Varignon's Theorem
VarignonsTheorem
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 ParallelogramExplore with Wolfram|Alpha
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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.Referenced on Wolfram|Alpha
Varignon's TheoremCite this as:
Weisstein, Eric W. "Varignon's Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/VarignonsTheorem.html