Question

which additional information is need to prove the triangles are congruent by the specified theorem.

1. aas congruence theorem

∠c≅∠f or ∠b≅∠e
∠c≅∠b or ∠f≅∠e
ab≅de or ac≅df
ab≅ac or de≅df

Explanation:

Step1: Recall AAS Congruence Theorem

AAS (Angle - Angle - Side) states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the triangles are congruent.

Step2: Analyze the given triangles

We already have one pair of sides (marked as equal in the figure) and one pair of angles (\(\angle A\) and \(\angle D\)). We need one more pair of angles.
If \(\angle C\cong\angle F\), then with the given side (non - included side) and \(\angle A\cong\angle D\), by AAS \(\triangle ABC\cong\triangle DEF\). If \(\angle B\cong\angle E\), then with the given side (non - included side) and \(\angle A\cong\angle D\), by AAS \(\triangle ABC\cong\triangle DEF\)

Answer:

A. \(\angle C\cong\angle F\) or \(\angle B\cong\angle E\)