copolar triangles | homologic triangles | homologous triangles

Two triangles Δ A B C and Δ A' B' C' are said to be perspective, or sometimes homologic, from a line if the extensions of their three pairs of corresponding sides meet in collinear points X, Y, and Z. The line joining these points is called the perspectrix. Two triangles are perspective from a point if their three pairs of corresponding polygon vertices are joined by lines which meet in a point of concurrence O. This point is called the perspector, perspective center, homology center, or pole. Desargues' theorem guarantees that if two triangles are perspective from a point, they are perspective from a line (called the perspectrix). Triangles in perspective are sometimes said to be homologous or copolar.

Cevian point | Cevian triangle | Desargues' theorem | dilation | homothetic triangles | paralogic triangles | perspector