Question

given: ∠a≅∠e, (overline{ac}congoverline{ec}) prove: (\triangle cadcong\triangle ceb)

Explanation:

Step1: State given information

We are given $\angle A\cong\angle E$ and $\overline{AC}\cong\overline{EC}$.

Step2: Identify vertical angles

$\angle ACD$ and $\angle ECB$ are vertical angles, so $\angle ACD\cong\angle ECB$.

Step3: Apply congruence criterion

With $\angle A\cong\angle E$, $\overline{AC}\cong\overline{EC}$ and $\angle ACD\cong\angle ECB$, by ASA criterion, $\triangle CAD\cong\triangle CEB$.

Answer:

1. $\angle A\cong\angle E$, $\overline{AC}\cong\overline{EC}$ - Given
2. $\angle ACD\cong\angle ECB$ - Vertical angles are congruent
3. $\triangle CAD\cong\triangle CEB$ - Angle - Side - Angle (ASA) congruence criterion