Question

in the figure below,PS=PR,TPS=QPR. prove that PT=PQ​

Answer 1

Answer:

Given PS=PR,∠TPS=∠QPR

we have to prove that PT=PQ

In△PSR,

PS=PR(given)

∴∠PSR=∠PRS−(i)

{ Angles opposite to equal sides of a △le are equal}

∴∠TPS+∠PTS=∠QPR+∠PQR

(An exterior angle of a △le is equal to the sum of its two interior opposite angle)

⟹∠PTS=∠PQR

∴∠PTQ=∠PQT∴PT=PQ

(sides opposite to equal angles of a △le are equal).