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.  

 

Answer 1

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