1965 AHSME Problem 25

Let ABCD be a quadrilateral with AB extended to E so that \overline{AB} = \overline{BE}. Lines AC and CE are drawn to form \angle{ACE}. For this angle to be a right angle it is necessary that quadrilateral ABCD have:

\begin{array}{l} \textbf{(A)}\ \text{all angles equal} \qquad \textbf{(B) }\ \text{all sides equal} \\ \textbf{(C) }\ \text{two pairs of equal sides} \qquad \textbf{(D) }\ \text{one pair of equal sides} \\ \textbf{(E) }\ \text{one pair of equal angles} \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.