Question

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

Answer 1

Given in the question, P is a point on the bisector of ∠ABC. If the line through P, parallel to BA meet BC at Q.

To prove: BPQ is an isosceles triangle.

Proof: ∠1 = ∠2  ...(i) [BP is the bisector of ∠ABC]

PQ is parallel to BA and BP cuts them.

So, ∠1 = ∠3   ...[Alternate interior angles as PQ || AB]

∠2 = ∠3   ...[Proved above]

PQ = BQ  ...[Sides opposite to equal angle are equal]

Hence, BPQ is an isosceles triangle.