Constructing a Square

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Use a dynamic software tool to construct a square in different ways.

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Quadrilateral with Squares on the Sides

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Explore the relationship of the two line segments formed by connecting the centers of the squares on the opposite sides of the quadrilateral.

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Quadrilateral with Maximum Area

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Find a quadrilateral with maximum area given a fixed angle and two fixed line segments.

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Maximum Quadrilateral

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Given three fixed line segments, find a fourth line segment so that the resulting quadrilateral formed by the four segments has maximum area.

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Inscribed Quadrilateral

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Do the angle bisectors of the opposite sides of an inscribed quadrilateral meet at right angles?

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Four Dogs

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Explore the paths of four dogs who each start moving from a different vertex of a square.

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Paper Folding

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Fold a sheet of paper into three equal areas.

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Inscribed Rectangle

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Find the inscribed rectangle with maximum area for a given triangle.

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Inscribed Square

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Find inscribed squares for a given triangle.

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Cutting the Cake

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Cut a square cake into n pieces so that all the pieces have equal amounts of cake and equal amounts of frosting.

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