Question

1. what additional information do you need to prove $\triangle abccong\triangle edc$ by the sas postulate?

$overline{bc}congoverline{dc}$
$overline{ac}congoverline{ec}$
$overline{ab}congoverline{de}$

Explanation:

Step1: Recall SAS Postulate

The Side - Angle - Side (SAS) 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. In \(\triangle ABC\) and \(\triangle EDC\), we already have a pair of vertical angles (\(\angle ACB\cong\angle ECD\)).

Step2: Identify needed sides

The included sides for the vertical - angle pair are \(AC\) and \(BC\) in \(\triangle ABC\) and \(EC\) and \(DC\) in \(\triangle EDC\). We need the sides that include the equal angles to be congruent. Since we know nothing about the relationship between \(AB\) and \(DE\) for the SAS postulate, and we need the sides adjacent to the equal angles. We need \(AC\cong EC\) and \(BC\cong DC\). Among the given options, we are missing \(AC\cong EC\).

Answer:

\(\overline{AC}\cong\overline{EC}\)