Question

In the figure given below PQR is a triangle in which,PL is the bisector of /_ QPR.if PL | QR, show that ∆PQR is isosceles.​

Answer 1

Angle QPL and angle LPR are equal as PL bisects angle QPR

Side PL is common for both triangles

And angle PLR and angle PLQ are equal as they are both 90 degrees

So Triangle PQL and PRL are congruent

By CPCT we find PQ and PR are equal

Therefore, PQR is an iscoceles triangle.

Hope this helps..