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Parallelogram?

© Copyright 2002, Jim Loy

Start with any general quadrilateral, and connect the midpoints of consecutive sides, making an inscribed quadrilateral as in the diagram. That inscribed quadrilateral, in the diagram, seems to be a parallelogram. Let me conjecture that this inscribed quadrilateral is a parallelogram with half the area of the original quadrilateral. Can you prove or disprove either part of my conjecture?

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