SOLUTION: How do I go about proving that if a parallelogram is inscribed within a circle, then the parallelogram is a rectangle?

Question 412570: How do I go about proving that if a parallelogram is inscribed within a circle, then the parallelogram is a rectangle?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
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.
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