In a quadrilateral, the two sides are parallel and the diagonals are mutually perpendicular. Prove that the other two sides are equal.
Mutual perpendicularity of the diagonals is possible only if they divide the corresponding angles in half. If the two sides are parallel in terms of the conditions, then the above is possible only if the other two sides are also parallel to each other. If the opposite sides are parallel, and the angles of the opposite vertices are also equal, then all sides of the quadrilateral are equal to each other, including those about which is asked in the conditions.
A square and a rhombus have similar properties.
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