Q10 of 47 Page 7

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.

Given that PQR is a triangle such that,


PQ = PR


And, S is any point on side PQ and ST ‖ QR


We have to prove PS = PT


Since,


PQ = PR


PQR is isosceles


∠Q = ∠R


Or, ∠PQR = ∠PRQ


Now,


∠PST = ∠PQR


And,


∠PTS = ∠PRQ (Corresponding angles as ST ‖ QR)


Since,


∠PQR = ∠PRQ


∠PST = PTS


Now, in


∠PST = ∠PTS


Therefore, ∆PST is an isosceles triangle


PS = PT


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