Question

P is a point on the bisector of an angle ∠ABC. If the line through P parallel to AB meets BC at Q, prove that triangle BPQ is isosceles.

Answer 1

In the following figure it is given that sides AB and PQ are parallel and BP is bisector of

We have to prove that is an isosceles triangle.

(Since BP is the bisector of) ........(1)

(Since and are parallel) .......(2)

Now from equation (1) and (2) we have

So

Now since and is a side of.

And since two sides and are equal, so

Hence is an isosceles triangle.