if: △abe ≅ △ace
then:
∠bde ≅ ∠cde.

Question

Accepted Answer

# Explanation:
## Step1: Use the property of congruent triangles
Since $\triangle ABE\cong\triangle ACE$, then $AB = AC$, $\angle BAE=\angle CAE$, and $BE = CE$.
## Step2: Prove $\triangle ABD\cong\triangle ACD$
In $\triangle ABD$ and $\triangle ACD$, $AB = AC$ (from $\triangle ABE\cong\triangle ACE$), $\angle BAD=\angle CAD$ (from $\triangle ABE\cong\triangle ACE$), and $AD = AD$ (common side). By the Side - Angle - Side (SAS) congruence criterion, $\triangle ABD\cong\triangle ACD$. So $BD = CD$.
## Step3: Prove $\triangle BDE\cong\triangle CDE$
In $\triangle BDE$ and $\triangle CDE$, $BD = CD$ (from $\triangle ABD\cong\triangle ACD$), $BE = CE$ (from $\triangle ABE\cong\triangle ACE$), and $DE = DE$ (common side). By the Side - Side - Side (SSS) congruence criterion, $\triangle BDE\cong\triangle CDE$.
## Step4: Use the property of congruent triangles
Since $\triangle BDE\cong\triangle CDE$, then $\angle BDE\cong\angle CDE$ (corresponding parts of congruent triangles are congruent).

# Answer:
$\angle BDE\cong\angle CDE$ is True.

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QUESTION IMAGE

Question

Explanation:

Step1: Use the property of congruent triangles

Step2: Prove \(\triangle ABD\cong\triangle ACD\)

Step3: Prove \(\triangle BDE\cong\triangle CDE\)

Step4: Use the property of congruent triangles

Answer: