Chapter 4.1, Problem 13PSB

To determine

To Prove: $\Delta FBC$ is Isosceles.

Explanation of Solution

Given information: $AB=AC,AD=AE.$

Formula Used: Congruency of triangles.

Verification:

  $\begin{array}{l}AB=AC,AD=AE(given)\\ \angle DAC=\angle EAB(common\_angle)\\ \therefore \Delta DAC=\Delta EAB(SAS)\\ \therefore \angle ACD=\angle ABE(CPCT)\\ Also,\therefore \angle ABC=\angle ACB\left(sidesoppositetoequalanglesareequal\right).\\ \therefore \angle ABC-\angle ABE=\angle ACB-\angle ACD\\ \therefore \angle FBC=\angle FCB.\\ \therefore \Delta FBCIsIsosceles.\end{array}$