# In Fig. 6.51, PQ = PS and ∠1 = ∠2.

(i) Is ∆PQR ≅ ∆PSR? Give reasons.

(ii) Is QR = SR? Give reasons

**Solution:**

Given, the figure represents two triangles PQR and PSR.

PQ = PS

∠1 = ∠2

(i) We have to determine if the triangles PQR and PSR are __congruent__.

Considering __triangles__ PQR and PSR,

Given, PQ = PS

Common side = PR

Given, ∠1 = ∠2

The SAS criterion states that If two sides of one triangle are respectively proportional to two __corresponding sides__ of another, and if the included angles are equal, then the two triangles are congruent.

By __SAS rule__, ∆PQR ≅ ∆PSR

(ii) We have to find if the sides QR and SR are equal.

Corresponding parts of congruent triangles or cpct tell us that corresponding sides and corresponding angles of the two triangles which are congruent are equal.

By CPCT,

The corresponding sides are QR and SR

Therefore, QR = SR

**✦ Try This: **In Fig, is the pair of triangles are congruent?

**☛ Also Check: **NCERT Solutions for Class 7 Maths Chapter 6

**NCERT Exemplar Class 7 Maths Chapter 6 Problem 150**

## In Fig. 6.51, PQ = PS and ∠1 = ∠2. (i) Is ∆PQR ≅ ∆PSR? Give reasons. (ii) Is QR = SR? Give reasons

**Summary:**

In Fig. 6.51, PQ = PS and ∠1 = ∠2. (i) ∆PQR ≅ ∆PSR by SAS congruence criterion, (ii) QR = SR by CPCT.

**☛ Related Questions:**

- In Fig. 6.52, DE = IH, EG = FI and ∠ E = ∠ I. Is ∆DEF ≅ ∆HIG? If yes, by which congruence criterion
- In Fig. 6.53, ∠1 = ∠ 2 and ∠ 3 = ∠ 4. (i) Is ∆ADC ≅ ∆ ABC? Why ? (ii) Show that AD = AB and CD = CB
- Observe Fig. 6.54 and state the three pairs of equal parts in triangles ABC and DBC. (i) Is ∆ABC ≅ ∆ . . . .

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