Desargues' theorem on perspective triangles

Triangles ABCABC and abcabc are said to be in perspective if the joins of corresponding points are concurrent.
[i.e. The lines Aa,Bb,CcAa, Bb, Cc meet at a point.]

For such triangles the meets of corresponding sides are collinear.
[i.e. ABab,ACac,BCbcAB \bigcap ab, AC \bigcap ac, BC \bigcap bc lie on a straight line.]

This can be summarised as:

Triangles which are in perspective from a point are in perspective from a line.

Last Updated August 2020