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