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    Four midpoints of any quadrilateral form a parallelogram.

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    How can one prove that the 4 midpoints of the four sides of any quadrilateral form the vertices of a parallelogram using graph geometry (ie. x1, y1 etc. to denote the four vertices)?

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    https://brainmass.com/math/geometry-and-topology/midpoints-quadrilateral-form-parallelogram-271892

    Solution Preview

    Label the 4 corners of the quadrilateral
    (x1,y1), (x2,y2), (x3,y3), (x4,y4),

    Note the four midpoints can be connected to make a new quadrilateral, but is it a parallelogram? If it is, then the slopes of the lines of opposite sides have identical ...

    Solution Summary

    Algebraic proof that the four midpoints of the four sides of any quadrilateral form the vertices of a parallelogram.

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