Make AC midpoint O, connect OB, OE and OD, and use the median line on the hypotenuse of a right triangle equal to half of the hypotenuse to get OB=OD. Because e is the midpoint of BD, there are OE⊥BD and AE⊥BD, so there are two intersecting straight lines in the vertical plane of BD, so there is BD⊥ AEC, so there is AEC⊥.

As for the congruence of a triangle, it can be proved by the hypotenuse right angle theorem, that is, the "HL" theorem.