Varignon's Theorem (original) (raw)
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The figure formed when the midpoints of the sides of a convex quadrilateral are joined in order is aparallelogram. 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." ยง3.1 in Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 51-56, 1967.
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Cite this as:
Weisstein, Eric W. "Varignon's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/VarignonsTheorem.html