1. The problem states that we have two triangles, \(\triangle ABC\) and \(\triangle EDC\), with given congruent angles \(\angle B \cong \angle E\) and \(\angle BCA \cong \angle EDC\). We want to determine what additional information is needed to prove the triangles are congruent using the Angle-Side-Angle (ASA) criterion. 2. The ASA criterion states that if two angles and the included side between them in one triangle are congruent to two angles and the included side in another triangle, then the triangles are congruent. 3. We already have two pairs of congruent angles: \(\angle B \cong \angle E\) and \(\angle BCA \cong \angle EDC\). 4. To apply ASA, the side between these two angles must be congruent. In \(\triangle ABC\), the side between \(\angle B\) and \(\angle BCA\) is \(BC\). 5. In \(\triangle EDC\), the side between \(\angle E\) and \(\angle EDC\) is \(ED\). 6. Therefore, the missing information needed is \(BC \cong ED\). Final answer: \(BC \cong ED\) is needed to prove the triangles are congruent by ASA.