Question 4
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 we have P is a point on the bisector of ∠ABC and draw the line through P parallel to BA and meet BC at Q.
Now, ∠1=∠2,AsBPisthebisectorof∠B.
and ∠1=∠3,Alternateinteriorangles.
Hence , ∠2=∠3 .
So, PQ = BQ. ( Sides opposite to equal angles are equal). Hence,ΔBPQisanisoscelestriangle.