 = AB2
Given: ΔABC is an isosceles triangle
Proof:
AC = CB ( Two sides of an isosceles triangle are equal, as the side opposite to right angle is largest, rest of the two sides are equal)
Pythagoras Theorem: It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Using Pythagoras theorem in ΔABC (i.e., right-angled at point C), we get
AC2 + CB2 = AB2
AC2 + AC2 = AB2 (AC = CB)
So,2AC2 = AB2
Hence, Proved.Question 5.
ABC is an isosceles triangle with AC = BC. If AB2 = 2AC2, prove that ABC is a right triangle.
Answer:
To Prove: ABC is a right angled triangle
Given: AB2 = 2AC2
Now 2 AC2 can be split into two parts
AB2 = AC2 + AC2
in an isosceles triangle ABC two sides are equal, and it is given that AC = BC. So,AB2 = AC2 + BC2 (As, AC = BC)
Now According to pythagoras theorem, in a right angled triangle, square of one side equals to the sum of squares of other two sidesAnd clearly above equation satisfies it. Thus, the equation satisfies pythagoras theorem and the triangle should be right angled for that.
Therefore, the given triangle is a right-angled triangle
Hence, Proved.
Question 6.
ABC is an equilateral triangle of side 2a. Find each of its altitudes
Answer:
Let AD be the altitude of the given equilateral triangle, ΔABC
We know that altitude bisects the opposite side
BD = DC = a
In triangle ADB,
∠ADB = 90O
Using Pythagoras theorem, we get
AD2 + DB2 = AB2
AD2 + a2 = (2a)2
AD2 + a2 = 4a2
AD2 = 3a2
AD = a
In an equilateral triangle, all the altitudes are equal in length.
Hence, the length of each altitude will be
Question 7.
Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.
Answer:
In Rhombus ABCD,
AB, BC, CD and AD are the sides of the rhombus.
BD and AC are the diagonals.
To prove: AB2 + BC2 + CD2 +AD2 = AC2 + BD2
Proof:
The figure is shownbelow:
In ΔAOB, ΔBOC, ΔCOD, ΔAOD,
Applying Pythagoras theorem, we obtain
AB2 = AO2 + OB2 .....................eq(i)
BC2 = BO2 + OC2 .......................eq (ii)
CD2 = CO2 + OD2 ....................eq(iii)
AD2 = AO2 + OD2.....................eq (iv)
Now after adding all equations, we get,
AB2 + BC2 + CD2 + AD2 = 2 (AO2 + OB2 + OC2 + OD2)
Diagonals of a rhombus bisect each other,Thus AO = AC/2, OB = BD/2, OC=AC/2, and OD= BD/2
=(AC)2 + (BD)2
Hence Sum of squares of sides of a rhombus equals to sum of squares of diagonals of rhombus.
Question 8.
In Fig. 6.54, O is a point in the interior of a triangle ABC, OD ⊥ BC, OE ⊥ AC and OF ⊥ AB. Show that
(i)
(ii)
Answer:
(i)
To Prove : OA2 + OB2 + OC2 – OD2 – OE2 – OF2 = AF2 + BD2 + EC2
Given: OD, OE and OF are perpendiculars on sides BC, AC and AB respectively
Construction : Join OA, OB and OC
Now according to pythagoras theorem, In a right angled triangle,
(hypotenuse)2 = (altitude)2 + (base)2
Applying Pythagoras theorem in ΔAOF, we obtain
OA2 = OF2 + AF2 ..................eq(i)
Similarly, in ΔBOD,
OB2 = OD2 + BD2 ..................eq(ii)
Similarly, in ΔCOE,
OC2 = OE2 + EC2 .................eq(iii)
Adding these equations, we get
OA2 + OB2 + OC2 = OF2 + AF2 + OD2 + BD2 + OE2 + EC2
Rearranging the equations we get,
OA2 + OB2 + OC2 – OD2 – OE2 – OF2 = AF2 + BD2 + EC2
Hence, Proved
(ii)
To Prove: AF2 + BD2 + EC2 = AE2 + CD2 + BF2
From the above given result from (i),
AF2 + BD2 + EC2 = (AO2 – OE2) + (OC2 – OD2) + (OB2 – OF2)
and from eq(i), (ii) and (iii)AO2 - OE2 = AE2 , OC2 - OD2 = CD2 , OB2 - OF2 - BF2
Putting these values in above equation we get,
AF2 + BD2 + EC2 = AE2 + CD2 + BF2
Hence, Proved
Question 9.
A ladder 10 m long reaches a window 8 m above theground. Find the distance of the foot of the ladder from base of the wall
Answer:
Let OA be the wall and AB be the ladder
By Pythagoras theorem,
AB2 = OA2 + BO2
(10)2 = (8)2 + OB2
100 = 64 + OB2
OB2 = 36
OB = 6 cm
Therefore, the distance of the foot of the ladder from the base of the wall is 6 m
Question 10.
A wire attached to a vertical pole of height 18 m is 24 m long and has a stack attached to the other end. How far from the base of the pole should the stack be driven so that the wire will be taut?
Answer:
To find: OA
Let OB be the pole and AB be the wire
By Pythagoras theorem,
Pythagoras Theorem : the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.AB2 = OB2 + OA2
(24)2 = (18)2 + OA2
OA2 = (576 – 324)
OA2 = 252
OA = 6√7 m
Question 11.
An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes afterhours?
Answer:
we know,
Distance = speed × time
Distance traveled by the plane flying towards north in = 1,000 x
= 1,500 km
Similarly, distance traveled by the plane flying towards west in = 1,200 x
= 1,800 km
Let these distances be represented by OA and OB respectively.
Pythagoras Theorem : It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Applying Pythagoras theorem,
Distances between planes is 300√61 km
Question 12.
Two poles of heights 6 m and 11 m stand on aplane ground. If the distance between the feetof the poles is 12 m, find the distance between their tops
Answer:
Let CD and AB be the poles of height 11 m and 6 m
Therefore, CP = 11 - 6 = 5 m
From the figure, it can be observed that AP = 12m
Applying Pythagoras theorem for ΔAPC, we obtain
AP2 + PC2 = AC2
(12)2 + (5)2 = AC2
AC2 = (144 + 25)
AC2 = 169
AC = 13 m
Therefore, the distance between their tops is 13 m
Question 13.
D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that AE2 + BD2 = AB2 + DE2
Answer:
To Prove: AE2 + BD2 = AB2 + DE2
Given: D and E are midpoints of AD and CB and ABC is right angled at C
Applying Pythagoras theorem in ΔACE, we obtain
AC2 + CE2 = AE2 ..........eqn(i)
Applying Pythagoras theorem in triangle BCD, we get
BC2 + CD2 = BD2 .........eqn(ii)
Adding equations (i) and (ii), we get
AC2 + CE2 + BC2 + CD2 = AE2 + BD2 .................eqn (iii)
Applying Pythagoras theorem in triangle CDE, we get
DE2 = CD2 + CE2
Applying Pythagoras in triangle ABC, we get
AB2 = AC2 + CB2
Putting these values in eqn(iii), we get
DE2 + AB2 = AE2 + BD2
Hence, Proved.Question 14.
The perpendicular from A on side BC of aΔABC intersects BC at D such that DB = 3 CD(see Fig. 6.55). Prove that 2AB2 = 2AC2 + BC2
Answer:
We have two right angled triangles now ΔACD and ΔABD
Applying Pythagoras theorem for ΔACD, we obtain
AC2 = AD2 + DC2
AD2 = AC2 – DC2 ......................eq(i)
Applying Pythagoras theorem in ΔABD, we obtain
AB2 = AD2 + DB2
AD2 = AB2 – DB2 ........................eq(ii)
Now we can see from equation i and equation ii that LHS is same. Thus,From (i) and (ii), we get
AC2 – DC2 = AB2 – DB2 (iii)
It is given that 3DC = DB
Therefore,
DC + DB = BC
4 DC = BC ........................eq(iv)
and also,
DC = DB/3
putting this in eq (iii)
DB =
So,
DC = and DB =
Putting these values in (iii), we get
AC2 – = AB2 –
16AC2 – BC2 = 16AB2 – 9BC2
16AB2 – 16AC2 = 8BC2
2AB2 = 2AC2 + BC2
Question 15.
In an equilateral triangle ABC, D is a point on side BC such that Prove that 9 AD2 = 7 AB2
Answer:
The figure is given below:
Given: BD = BC/3
To Prove: 9 AD2 = 7 AB2
Proof:
Let the side of the equilateral triangle be a, and AM be the altitude of ΔABC
BM = MC = BC/2 = a/2 [ Altitude of an equilateral triangle bisect the side]
And, then, in ΔABM, by pythagoras theorem we write,
Pythagoras Theorem : Square of the Hypotenuse equals to the sum of the squares of other two sides.
AM2 = AB2 - BM2
or AM2 = a2 - a2/4
BD = a/3 [ BC = a]
DM = BM – BD
= a/2 – a/3
= a/6
According to pythagoras theorem in a right angled triangle,
(hypotenuse)2 = (altitude)2 + (base)2
Applying Pythagoras theorem in ΔADM, we obtain
AD2 = AM2 + DM2
Now, a = AB or a2 = AB2
36 AD2 = 28 AB2
9 AD2 = 7 AB2
Hence, Proved
Question 16.
In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes
Answer:
Let the side of the equilateral triangle be a, and AE be the altitude of ΔABC
To Prove : 4 × (Square of altitude) = 3 × (Square of one side)
Proof:
Altitude of equilateral triangle divides the side in two equal parts. Therefore,
Pythagoras Theorem : It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Applying Pythagoras theorem in ΔABE, we obtain
AB2 = AE2 + BE2
4 × (Square of altitude) = 3 × (Square of one side)
Question 17.
Tick the correct answer and justify:
In ΔABC, AB = 6√3 cm, AC = 12 cm and BC = 6 cm, the angle B is:
A. 120° B. 60°
C. 90° D. 45°
Answer:
Given that, AB = 6 cm,
AC = 12 cm,
And BC = 6 cm
It can be observed that
AB2 = 108
AC2 = 144
And, BC2 = 36
AB2 +BC2 = AC2
ΔABC, is satisfying Pythagoras theorem.
Therefore, the triangle is a right triangle, right-angled at B
∠B = 90°
Hence, the correct answer is (C)
Exercise 6.6
Question 1.In Fig. 6.56, PS is the bisector of ∠QPR of Δ PQR. Prove that![](data:image/png;base64,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)
![](data:image/png;base64,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)
Answer:Construct a line segment RT parallel to SP which intersects the extended line segment QP at point T
![](data:image/png;base64,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)
Given: PS is the angle bisector of ∠QPR.
Proof:
∠QPS = ∠SPR (i)
By construction,
∠SPR = ∠PRT (As PS || TR, By interior alternate angles) (ii)
∠QPS = ∠QTR (As PS || TR, By interior alternate angles) (iii)
Using these equations, we get:
∠PRT = ∠QTR
PT = PR
By construction,
PS || TR
Basic Proportionality Theorem: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.
By using basic proportionality theorem for ΔQTR,
![](data:image/png;base64,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)
Hence, Proved
Question 2.In Fig. 6.57, D is a point on hypotenuse AC of Δ ABC, DM ⊥ BC and DN ⊥ AB. Prove that:
(i)
(ii) ![](data:image/png;base64,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)
![](data:image/png;base64,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)
Answer:(i) To Prove: DM2 = DN. MC
Construction:join DB
We have, DN || CB,
DM || AB,
And ∠B = 90° (Given)
As opposite sides are parallel and equal and also each angle is 90°, DMBN is a rectangle
![](data:image/png;base64,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)
DN = MB and DM = NB
The condition to be proved is the case when D is the foot of the perpendicular drawn from B to AC
∠CDB = 90°
Now from the figure we can say that
∠2 + ∠3 = 90° ........eq(i)
In ΔCDM,
∠1 + ∠2 + ∠DMC = 180° [ Sum of angles of a triangle = 180°]
∠1 + ∠2 = 90° ...........eq(ii)
In Δ DMB,
∠3 + ∠DMB + ∠4 = 180° [ Sum of angles of a triangle = 180°]
⇒∠3 + ∠4 = 90° ........eq(iii)
From (i) and (ii), we get
∠1 = ∠3
From (i) and (iii), we get
∠2 = ∠4
In ΔDCM and ΔBDM,
∠1 = ∠3 (Proved above)
∠2 = ∠4 (Proved above)
ΔDCM similar to ΔBDM (AA similarity)
(AA Similarity : When you have two triangles where one is a smaller version of the other, you are looking at two similar triangles.)
BM/DM = DM/MC
Cross multiplying we get,
DN/DM = DM/MC (BM = DN)
DM2 = DN × MC
Hence, Proved.
(ii)
To Prove: DN2= AN x DM
In right triangle DBN,
∠5 + ∠7 = 90° (iv)
In right triangle DAN,
∠6 + ∠8 = 90° (v)
D is the foot of the perpendicular drawn from B to AC
∠ADB = 90°
∠5 + ∠6 = 90° (vi)
From equation (iv) and (vi), we obtain
∠6 = ∠7
From equation (v) and (vi), we obtain
∠8 = ∠5
In ΔDNA and ΔBND,
∠6 = ∠7 (Proved above)
∠8 = ∠5 (Proved above)
Hence,
ΔDNA similar to ΔBND (AA similarity criterion)
( AA similarity Criterion: When you have two triangles where one is a smaller version of the other, you are looking at two similar triangles.)
AN/DN = DN/NB
DN2 = AN x NB
DN2= AN x DM (As NB = DM)
Hence, Proved
Question 3.In Fig. 6.58, ABC is a triangle in which ∠ ABC > 90° and AD ⊥ CB produced. Prove that![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPQAAAAeCAMAAAAsLsMoAAAAAXNSR0ICQMB9xQAAAHVQTFRFgYGBiIhmZoiIgG5uf39dXX9/f25ZWW5/f25IWW5uSG5/bltISFtugFszM1uAbls1W0g1bEYdHUZsMzNbMzNIHTNaHjNHWjMAADNaHR1INB0dHR00SBwAABxIMh0AAB0yMgAdAB0dMwAAAAAzHQAAAAAdAAAABSdMyAAAACZ0Uk5TAAwMGBkZJSUxMTFKSkxMWHFzc3+LjZqhoam3t7y8ysrK2d3d7OyNPVnTAAACUUlEQVR42u1Wa1PCQAxMoUgVDm0Vi4iiWPP/f6JzT5J7FXB0HOfyiUd2N2n20gMoUaJEiRIl/kFUO8TPm1+BXSj1A1HfA4iXyW/ALpT6XgjElf282CLi++O1+tI8TU7CCVTxPIcszEtjWkmpSmZ9ricxBlZsmNAM6P9/jB5xczSaDtlN/Zb3nMMZKfyYQQ7G05hWWsqAtBEYAy82IqGbRsR1+EDrw6Z3deyXADBdbFcAQv+YdqXDCewA4Gqn1NMwlsa0MlJCDqoZdGOUgRcbk2gG+WV6N9iZslpWwnKSk9VvRk/FESfZoZXbKAOjaUxrVAraUIgVG5XQTcvpEC9YyY9ZfVCyPdmh2hurnLsdzjzfwzoGE503BpnGtHIY27TOpgx9bOEzCds0iGDUqnDFUO1GDJ3A2ZO0n0fn23kHTqXltfym6wM705IhTsAqcU1buOcc9YTC/+jO0tFFcG59YHdK0ziiFTZd2akShjgBq8Q1HTwg/YOiOGvSBGdP0mKIOs6zt047Z9KuZ8qQmjSpJD1pu9fVEjrjXkRxRsqum4hByNE3aUktjlGP16VShsyZNhLpM90SQ0QXYsLeHJdoOjppezAy/qaTbobjrqAMue3Nm65fvbqqnYYaf+N+OfFefSl3E5yWqm5PsrdJy2qRpsVAeqMMHkGrpskk2Hu6JdN2FlBuqV/DS07K3QR3wSLLa4kucKJqnTFwAts0W2TkRkabbvmOqPR19mE+elugOHvjXZ70yrJpGa2Rpg0DI2BN6wR2925xAyVKlChRokSJPx1fIaF05fFevIEAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
Answer:Using Pythagoras theorem in ΔADB, we get:
AB2 = AD2 + DB2 (i)
Applying Pythagoras theorem in ΔACD, we obtain
AC2 = AD2 + DC2
AC2 = AD2 + (DB + BC)2
AC2 = AD2 + DB2 + BC2 + 2DB x BC
AC2 = AB2 + BC2+ 2DB x BC [Using equation (i)]
Question 4.In Fig. 6.59, ABC is a triangle in which ∠ ABC < 90° and AD ⊥ BC. Prove that![](data:image/png;base64,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)
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Answer:![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/4RDuRXhpZgAATU0AKgAAAAgABAE7AAIAAAAMAAAISodpAAQAAAABAAAIVpydAAEAAAAYAAAQzuocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAGFobWFkIGF2YWlzAAAFkAMAAgAAABQAABCkkAQAAgAAABQAABC4kpEAAgAAAAM0MgAAkpIAAgAAAAM0MgAA6hwABwAACAwAAAiYAAAAABzqAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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To Prove: AC2 = AB2 + BC2 - 2BC x BD
Given: AD is Perpendicular on BC and angle ABC < 90°
Proof:
Pythagoras Theorem : It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Applying Pythagoras theorem in Δ ADB, we obtain
AD2 + DB2 = AB2
AD2 = AB2 – DB2 .....eq(i)
Applying Pythagoras theorem in Δ ADC, we obtain
AD2 + DC2 = AC2
AB2– BD2 + DC2 = AC2 [Using equation (i)]
AB2– BD2 + (BC - BD)2 = AC2 [ DC = BC - BD]
AC2 = AB2– BD2 + BC2 + BD2 -2BC x BD
AC2 = AB2 + BC2 - 2BC x BD
Hence, Proved.
Question 5.In Fig. 6.60, AD is a median of a triangle ABC and AM⊥ BC. Prove that:
![](data:image/jpeg;base64,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)
(i) ![](data:image/png;base64,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)
(ii) ![](data:image/png;base64,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)
(iii) ![](data:image/png;base64,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)
Answer:(i) Using, Pythagoras theorem in ΔAMD, we get
AM2 + MD2 = AD2 (i)
Applying Pythagoras theorem in ΔAMC, we obtain
AM2 + MC2 = AC2
AM2 + (MD + DC)2 = AC2
(AM2 + MD2) + DC2 + 2MD.DC = AC2
AD2 + DC2 + 2MD.DC = AC2[Using equation (i)]
Using, DC = BC/2 we get
AD2 + (BC/2)2 + 2MD * (BC/2) = AC2
AD2 + (BC/2)2 + MD * BC = AC2
(ii) Using Pythagoras theorem in ΔABM, we obtain
AB2 = AM2 + MB2
= (AD2– DM2) + MB2
= (AD2– DM2) + (BD - MD)2
= AD2– DM2 + BD2 + MD2 - 2BD × MD
= AD2 + BD2 - 2BD × MD
= AD2 + (BC/2)2 – 2 (BC/2) * MD
= AD2 + (BC/2)2 – BC * MD
(iii)Using Pythagoras theorem in ΔABM, we obtain
AM2 + MB2 = AB2 (1)
Applying Pythagoras theorem in ΔAMC, we obtain
AM2 + MC2 = AC2(2)
Adding equations (1) and (2), we obtain
2AM2 + MB2 + MC2 = AB2 + AC2
2AM2 + (BD - DM)2 + (MD + DC)2 = AB2 + AC2
2AM2+BD2 + DM2 - 2BD.DM + MD2 + DC2 + 2MD.DC = AB2 + AC2
2AM2 + 2MD2 + BD2 + DC2 + 2MD ( - BD + DC) = AB2 + AC2
2 (AM2 + MD2) + (BC/2)2 + (BC/2)2 + 2MD (-BC/2 + BC/2) = AB2 + AC2
2AD2 + BC2/2 = AB2 + AC2
Question 6.Prove that the sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides
Answer:ABCD is a parallelogram in which AB = CD and AD = BC
Perpendicular AN is drawn on DC and perpendicular DM is drawn on AB extend up to M
![](data:image/png;base64,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)
In Δ AMD,
AD2 = DM2 + AM2 ...............eq(i)
In Δ BMD,
BD2 = DM2 + (AM + AB)2
Or,
(AM + AB)2 = AM2 + AB2 + 2 AM x AB
BD2 = DM2 + AM2 + AB2 + 2AM x AB ..................eq(ii)
Substituting the value of AM2 from (i) in (ii), we get
BD2 = AD2 + AB2 + 2 x AM x AB .............eq(iii)
In Δ AND,
AD2 = AN2 + DN2 ......................eq(iv)
In Δ ANC,
AC2 = AN2 + (DC – DN)2
Or,
AC2 = AN2 + DN2 + DC2 – 2 x DC x DN ............eq(v)
Substituting the value of AD2 from (iv) in (v), we get
AC2 = AD2 + DC2 – 2 x DC x DN ...............eq(vi)
We also have,
AM = DN and AB = CD
Substituting these values in (vi), we get
AC2 = AD2 + DC2 – 2 x AM x AB .................eq(vii)
Adding (iii) and (vii), we get
AC2 + BD2 = AD2 + AB2 + 2 x AM x AB + AD2 + DC2 – 2 x AM x AB
Or,
AC2 + BD2 = AB2 + BC2 + DC2 + AD2
Hence, proved.
Question 7.In Fig. 6.61, two chords AB and CD intersect each other at the point P. Prove that:
(i) Δ APC ~ Δ DPB
(ii) AP . PB = CP . DP
![](data:image/png;base64,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)
Answer:(i) In triangle APC and DPB,
∠CAP = ∠BDP (Angles on the same side of a chord are equal)
∠APC = ∠DPB (Opposite angles)
Hence,
Δ APC ~ Δ DPB (By AAA similarity)
(ii) Since, the two triangles are similar
Hence,
![](data:image/png;base64,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)
Or,
AP * PB = CP * DP
Hence, proved
Question 8.In Fig. 6.62, two chords AB and CD of a circle intersect each other at the point P(when produced) outside the circle. Prove that
(i) Δ PAC ~ Δ PDB
(ii) PA . PB = PC . PD
![](data:image/png;base64,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)
Answer:(i) In triangle PAC and PDB
∠PAC + ∠CAB = 180o (Linear pair)
∠CAB + ∠BDC = 180O (Opposite angles of a cyclic quadrilateral are supplementary)
Hence,
∠PAC = ∠PDB
Similarly,
∠PCA = ∠PBD
Hence,
Δ PAC ~ Δ PDB
(ii) Since the two triangles are similar, so
![](data:image/png;base64,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)
Or,
PA * PB = PC * PD
Hence, proved
Question 9.In Fig. 6.63, D is a point on side BC of Δ ABC such that
Prove that AD is the bisector of ∠ BAC
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Answer: 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)
To Prove : AD bisects ∠BAC
![](data:image/png;base64,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)
Now from ΔABD and ΔADC,
As it is given that
![](data:image/png;base64,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)
And, AD is common to both triangles,
Therefore,
ΔABD ∼ ΔADC (BY SSS theorem)
Now by similarity ∠BAD = ∠DAC
Hence, AD must be the bisector of the angle BAC
Question 10.Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip ofthe rod. Assuming that her string(from the tip of her rod to the fly) is taut,how much string does she have out(see Fig. 6.64)? If she pulls in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?
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)
Answer:
![](data:image/png;base64,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)
As per the question:
AD = 1.8 m
BD = 2.4 m
CD = 1.2 m
speed of string when she pulls in = 5 cm per second
To find: Length of string, AB and
In triangle ABD, length of string i.e. AB can be calculated as follows [By Pythagoras theorem]
AB2 = AD2 + BD2
= (1.8)2 + (2.4)2
= 3.24 + 5.76
= 9
Or, AB = 3 m
![](data:image/png;base64,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)
Let us assume that the string reaches at point M after 12 seconds
Now, To find: Distance of fly, from the girl.
Length of string pulled in, after 1 second = 5 cm
Length of string pulled in, after 12 seconds = 5 * 12 = 60 cm
= 0.6 m [As, 1 m = 100 cm]
Remaining length, AM = 3 – 0.6 = 2.4 m
In triangle AMD, we can find MD by using Pythagoras theorem,
MD2 = AM2 – AD2
= 2.42 – 1.82
= 5.76 – 3.24
= 2.52 m
Or, MD = 1.58 m
Also,
Horizontal distance between the girl and the fly = CD + MD
= 1.2 + 1.58 = 2.78 m
In Fig. 6.56, PS is the bisector of ∠QPR of Δ PQR. Prove that
Answer:
Construct a line segment RT parallel to SP which intersects the extended line segment QP at point T
Given: PS is the angle bisector of ∠QPR.
Proof:
∠QPS = ∠SPR (i)
By construction,
∠SPR = ∠PRT (As PS || TR, By interior alternate angles) (ii)
∠QPS = ∠QTR (As PS || TR, By interior alternate angles) (iii)
Using these equations, we get:
∠PRT = ∠QTR
PT = PR
By construction,
PS || TR
Basic Proportionality Theorem: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.
By using basic proportionality theorem for ΔQTR,
Hence, Proved
Question 2.
In Fig. 6.57, D is a point on hypotenuse AC of Δ ABC, DM ⊥ BC and DN ⊥ AB. Prove that:
(i) (ii)
Answer:
(i) To Prove: DM2 = DN. MC
Construction:join DB
We have, DN || CB,
DM || AB,
And ∠B = 90° (Given)
As opposite sides are parallel and equal and also each angle is 90°, DMBN is a rectangle
DN = MB and DM = NB
The condition to be proved is the case when D is the foot of the perpendicular drawn from B to AC
∠CDB = 90°
Now from the figure we can say that
∠2 + ∠3 = 90° ........eq(i)
In ΔCDM,
∠1 + ∠2 + ∠DMC = 180° [ Sum of angles of a triangle = 180°]
∠1 + ∠2 = 90° ...........eq(ii)
In Δ DMB,
∠3 + ∠DMB + ∠4 = 180° [ Sum of angles of a triangle = 180°]
⇒∠3 + ∠4 = 90° ........eq(iii)
From (i) and (ii), we get
∠1 = ∠3
From (i) and (iii), we get
∠2 = ∠4
In ΔDCM and ΔBDM,
∠1 = ∠3 (Proved above)
∠2 = ∠4 (Proved above)
ΔDCM similar to ΔBDM (AA similarity)
(AA Similarity : When you have two triangles where one is a smaller version of the other, you are looking at two similar triangles.)
BM/DM = DM/MC
Cross multiplying we get,
DN/DM = DM/MC (BM = DN)
DM2 = DN × MC
Hence, Proved.
(ii)
To Prove: DN2= AN x DM
In right triangle DBN,
∠5 + ∠7 = 90° (iv)
In right triangle DAN,
∠6 + ∠8 = 90° (v)
D is the foot of the perpendicular drawn from B to AC
∠ADB = 90°
∠5 + ∠6 = 90° (vi)
From equation (iv) and (vi), we obtain
∠6 = ∠7
From equation (v) and (vi), we obtain
∠8 = ∠5
In ΔDNA and ΔBND,
∠6 = ∠7 (Proved above)
∠8 = ∠5 (Proved above)
Hence,
ΔDNA similar to ΔBND (AA similarity criterion)
( AA similarity Criterion: When you have two triangles where one is a smaller version of the other, you are looking at two similar triangles.)
AN/DN = DN/NB
DN2 = AN x NB
DN2= AN x DM (As NB = DM)
Hence, Proved
Question 3.
In Fig. 6.58, ABC is a triangle in which ∠ ABC > 90° and AD ⊥ CB produced. Prove that
Answer:
Using Pythagoras theorem in ΔADB, we get:
AB2 = AD2 + DB2 (i)
Applying Pythagoras theorem in ΔACD, we obtain
AC2 = AD2 + DC2
AC2 = AD2 + (DB + BC)2
AC2 = AD2 + DB2 + BC2 + 2DB x BC
AC2 = AB2 + BC2+ 2DB x BC [Using equation (i)]
Question 4.
In Fig. 6.59, ABC is a triangle in which ∠ ABC < 90° and AD ⊥ BC. Prove that
Answer:
To Prove: AC2 = AB2 + BC2 - 2BC x BD
Given: AD is Perpendicular on BC and angle ABC < 90°
Proof:
Pythagoras Theorem : It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Applying Pythagoras theorem in Δ ADB, we obtain
AD2 + DB2 = AB2
AD2 = AB2 – DB2 .....eq(i)
Applying Pythagoras theorem in Δ ADC, we obtain
AD2 + DC2 = AC2
AB2– BD2 + DC2 = AC2 [Using equation (i)]
AB2– BD2 + (BC - BD)2 = AC2 [ DC = BC - BD]
AC2 = AB2– BD2 + BC2 + BD2 -2BC x BD
AC2 = AB2 + BC2 - 2BC x BD
Hence, Proved.
Question 5.
In Fig. 6.60, AD is a median of a triangle ABC and AM⊥ BC. Prove that:
(i)
(ii)
(iii)
Answer:
(i) Using, Pythagoras theorem in ΔAMD, we get
AM2 + MD2 = AD2 (i)
Applying Pythagoras theorem in ΔAMC, we obtain
AM2 + MC2 = AC2
AM2 + (MD + DC)2 = AC2
(AM2 + MD2) + DC2 + 2MD.DC = AC2
AD2 + DC2 + 2MD.DC = AC2[Using equation (i)]
Using, DC = BC/2 we get
AD2 + (BC/2)2 + 2MD * (BC/2) = AC2
AD2 + (BC/2)2 + MD * BC = AC2
(ii) Using Pythagoras theorem in ΔABM, we obtain
AB2 = AM2 + MB2
= (AD2– DM2) + MB2
= (AD2– DM2) + (BD - MD)2
= AD2– DM2 + BD2 + MD2 - 2BD × MD
= AD2 + BD2 - 2BD × MD
= AD2 + (BC/2)2 – 2 (BC/2) * MD
= AD2 + (BC/2)2 – BC * MD
(iii)Using Pythagoras theorem in ΔABM, we obtain
AM2 + MB2 = AB2 (1)
Applying Pythagoras theorem in ΔAMC, we obtain
AM2 + MC2 = AC2(2)
Adding equations (1) and (2), we obtain
2AM2 + MB2 + MC2 = AB2 + AC2
2AM2 + (BD - DM)2 + (MD + DC)2 = AB2 + AC2
2AM2+BD2 + DM2 - 2BD.DM + MD2 + DC2 + 2MD.DC = AB2 + AC2
2AM2 + 2MD2 + BD2 + DC2 + 2MD ( - BD + DC) = AB2 + AC2
2 (AM2 + MD2) + (BC/2)2 + (BC/2)2 + 2MD (-BC/2 + BC/2) = AB2 + AC2
2AD2 + BC2/2 = AB2 + AC2
Question 6.
Prove that the sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides
Answer:
ABCD is a parallelogram in which AB = CD and AD = BC
Perpendicular AN is drawn on DC and perpendicular DM is drawn on AB extend up to M
In Δ AMD,
AD2 = DM2 + AM2 ...............eq(i)
In Δ BMD,
BD2 = DM2 + (AM + AB)2
Or,
(AM + AB)2 = AM2 + AB2 + 2 AM x ABBD2 = DM2 + AM2 + AB2 + 2AM x AB ..................eq(ii)
Substituting the value of AM2 from (i) in (ii), we get
BD2 = AD2 + AB2 + 2 x AM x AB .............eq(iii)
In Δ AND,
AD2 = AN2 + DN2 ......................eq(iv)
In Δ ANC,
AC2 = AN2 + (DC – DN)2
Or,
AC2 = AN2 + DN2 + DC2 – 2 x DC x DN ............eq(v)
Substituting the value of AD2 from (iv) in (v), we get
AC2 = AD2 + DC2 – 2 x DC x DN ...............eq(vi)
We also have,
AM = DN and AB = CD
Substituting these values in (vi), we get
AC2 = AD2 + DC2 – 2 x AM x AB .................eq(vii)
Adding (iii) and (vii), we get
AC2 + BD2 = AD2 + AB2 + 2 x AM x AB + AD2 + DC2 – 2 x AM x AB
Or,
AC2 + BD2 = AB2 + BC2 + DC2 + AD2
Hence, proved.
Question 7.
In Fig. 6.61, two chords AB and CD intersect each other at the point P. Prove that:
(i) Δ APC ~ Δ DPB
(ii) AP . PB = CP . DP
Answer:
(i) In triangle APC and DPB,
∠CAP = ∠BDP (Angles on the same side of a chord are equal)
∠APC = ∠DPB (Opposite angles)
Hence,
Δ APC ~ Δ DPB (By AAA similarity)
(ii) Since, the two triangles are similar
Hence,
Or,
AP * PB = CP * DP
Hence, proved
Question 8.
In Fig. 6.62, two chords AB and CD of a circle intersect each other at the point P(when produced) outside the circle. Prove that
(i) Δ PAC ~ Δ PDB
(ii) PA . PB = PC . PD
Answer:
(i) In triangle PAC and PDB
∠PAC + ∠CAB = 180o (Linear pair)
∠CAB + ∠BDC = 180O (Opposite angles of a cyclic quadrilateral are supplementary)
Hence,
∠PAC = ∠PDB
Similarly,
∠PCA = ∠PBD
Hence,
Δ PAC ~ Δ PDB
(ii) Since the two triangles are similar, so
Or,
PA * PB = PC * PD
Hence, proved
Question 9.
In Fig. 6.63, D is a point on side BC of Δ ABC such thatProve that AD is the bisector of ∠ BAC
Answer:
To Prove : AD bisects ∠BAC
Now from ΔABD and ΔADC,
As it is given that
And, AD is common to both triangles,
Therefore,
ΔABD ∼ ΔADC (BY SSS theorem)
Now by similarity ∠BAD = ∠DAC
Hence, AD must be the bisector of the angle BAC
Question 10.
Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip ofthe rod. Assuming that her string(from the tip of her rod to the fly) is taut,how much string does she have out(see Fig. 6.64)? If she pulls in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?
Answer:
As per the question:
AD = 1.8 m
BD = 2.4 m
CD = 1.2 m
speed of string when she pulls in = 5 cm per second
To find: Length of string, AB and
In triangle ABD, length of string i.e. AB can be calculated as follows [By Pythagoras theorem]
AB2 = AD2 + BD2
= (1.8)2 + (2.4)2
= 3.24 + 5.76
= 9
Or, AB = 3 m
Let us assume that the string reaches at point M after 12 seconds
Now, To find: Distance of fly, from the girl.Length of string pulled in, after 1 second = 5 cm
Length of string pulled in, after 12 seconds = 5 * 12 = 60 cm
= 0.6 m [As, 1 m = 100 cm]Remaining length, AM = 3 – 0.6 = 2.4 m
In triangle AMD, we can find MD by using Pythagoras theorem,
MD2 = AM2 – AD2
= 2.42 – 1.82
= 5.76 – 3.24
= 2.52 m
Or, MD = 1.58 m
Also,
Horizontal distance between the girl and the fly = CD + MD
= 1.2 + 1.58 = 2.78 m