# Chapter 3 - Triangles

Mathematics Part II Solutions for Class 9 Math

PRACTICE SET 3.1

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

**Practice Set 3.2**

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

**Practice Set 3.3**

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

**Practice Set 3.4**

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

**Practice Set 3.5**

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

**Problem Set 3**

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