Question

ac≅ac
△abc≅△cda
∠bca≅∠cad
∠bec≅∠dea
△bce≅△dae
note: ac and b
attempt 2 out of 2
reflexive property
sss
vertical angles are congruent
vertical angles are congruent
search for reasons
reflexive property
transitive property
substitution
corresponding parts of congruent triangles are congruent (cpctc)
vertical angles are congruent
if two angles are complements of the same angle (or congruent angles), then they are congruent
if two angles are supplements of the same angle (or congruent angles), then they are congruent
all right angles are congruent

Explanation:

Step1: Identify given congruences

We know that $\angle BCA\cong\angle CAD$ and $\angle BEC\cong\angle DEA$. Also, we assume there is some side - length relationship (not shown fully in the problem but for triangle congruence we need side - angle - side, angle - side - angle etc. conditions). Since we have two pairs of congruent angles and we can assume (from the context of triangle congruence) that there is a pair of congruent sides (perhaps by previous congruences like $\triangle ABC\cong\triangle CDA$ which gives us some equal side - lengths that can be used here).

Step2: Apply congruence postulate

The Angle - Angle - Side (AAS) or Angle - Side - Angle (ASA) congruence postulates can be used. If we have two pairs of congruent angles and a non - included (AAS) or included (ASA) side congruent respectively, we can prove $\triangle BCE\cong\triangle DAE$. In this case, since we have two pairs of angles congruent and we can infer the side - length relationship from previous congruences in the figure, we use the AAS or ASA postulate.

Answer:

The reason for $\triangle BCE\cong\triangle DAE$ could be Angle - Angle - Side (AAS) or Angle - Side - Angle (ASA) depending on the side - length relationships established from previous congruences in the figure.