Varignon's theorem is a statement in Euclidean geometry by Pierre Varignon that was first published in 1731. It deals with the construction of a particular parallelogram (Varignon parallelogram) from an arbitrary quadrangle.
- The midpoints of the sides of an arbitrary quadrangle form a parallelogram. If the quadrangle is convex or reentrant, i.e. not a crossing quadrangle, then the area of the parallelogram is half as big as the area of the quadrangle.
If one introduces the concept of oriented areas for n-gons, then the area equality above holds for crossed quadrangles as well.
The Varignon parallelogram exists even for a skew quadrilateral, and is planar whether or not the quadrilateral is planar.
Read more about Varignon's Theorem: Special Cases, Proof, See Also
Famous quotes containing the word theorem:
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)