Chapter 4.2, Problem 12PSB

To determine

To Prove: $\Delta BPC$ is isosceles.

Explanation of Solution

Given information: AB=BC, BP and CP are angle bisectors

Formula used: Properties of triangles.

Proof:

  

  $\begin{array}{l}AB=BC \left(given\right)\\ \therefore \angle ABC=\angle ACB \left(Anglesoppositetoequalsidesareequal\right)\\ \therefore \frac{1}{2}\angle ABC=\frac{1}{2}\angle ACB. \\ \therefore \angle PBM=\angle PCM(BP\&PCareanglebisector)\\ \therefore PB=PC(Sidesoppositestoequalanglesareequal)\end{array}$