1. The problem asks what additional information is needed to prove that triangle $\triangle ABC$ is congruent to triangle $\triangle DEF$ by the ASA (Angle-Side-Angle) criterion. 2. The ASA criterion states that two triangles are congruent if two angles and the included side of one triangle are congruent to two angles and the included side of the other triangle. 3. From the graph description, angles at $A$ and $B$ in $\triangle ABC$ correspond to angles at $E$ and $D$ in $\triangle DEF$ respectively. 4. To use ASA, we need the side between these two angles in each triangle to be congruent. In $\triangle ABC$, the side between angles $A$ and $B$ is $\overline{AB}$. 5. In $\triangle DEF$, the side between angles $E$ and $D$ is $\overline{DE}$. 6. Therefore, the additional information needed is $\overline{AB} \cong \overline{DE}$. 7. This corresponds to option A. Final answer: A. $\overline{AB} \cong \overline{DE}$