Question

congruent or not congruent? if congruent - name the postulate.

Explanation:

Step1: Identify vertical angles

$\angle DEB$ and $\angle BEA$ are vertical angles, so $\angle DEB=\angle BEA$.

Step2: Check right angles

$\angle C = \angle A=90^{\circ}$.

Step3: Check side - side equality

$CE = AE$ (given).

Step4: Apply congruence postulate

By the Angle - Angle - Side (AAS) congruence postulate, $\triangle DCE\cong\triangle BAE$.

Answer:

Congruent; AAS (Angle - Angle - Side) postulate.