Question

In ΔPQR, S and T are points on PQ and PR respectively. `(PS)/(SQ) = (PT)/(TR)` and ∠PST = ∠PRQ. Prove that PQR is an isosceles triangle.

Answer 1

Given `(PS)/(SQ) = (PT)/(TR)`

∠PST = ∠PRQ

To prove : PQR is an isosceles triangle

Proof : `(PS)/(SQ) = (PT)/(TR)`

∠PST = ∠PQR  ...(Corresponding angles)

But ∠PST = ∠PRQ

∠PQR = ∠PRQ

PR = PQ  ...(Sides opposite to equal angles are equal)

ΔPQR is isosceles triangle.