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