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

Given that P is a point on the bisector of an angle ΔABC, and PQ||AB.

We have to prove that ΔBPQ is isosceles

Since,

BP is bisector of ∠ABC

⇒ ∠ABP=∠PBC ......(1)