Question

PQR is a triangle in which PQ = PR and S is any point on the side PQ. Through S, a line is drawn parallel to QR and intersecting PR at T. Prove that PS = PT.

Answer 1

Given : In $\Delta PQR,PQ=PR$

S is a point on PQ and PT || QR

To prove : PS = PT

Proof : $\because ST||QR$

$\therefore \angle S=\angle Qand\angle T=\angle R$

(Corresponding angles)

But $\angle Q=\angle R(\because PQ=PR)$

$\therefore PS=PT\text{(Sides opposite to equal angles)}$