Question

if point ( c ) is the midpoint of both ( overline{bd} ) and ( overline{ae} ), what additional information would you need to be able to state that ( \triangle abccong\triangle edc ) by the sas congruence theorem? (1 point) ( overline{bc}congoverline{dc} ) ( overline{ab}congoverline{ed} ) ( angle acbcongangle ecd ) ( angle acongangle e )

Explanation:

Step1: Recall the SAS Congruence Theorem

SAS (Side - Angle - Side) 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 information

Since \(C\) is the mid - point of \(BD\) and \(AE\), we have \(AC = EC\) and \(BC=DC\).

Step3: Identify the missing part for SAS

We already have two pairs of sides (\(AC = EC\) and \(BC = DC\)). For the SAS theorem, we need the included angles. The included angles for the sides \(AC, BC\) in \(\triangle ABC\) and \(EC, DC\) in \(\triangle EDC\) are \(\angle ACB\) and \(\angle ECD\) respectively.

Answer:

\(\angle ACB\cong\angle ECD\)