Varignon's Theorem

Author

Eric W. Weisstein
March 20, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneGeometry/VarignonsTheorem.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/VarignonsTheorem.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Initialization

<<PlaneGeometry`

Graphic

q=Quadrilateral[{{0,0},{.8,.1},{1.2,.5},{.2,.8}}];
Show[Graphics[{
q,
EqualSideTicksAboutMidpoints[q,.015,.02],
{Red,mq=MidpointPolygon[q]}
}],
AspectRatio->Automatic]

p=Table[Random[],{4},{2}]

pp=ConvexPolygon[p]/.Polygon:>Identity;
b=Flatten[Bimedians[pp]/.Line:>Identity,1][[{1,3,2,4}]];

Show[Graphics[{
polygon[pp],
Bimedians[pp],
{Dashing[{.02,.02}],polygon[b]}
}],AspectRatio->Automatic]