I love constructing Desargues' Theorem for some reason.
Geogebra offered a very neat and easy way to make it. I will be modifying it but for now play around with my first attempt.
Here is a version I created with Sketchpad
[url]http://mste.illinois.edu/dildine/sketches/desargues.htm[/url]
But here are other sites with better descriptions and more interactive drawings:
[url]http://aleph0.clarku.edu/~djoyce/java/round/desargues.html[/url]
[url]http://www.geom.uiuc.edu/~banchoff/mongepappus/MP.html[/url]
[url]http://mathworld.wolfram.com/DesarguesTheorem.html[/url]
[url]http://en.wikipedia.org/wiki/Desargues'_theorem[/url]
[url]http://www.cut-the-knot.org/Curriculum/Geometry/Desargues.shtml[/url]