Question

given:
∠e ≅ ∠a
overline{ep} ≅ overline{an}
△can ≅ △__ by__

Explanation:

Step1: Analyze vertical angles

$\angle ECP=\angle ACN$ (vertical angles are congruent).

Step2: Apply congruence criterion

We are given $\angle E\cong\angle A$ and $\overline{EP}\cong\overline{AN}$. With $\angle ECP=\angle ACN$, by the Angle - Angle - Side ($AAS$) congruence criterion, $\triangle CAN\cong\triangle CEP$.

Answer:

$\triangle CEP$; $AAS$