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, is an isosceles triangle


PS = PT


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