Question

state the third congruence that must be given to prove that \\( \triangle def \cong \triangle abc \\) using asa congruence theorem. \\( \overline{fe} \cong \overline{cb} \\) \\( \angle f \cong \angle c \\)

Explanation:

Step1: Recall ASA Congruence Theorem

ASA (Angle - Side - Angle) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
We are given \(\overline{FE}\cong\overline{CB}\). For ASA, we need two angles.

Step2: Identify the angles

One of the angles is \(\angle F\cong\angle C\) (already given). The other angle should be the angle adjacent to the given side in each triangle. In \(\triangle DEF\), the angle adjacent to \(\overline{FE}\) is \(\angle E\), and in \(\triangle ABC\), the angle adjacent to \(\overline{CB}\) is \(\angle B\).

Answer:

\(\angle B\)