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In Fig. 6.16, PS/SQ=PT/TR and PST = PRQ. Prove that PQR is an isosceles triangle.

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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.

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