In Fig 7.1, PQ = PR and ∠Q = ∠R. Prove that ∆ PQS ≅ ∆ PRT.

Solution:

Given, PQ = PR

Also, ∠Q = ∠R

We have to prove that the triangles PQS and PRT are congruent.

Considering triangles PQS and PRT,

PQ = PR (given)

∠Q = ∠R (given)

∠P is common to both triangles

So, ∠QPS = ∠RPT

ASA criterion states that two triangles are congruent, if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle.

By ASA criterion, the triangles PQS and PRT are congruent

Therefore, ∆ PQS ≅ ∆ PRT

✦ Try This: In ∆ PQR, ∠R = ∠P and QR = 4 cm and PR = 5 cm. Then the length of PQ is

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 7

NCERT Exemplar Class 9 Maths Exercise 7.3 Sample Problem 1

In Fig 7.1, PQ = PR and ∠Q = ∠R. Prove that ∆ PQS ≅ ∆ PRT

Summary:

In Fig 7.1, PQ = PR and ∠Q = ∠R. It is proven that ∆ PQS ≅ ∆ PRT by ASA criterion of triangles

☛ Related Questions:

• In Fig.7.2, two lines AB and CD intersect each other at the point O such that BC || DA and BC = DA. . . . .
• In Fig.7.3, PQ > PR and QS and RS are the bisectors of ∠Q and ∠R, respectively. Show that SQ > SR
• ABC is an isosceles triangle with AB = AC and BD and CE are its two medians. Show that BD = CE