PQR is a triangle in which PQ = PR and is any point on the side PQ.

Given that PQR is a triangle such that PQ = PR ant S is any point on the side PQ and ST ∥ QR.

To Prove,

PS = PT

Since, PQ = PR

PQR is an isosceles triangle.

∠Q = ∠R (or) ∠PQR = ∠PRQ

Now, ∠PST = ∠PQR and ∠PTS = ∠PRQ [Corresponding angles as ST parallel to QR]

Since, ∠PQR = ∠PRQ

∠PST = ∠PTS

Now, In ΔPST, ∠PST = ∠PTS

ΔPST is an isosceles triangle

Therefore, PS = PT