decide whether enough information is given to prove that $ \triangle abd $ and $ \triangle cdb $ are congruent using the sas congruence theorem. explain.

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Accepted Answer

# Explanation:
## Step1: Recall SAS Congruence Theorem
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: Identify sides and angle in triangles
In $\triangle ABD$ and $\triangle CDB$:
- $AD = CB$ (given by the marks on the sides).
- $BD=DB$ (common side, so $BD\cong DB$).
- $\angle ADB=\angle CBD$ (given by the angle marks).
## Step3: Check if it satisfies SAS
The sides $AD$ and $BD$ in $\triangle ABD$ and sides $CB$ and $DB$ in $\triangle CDB$ along with the included angles $\angle ADB$ and $\angle CBD$ satisfy the SAS Congruence Theorem.

# Answer:
Yes, enough information is given. By SAS, $\triangle ABD\cong\triangle CDB$ since $AD = CB$, $\angle ADB=\angle CBD$, and $BD = DB$.

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Question

Explanation:

Step1: Recall SAS Congruence Theorem

Step2: Identify sides and angle in triangles

Step3: Check if it satisfies SAS

Answer: