Question

given B is the midpoint of line CE, Angle C is congruent to angle E. prove angle a is congruent to angle D ​

Answer 1

see below

Explanation:

The ASA congruence postulate is being invoked, so you're looking to show two angles and the side between them are congruent.

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Personally, I'd go at it differently. I'd say that alternate interior angles ∠C≅∠E means AE║CD, so ∠A≅∠D because they're alternate interior angles. B does not need to be a midpoint for this proof.