Question

Q is a point on the side SR of a ∆PSR such that PQ = PR. Prove that PS > PQ.

Answer 1

In triangle PSR, Q is a point on the side SR such that PQ = PR.

To proof that PS > PQ

Proof: In triangle PRQ,

PQ = PR  ...[Given]

∠R = ∠PQR   ...(i) [Angle opposite to equal sides are equal]

∠PQR > ∠S   ...(ii) [Exterior angle of a triangle is greater than each of the opposite interior angle]

Now, from equation (i) and (ii), we get

∠R > ∠S

PS > PR  ...[Side opposite to greater angle is longer]

PS > PQ  ...[PQ = PR]