A derived polygon with side ratios chosen as so that inscribed polygons are constructed by connecting the midpoints of the base polygon. For a triangle , the midpoint-inscribed polygons , , ... are similar triangles. For a quadrilateral , the midpoint-inscribed polygon is a parallelogram known as the Varignon parallelogram, and , , , ... are similar parallelograms, as are , , , ....

# Midpoint Polygon

## See also

Derived Polygon, Midpoint, Varignon Parallelogram, Varignon's Theorem## Explore with Wolfram|Alpha

## References

Tischel, G. "Ein Konvergenzsatz für Mittenpolygone."*Mitt. Math. Ges. Hamburg*

**18**, 169-184, 1999.

## Referenced on Wolfram|Alpha

Midpoint Polygon## Cite this as:

Weisstein, Eric W. "Midpoint Polygon."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/MidpointPolygon.html