Question

P is a point on the bisector of $\angle ABC$. If a line through P is drawn parallel to BA to meet BC at Q, then BPQ is a/an ______ triangle.

• A. isosceles
• B. equilateral
• C. right angled
• D. scalene

Answer 1

The correct option is A isosceles

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


Now,
$\angle 1=\angle 2$ (BP is the bisector of $\angle B$)
and $\angle 1=\angle 3$ (Alternate interior angles)
Hence, $\angle 2=\angle 3$.
So, PQ = BQ (Sides opposite to equal angles are equal).
$\therefore \Delta BPQ$ is an isosceles triangle.