Question

state the third congruence that must be given to prove that \\( \triangle a b c \cong \triangle d e f \\) using sas congruence postulate. \\( \angle b \cong \angle e \\) \\( \overline{b c} \cong \overline{e f} \\)

Explanation:

Step1: Recall SAS Congruence Postulate

The SAS (Side - Angle - Side) Congruence Postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Step2: Identify the given parts

We are given that \(\angle B\cong\angle E\) (the included angle). For the SAS postulate, we already have one side - angle pair. We need another pair of sides.

Step3: Determine the required side

Since \(\angle B\) is between sides \(AB\) and \(BC\) in \(\triangle ABC\), and \(\angle E\) is between sides \(DE\) and \(EF\) in \(\triangle DEF\). To use SAS, if we assume \(AB\cong DE\), then with \(\angle B\cong\angle E\) and \(BC\cong EF\) (already given in the problem statement in a partial form), \(\triangle ABC\cong\triangle DEF\) by SAS.

Answer:

\(AB\cong DE\)