Question

PQR is a triangle in which PQ = PR. S and T are points on PQ and PR
such that QT and RS are respectively the bisectors of anglePQR and angleQRP
.
Prove that triangleTQR congruent triangleSRQ.




plz answer it as early as possible ​

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) 

hope it helps.

Answer 2

Step-by-step explanation:

in ∆PQR and ∆SPR

<PRQ=<SRP(common angle)

<QPR=<PSR(given)

<PQR=<PSR(properties of triangle)

∆PQR~∆SPR(byAAA)

hope this helped

All the best

May God bless you