Varignon's parallelogram

Given any quadrilateral $ABCD$, let $E$, $F$, $G$, and $H$ be the midpoints of $AB$, $BC$, $CD$, and $DA$ respectively. The quadrilateral $EFGH$ formed by joining these midpoints in order is always a parallelogram, regardless of the shape of $ABCD$.

Important properties

• The opposite sides of Varignon's parallelogram are parallel and equal in length.

• The area of Varignon's parallelogram is always half the area of the original quadrilateral.

• If the original quadrilateral is a rectangle, Varignon's parallelogram is a rhombus.