Desargues’ Theorem

Let lines (AA’), (BB’) and (CC’) be three distinct and concurrent lines with D as the common intersection point. Then let

A” = ((BC) (B’C’))

B” = ((AC)(A’C’))

C” = ((AB)(A’B’))

the three intersection points of pairs of corresponding lines as indicated (assuming none are parallel lines).

Then A”, B”, and C” are collinear.

Cinderella

Geometer’s Sketchpad

KSEG