Question 412570
One property of cyclic quadrilaterals is that if the sum of two opposite angles is 180 degrees, then the quadrilateral is cyclic, and can be inscribed in a circle. In a parallelogram, the two opposite angles are equal, so if they sum up to 180 degrees, the parallelogram is cyclic. This only occurs when the two angles are both 90 degrees. By a symmetry argument, the other two must also be 90 degrees, and the quadrilateral must be a rectangle.