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}

Answer

Expert–verified

Hide Steps

Answer

Final Answer: $\boxed{\angle 2 \cong \angle 3}$

Steps

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: $\boxed{\angle 2 \cong \angle 3}$