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) Congruence Theorem 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 \(\overline{FE}\cong\overline{CB}\) (a side) and \(\angle F\cong\angle C\) (an angle).

Step2: Identify the missing angle

For \(\triangle DEF\) and \(\triangle ABC\) to be congruent by ASA, we need another pair of congruent angles. The angles adjacent to the given sides \(\overline{FE}\) and \(\overline{CB}\) are \(\angle E\) and \(\angle B\) respectively.

Answer:

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