Question

In the adjoining figure, PQ = PR and ∠Q =∠R. Prove that
(i) ∆PQS ≅ ∆PRT (ii) QS = RT

Answer 1

Answer:

in triangle PQS and PRT

PQ=PR

Q=R

QS=RT

Explanation:

1.in triangle PQS and PRT

PQ=PR

Q=R

QS=RT

PQS=PRT BY SSS CONGRUENCY

2.

Answer 2

Question :-

In figure, ∠PQR = ∠PRQ, then prove that ∠PQS = ∠PRT.

Answer :-

ST is a straight line.

∴ ∠PQR + ∠PQS = 180° …(1) [Linear pair]

Similarly, ∠PRT + ∠PRQ = 180° …(2) [Linear Pair]

From (1) and (2), we have

∠PQS + ∠PQR = ∠PRT + ∠PRQ

But ∠PQR = ∠PRQ [Given]

∴ ∠PQS = ∠PRT

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