Question

what must be true in order for △abc≅△edc by the sas congruence postulate? a. ∠b≅∠d b. ∠a≅∠e c. (overline{ac}congoverline{ce}) d. (overline{ab}congoverline{de})

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: Analyze the given triangles

In \(\triangle ABC\) and \(\triangle EDC\), we already have a pair of vertical angles \(\angle ACB\cong\angle ECD\) (vertical angles are congruent). We need the sides that include these angles to be congruent. That is, we need \(AC\cong CE\) and \(BC\cong CD\). Looking at the options, the side - congruence option relevant for SAS is the one that gives the congruence of the sides adjacent to the included angle.

Answer:

C. \(\overline{AC}\cong\overline{CE}\)