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. Referenced
on Wolfram|Alpha Varignon's Theorem
Cite this as:
Weisstein, Eric W. "Varignon's Theorem."
From MathWorld https://mathworld.wolfram.com/VarignonsTheorem.html
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