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Connect Midpoints of Sides of Squares to Get Another Square

Source: ILL 1970 - Problem 11.

May 24, 2011
geometryvectorparallelogram

Problem Statement

Let ABCDABCD and A′B′C′D′A'B'C'D' be two arbitrary squares in the plane that are oriented in the same direction. Prove that the quadrilateral formed by the midpoints of AA′,BB′,CC′,DD′AA',BB',CC',DD' is a square.
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