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Varignon's Theorem

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VarignonsTheorem

Varignon's theorem states that 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 the Varignon parallelogram of a convex quadrilateral is half that of the quadrilateral, and the perimeter is equal to the sum of the diagonals of the original quadrilateral.

See also

Bimedian, Midpoint, Midpoint Polygon, Quadrilateral, Varignon Parallelogram

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References

Coxeter, H. S. M. and Greitzer, S. L. "Quadrangles; Varignon's Theorem." §3.1 in Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 51-56, 1967.

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Varignon's Theorem

Cite this as:

Weisstein, Eric W. "Varignon's Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/VarignonsTheorem.html

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