Problem
Given: $\overline{A D}$ bisects $\angle \mathrm{BAC}$. \[ \angle 1 \cong \angle 3 \] Prove: $\angle 2 \cong \angle 3$ Statements Reasons \begin{tabular}{|l|l|} \hline 1. $\overline{A D}$ bisects $\angle \mathrm{BAC}$ & \\ $\angle 1 \cong \angle 3$ & \\ \hline 2. $\angle 1 \cong \angle 2$ & \\ \hline 3. $\angle 2 \cong \angle 3$ & \\ \hline \end{tabular}
Solution
Step 1 ：Given: $\overline{A D}$ bisects $\angle \mathrm{BAC}$, $\angle 1 \cong \angle 3$
Step 2 ：$\angle 1 \cong \angle 2$ (Definition of angle bisector)
Step 3 ：$\angle 2 \cong \angle 3$ (Transitive Property of Congruence)
Step 4 ：Final Answer: \(\boxed{\angle 2 \cong \angle 3}\)
