Chapter 3 - Triangles
Mathematics Part II Solutions for Class 9 Math
PRACTICE SET 3.1

1. In figure 3.8, ∠ACD is an exterior angle of ΔABC. ∠B = 40°, ∠A = 70°. Find the measure…
2. In ΔPQR, ∠P = 70° ∠Q = 65° then find ∠R.
3. The measures of angles of a triangle are x°, (x - 20)°, (x - 40)°. Find the measure of…
4. The measure of one of the angles of a triangle is twice the measure of its smallest…
5. In figure 3.9, measures of some angles are given. Using the measures find the values of…
6. In figure 3.10, line AB || line DE. Find the measures of ∠DRE and ∠ARE using given…
7. In ΔABC, bisectors of ∠A and ∠B intersect at point O. If ∠C= 70^0 Find measure of ∠AOB.…
8. In Figure 3.11, line AB || line CD and line PQ is the transversal. Ray PT and ray QT…
9. Using the information in figure 3.12, find the measures of ∠a, ∠b and ∠c.…
10. In figure 3.13, line DE || line GF ray EG and ray FG are bisectors of ∠DEF and ∠DFM…

Practice Set 3.2

1. In each of the examples given below, a pair of triangles is shown. Equal parts of…
2. In each of the examples given below, a pair of triangles is shown. Equal parts of…
3. In each of the examples given below, a pair of triangles is shown. Equal parts of…
4. In each of the examples given below, a pair of triangles is shown. Equal parts of…
5. triangle From the information shown in the figure, in ΔABC and ΔPQR ∠ABC ≅ ∠PQR seg BC…
6. a From the information shown in the figure., In ΔPTQ and ΔSTR ∠PTQ = ∠STR ………………………..…
7. From the information shown in the figure, state the test assuring the congruence of…
8. As shown in the following figure, in ΔLMN and ΔPMN, LM = PN, LN = PM. Write the test…
9. In figure 3.24, seg AB ≅ seg CB and seg AD ≅ seg CD. Prove that ΔABD ≅ ΔCBD…
10. In figure 3.25, ∠P ≅ ∠R seg PQ ≅ seg RQ Prove that, ΔPQT ≅ ΔPQS delta…

Practice Set 3.3

1. Find the values of x and y using the information shown in figure 3.37. Find the measure…
2. The length of hypotenuse of a right-angled triangle is 15. Find the length of median of…
3. In ΔPQR, ∠Q =90^0 , PQ = 12, QR = 5 and QS is a median. Find t(QS).…
4. In figure 3.38, point G is the point of concurrence of the medians of ΔPQR. If GT =…

Practice Set 3.4

1. In figure 3.48, point A is on the bisector of ∠XYZ. If AX = 2cm then find AZ.…
2. In figure 3.49, ∠RST = 56°, seg PT ⊥ ray ST, seg PT ⊥ ray ST, seg PR ⊥ ray SR and PR ≅…
3. In ΔPQR, PQ = 10 cm, QR = 12 cm, PR = 8 cm. Find out the greatest and the smallest…
4. In ΔFAN, ∠F = 80°, ∠A = 40°. Find out the greatest and the smallest side of the…
5. Prove that an equilateral triangle is equiangular
6. Prove that, if the bisector of ∠BAC of ΔABC is perpendicular to side BC, then ΔABC is…
7. In figure 3.50, if seg PR ≅ seg PQ, show that seg PS seg PQ.
8. In figure 3.51, in ΔABC, seg AD and seg BE are altitudes and AE = BD. Prove that seg AD…

Practice Set 3.5

1. If ΔXYZ ∼ ΔLMN write the corresponding angles of the two triangles and also write the…
2. In In ΔXYZ, XY = 4 cm, YZ = 6 cm, XZ = 5 cm, If ΔXYZ ∼ ΔPQR and PQ = 8 cm then find the…
3. Draw a sketch of a pair of similar triangles. Label them. Show their corresponding…

Problem Set 3

1. If two sides of a triangle are 5 cm and 1.5 cm, the length of its third side cannot be…
2. In ΔPQR, If ∠R ∠Q then …………. Choose the correct alternative answer for the following…
3. In ΔTPQ, ∠T = 65^0 , ∠P = 95^0 which of the following is a true statement? Choose the…
4. ΔABC is isosceles in which AB = AC. seg BD and seg CE are medians. Show that BD = CE.…
5. In ΔPQR, If PQPR and bisectors of ∠Q and ∠R intersect at S. Show that SQSR.…
6. In figure 3.59, point D and E are on side BC of ΔABD, such that BD = CE and AD = AE.…
7. In figure 3.60, point S is any point on side QR of ΔPQR. Prove that: PQ + QR + RP 2PS…
8. In figure 3.61, bisector of ∠BAC intersects side BC at point D. Prove that AB BD left…
9. In figure 3.62, seg PT is the bisector of ∠QPR. A line through R intersects ray QP at…
10. In figure 3.63, seg AD ⊥ seg BC. seg AE is the bisector of ∠CAB and C - E - D. Prove…

MHB Class 9 Mathematics Part II

Chapter List

1. Basic concepts in Geometry

2. Parallel Lines

3. Triangles

4. Constructions of Triangles

5. Quadrilaterals

6. Circles

7. Coordinate Geometry

8. Trigonometry

9. Surface Area and Volume