1965 AMC 12 第 25 题

Because $AB=BE,$ point $B$ is the midpoint of $AE$

In a right triangle, the midpoint of the hypotenuse is equidistant from all three vertices

If $\angle ACE=90^\circ,$ then $AE$ is the hypotenuse of right triangle $ACE.$ Its midpoint $B$ is equidistant from $A,C,E.$ Thus $AB=BC,$ so quadrilateral $ABCD$ necessarily has at least one pair of equal sides. No condition involving $D$ follows.

Therefore, the correct answer is D.