# Varignon's theorem (Varignon parallelogram)

## Description

The Varigons theorem states that :

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 the area of the quadrangle.

The perimeter of the Varignon parallelogram equals the sum of the diagonals of the original quadrilateral.

## Variables

a | Side of the Varignon parallelogram (m) |

b | Side of the Varignon parallelogram (m) |

c | Side of the Varignon parallelogram (m) |

d | Side of the Varignon parallelogram (m) |

m | One of the diagonals (m) |

n | The other diagonal (m) |