It is given that PS/SQ=PT/TR.
So, ST || QR (Theorem 6.2)
Therefore, ∠PST =∠PQR (Corresponding angles) ......(1)
Also, it is given that
∠PST = ∠PRQ .........(2)
So, ∠PRQ = ∠PQR [From (1) and (2)]
Therefore, PQ = PR (Sides opposite the equal angles)
i.e., PQR is an isosceles triangle.