Question

In triangle pqr, PQ is equals to PR then prove that angle pqs is equal to angle prt.

Answer 1

Solutions:

Since rays QP and RP stand on ST.

Hence, ∠SQP + ∠PQR = 180° and ∠SRP + ∠PRT = 180°

=> ∠PQS + ∠PQR = 180° and ∠PRQ + ∠PRT = 180°

=> ∠PQS + ∠PQR = ∠PRQ + ∠PRT

=> ∠PQS + ∠PQR = ∠PQR + ∠PRT ________[Since, ∠PRQ = ∠PQR (Given)]

=> ∠PQS = ∠PRT

( Refer to the attachment )

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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