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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.
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Solution
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.
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