# Four midpoints of any quadrilateral form a parallelogram.

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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#### 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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