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Varignon's Theorem

The figure formed when the Midpoints of the sides of a convex Quadrilateral are joined in order is a Parallelogram. Equivalently, the Bimedians bisect each other. The Area of this Varignon Parallelogram is half that of the Quadrilateral. The Perimeter is equal to the sum of the diagonals of the original Quadrilateral.

See also Bimedian, Midpoint, Quadrilateral, Varignon Parallelogram


Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 51-56, 1967.

© 1996-9 Eric W. Weisstein