complete the proof.
given: $ \angle abd \cong \angle cbd, \angle bda \cong \angle bdc $
prove: $ \overline{ab} \cong \overline{cb} $
1. $ \angle abd \cong \angle cbd, \angle bda \cong \angle bdc $ 1. given
2. $ \overline{bd} \cong \overline{bd} $ 2. reflexive property of $ \cong $
3. $ \triangle abd \cong \triangle cbd $ 3.

Question

Accepted Answer

# Explanation:
## Step1: Recall the ASA (Angle - Side - Angle) Congruence Criterion
Two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.
## Step2: Identify the parts in triangles $ \triangle ABD$ and $ \triangle CBD$
We have $ \angle ABD\cong\angle CBD$ (given angle), $ \overline{BD}\cong\overline{BD}$ (common side, reflexive property), and $ \angle BDA\cong\angle BDC$ (given angle).
## Step3: Apply the ASA Criterion
Since two angles ($ \angle ABD,\angle BDA$) and the included side ($ \overline{BD}$) of $ \triangle ABD$ are congruent to two angles ($ \angle CBD,\angle BDC$) and the included side ($ \overline{BD}$) of $ \triangle CBD$, by the ASA (Angle - Side - Angle) congruence criterion, $ \triangle ABD\cong\triangle CBD$.

# Answer:
ASA (Angle - Side - Angle)

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the ASA (Angle - Side - Angle) Congruence Criterion

Step2: Identify the parts in triangles \( \triangle ABD\) and \( \triangle CBD\)

Step3: Apply the ASA Criterion

Answer: