AE and EC are congruent because it's given that E is the midpoint of AC. However, DE and EB cannot be congruent because it does not state that point E is the midpoint of DB.
You cannot assume that all the triangles DEA, AEB, BEC, and CED are all congruent just from being given that E is the midpoint of AC. You would need to be given other information such as "Quadrilateral ABCD is a parallelogram. "
