if you wanted to explain why $ \triangle abd \cong cbd $ by the sas congruence theorem, which of the following would be helpful to know?
(1 point)
$ \overline { a c } $ is the angle bisector of $ \angle b c d $.
$ \overline { a c } $ is the angle bisector of $ \angle b a d $.
$ \overline { b d } $ is the angle bisector of $ \angle b c d $.
$ \overline { b d } $ is the angle bisector of $ \angle a b c $.

Question

Accepted Answer

# Explanation:
## Step1: Recall 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 triangles $\triangle ABD$ and $\triangle CBD$
We know that $BD = BD$ (common side). If $BD$ is the angle bisector of $\angle ABC$, then $\angle ABD=\angle CBD$. Also, if we assume $AB = CB$ (not given in the problem statement but for the sake of using SAS, we need the included angle). The included angle for sides $AB$ and $BD$ in $\triangle ABD$ and sides $CB$ and $BD$ in $\triangle CBD$ is $\angle ABD$ and $\angle CBD$ respectively.

# Answer:
$\overline{BD}$ is the angle bisector of $\angle ABC$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall SAS Congruence Theorem

Step2: Analyze the triangles \(\triangle ABD\) and \(\triangle CBD\)

Answer: