Chapter 2.5, Problem 11PSB

To determine

To Prove: $\angle BAC\cong \angle FAE$

Answer to Problem 11PSB

Conclusion $\angle BAC\cong \angle FAE$

Explanation of Solution

Given information:

  $\angle BAC\cong \angle FAE$

  $\overline{AD}$ Bisects $\angle AE$ .

  $\because \angle BAD\cong \angle FAD$

  $\because \overline{AD}$ Bisects $\angle AE$ .

  $\begin{array}{l}\therefore \angle CAD\cong \angle EAD\\ \because \angle BAD\cong \angle FAD\\ \angle BAC+\angle C\cancel{A}D\cong \angle FAE+\angle E\cancel{A}D\\ \therefore \angle BAC\cong \angle FAE\end{array}$

Hence proved