if point c is the midpoint of both $ \overline { b d } $ and $ \overline { a e } $, what additional information would you need to be able to state that $ \triangle a b c \cong \triangle e d c $ by the sas congruence theorem?
(1 point)
$ \bigcirc \overline { b d } \cong \overline { d e } $
$ \bigcirc \angle a c b \cong \angle e c d $
$ \bigcirc \angle a \cong \angle e $
$ \bigcirc \overline { a b } \cong \overline { e d } $

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Accepted Answer

# Explanation:
## Step1: Recall the SAS Congruence Theorem
The SAS (Side - Angle - Side) Congruence Theorem 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 $BC = CD$ and $AC=CE$.

## Step3: Determine the needed angle
For $\triangle ABC$ and $\triangle EDC$, the sides $BC$ and $CD$, $AC$ and $CE$ are congruent. The included angles for $\triangle ABC$ and $\triangle EDC$ are $\angle ACB$ and $\angle ECD$ respectively.

# Answer:
$\angle ACB\cong\angle ECD$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the SAS Congruence Theorem

Step2: Analyze the given information

Step3: Determine the needed angle

Answer: