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:

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• 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 ≅ ∆ . . . .