Chapter 12.4, Problem 37E

To determine

To Prove: Corollary to base angles theorem follows the base angle theorem.

Explanation of Solution

Given: Base angle theorem.

Let $ABC$ is an isosceles triangle with $AB\cong BC$ .

Construct $CD$ the bisector of $\angle ACB$

Thus

  $\begin{array}{l}AC\cong CB\\ CD\cong CD(common)\\ \angle ACB\cong \angle BCD\\ Thus\\ bySAS\\ \Delta ACD\cong \Delta BCD\\ \angle BAC\cong \angle ABC\end{array}$

If a triangle is equilateral, then is equiangular.

  

Hence, we obtain the two congruent triangles both base angles are the parts of the congruent triangles.

Hence proved.