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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.
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Solution
Given that PQR is a triangle such that PQ = PRand S is any point on the side PQ and ST ||QR.
We have to prove PS = PT
Since, PQ =PR⇒ΔPQR is isosceles
⇒ ∠Q= ∠R(or) ∠PQR= ∠ PRQ
Now,
∠PST=∠PQR and ∠PTS=∠PRQ [Corresponding angles as STllQR ]
Since, ∠PQR=∠PRQ⇒∠PST=∠PTS
Now, In ΔPST,∠PST=∠PTS
⇒ ΔPST is an isosceles triangle
⇒ PS=PT
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