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Quadrilateral with Squares on the Sides

Given any quadrilateral, construct a square and locate its center on each side of the quadrilateral. Explore the relationship of the two segments defined by connecting the centers of squares on the opposite sides of the quadrilateral.



Do your conjectures hold if the quadrilateral is not convex? Explore.

Suppose the Quadrilateral is a parallelogram. What additional conjectures and proofs can you find?

Extension: Consider also a quadrilateral formed by the centers of the four squares.

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