Question

state the third congruence that must be given to prove that \\( \triangle def \cong \triangle abc \\) using aas congruence theorem. \\( \overline{de} \cong \overline{ab} \\) \\( \angle d \cong \angle a \\)

Explanation:

Step1: Recall AAS Congruence Theorem

AAS (Angle - Angle - Side) Congruence Theorem 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 two triangles are congruent.
We already have \( \overline{DE}\cong\overline{AB}\) (side) and \( \angle D\cong\angle A\) (angle).

Step2: Determine the second angle

We need another pair of congruent angles. Looking at the triangles \(\triangle DEF\) and \(\triangle ABC\), the non - included angles (relative to the given side \(DE\) and \(AB\)) are \(\angle E\) and \(\angle B\).

Answer:

\(\angle E\cong\angle B\)