if you wanted to explain why $ \triangle a b d \cong c b d $ 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 a d $. $ \overline { b d } $ is the angle bisector of $ \angle a b c $ $ \overline { a c } $ is the angle bisector of $ \angle b c d $. $ \overline { b d } $ is the angle bisector of $ \angle b c d $.

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# 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 triangles $ \triangle ABD $ and $ \triangle CBD $
In $ \triangle ABD $ and $ \triangle CBD $, we already have $ AB = CB $ (sides) and $ BD=BD $ (common side). We need to find the included angle.
If $ \overline{AC} $ is the angle bisector of $ \angle BAD $, it doesn't give us the included angle for $ \triangle ABD $ and $ \triangle CBD $.
If $ \overline{BD} $ is the angle bisector of $ \angle ABC $, it also doesn't give us the included angle for $ \triangle ABD $ and $ \triangle CBD $.
If $ \overline{BD} $ is the angle bisector of $ \angle BCD $,  it doesn't give us the included angle for $ \triangle ABD $ and $ \triangle CBD $.
If $ \overline{AC} $ is the angle bisector of $ \angle BCD $, we can get the included angle for $ \triangle ABD $ and $ \triangle CBD $ (the angle between $ BC $ and $ BD $ in $ \triangle CBD $ and  the angle between $ AD $ and $ BD $ in $ \triangle ABD $)

# Answer:
$\overline{AC}$ is the angle bisector of $\angle BCD$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the SAS Congruence Theorem

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

Answer: