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Line 5: ==Theorem== The ~~midpointes~~midpoints of the sides of an arbitrary quadrilateral form a parallelogram. If the quadrilateral is [[convex polygon\|convex]] or [[concave polygon\|concave]] (not [[Quadrilateral#Complex_quadrilaterals\|complex]]), then the area of the parallelogram is half the area of the quadrilateral. If one introduces the concept of oriented areas for [[Polygon\|''n''-gons]], then this area equality also holds for complex quadrilaterals.<ref name=Coxeter>[[Coxeter\|Coxeter, H. S. M.]] and Gritzer, S. L. "Quadrangle; Varignon's theorem" §3.1 in Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 52–54, 1967.</ref>

Varignon's theorem: Difference between revisions