Question

PQR is a triangle in which PQ = PR. S is any point on the side PQ. Through S a line is drawn parallel to QR intersecting PR at T prove that PS = PT

Answer 1

in triangle PQR,
PQ=PR [Given]
= angle PRQ=angle PQR[angle opposite to the equal sides are equal]......(1)
since ST|| QR and PQ is a transversal,then
angle PQR = angle PST (corresponding angles).....(2)
since PQ || QR and PR is a transversal,then
angle PRQ=angle PST (corresponding angles).....(3)
but angle PQR = angle PRQ , then from (2) and (3) we get
angle PST = angle PTS
In triangle PST
angle PST = angle PTS (proved)
therefore PT = PS (sides opposite to equal angles are equal) 

Answer 2

Answer: In traingle PSR And PTS

PQ=PR (given)

RS=PT (given)

Angle A is common

So,traingles are congruent(SAS) .

So corresponding sides QT=RS

Step-by-step explanation: