Question

If $\Delta PQR$ is an equilateral triangle and $PA$ is the angle bisector of $\angle P$, then $\Delta PQA\cong \Delta PRA$?

• A. Yes
• B. No
• C. Data Insufficient

Answer 1

The correct option is A Yes

For the given diagram, $PA$ is the angle bisector of $\angle P$.
$\Rightarrow \angle QPA=\angle RPA$
Also, the side $PA$ is common.
And, since $\Delta PQR$ is an equilateral triangle.
$\Rightarrow PQ=PR$
$\therefore$ From all these conditions, we can imply that the two triangles are congruent.
$\Rightarrow \Delta PQA\cong \Delta PRA$