Question

Q is a point on the side SR of a triangle PSR such that PQ=PR prove that PS>PQ

Answer 1

Answer

Given:

Q is a point on side SR in ΔPSR such that PQ=PR

⇒PS>PR …… (1)

Proof:

In ΔPQR,

PQ=PR

⇒∠PQR=∠PRQ

Now, from (1)

∠PRQ>∠PSQ or ∠PRS>∠PSR

Now, in ΔPSR,

∠PRS>∠PSR

⇒PS>PR

⇒PS>PQ

Hence, proved