Question

Question 4
P is a point on the bisector of $\angle ABC$. If the line through P, parallel to BA meet BC at Q, prove that BPQ is an isosceles triangle.

Answer 1

Given we have P is a point on the bisector of $\angle ABC$ and draw the line through P parallel to BA and meet BC at Q.

Now, $\angle 1=\angle 2,AsBPisthebisectorof\angle B$.
and $\angle 1=\angle 3,Alternateinteriorangles$.
Hence , $\angle 2=\angle 3$ .
So, PQ = BQ. ( Sides opposite to equal angles are equal).
$Hence,\Delta BPQisanisoscelestriangle$.