Varignon's theorem

The set of Varignon describes the geometry of a property of quadrilaterals. It is named after Pierre de Varignon ( 1654-1722 ).

• 2.1 Scope of the Varignon parallelogram
• 2.2 area of ​​the parallelogram Varignon

Formulation

If one connects the centers of adjacent sides of a square, then you get a parallelogram.

Evidence

Prerequisite

Assertion

The quadrilateral EFGH is a parallelogram.

Passage of the proof

The opposed sides of the quadrilateral EFGH in parallel, which corresponds to the definition of a parallelogram.

Conclusions

Perimeter of the parallelogram Varignon

The scope of the Varignon parallelogram is exactly as large as the sum of the diagonals in the origin square.

Area of ​​the parallelogram Varignon

The area of ​​the parallelogram Varignon is half as large as the area of the original quadrangle.