van Aubel's Theorem

Author

Eric W. Weisstein
February 9, 2005

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

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

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

Figure

q=Quadrilateral[{{0,0},{1,-1},{2,-2/10},{11/10,1/2}}];
squares=ErectPolygons[q,4,-1];
polys=Quadrilateral/@Rest/@First/@squares;
centers=Centroid/@polys;
lines=Line/@Transpose[Partition[Coordinates/@centers,2]];
Show[Graphics[{
{
Red,
squares,
{Dashing[{.02}],Diagonals/@polys}
},
{
Blue,
lines,
PerpSquare[lines,.12,3],
PointSize[.02],centers
},
{Thickness[.01],q}
}],AspectRatio->Automatic]

PerpendicularQ@@lines

Equal@@Norm/@Subtract@@@Coordinates/@lines