Varignon Parallelogram of a Quadrilateral Definition
A Varignon Parallelogram of a Quadrilateral is a parallelogram formed by connecting the midpoints of adjacent sides of a quadrilateral.
Properties
A planar Varignon Parallelogram also has the following properties:
Each pair of opposite sides of the Varignon parallelogram are parallel to a diagonal in the original quadrilateral.
A side of the Varignon parallelogram is half as long as the diagonal in the original quadrilateral it is parallel to.
The area of the Varignon parallelogram equals half the area of the original quadrilateral. This is true in convex, concave and crossed quadrilaterals provided the area of the latter is defined to be the difference of the areas of the two triangles it is composed of.
The perimeter of the Varignon parallelogram equals the sum of the diagonals of the original quadrilateral.
The diagonals of the Varignon parallelogram are the bimedians of the original quadrilateral.
The two bimedians in a quadrilateral and the line segment joining the midpoints of the diagonals in that quadrilateral are concurrent and are all bisected by their point of intersection.
Sources
“Varignon's Theorem.” Wikipedia, Wikimedia Foundation, 27 Feb. 2020, en.wikipedia.org/wiki/Varignon's_theorem.
