Two triangles and 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 , , and . 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 . 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.

Coxeter, H. S. M. and Greitzer, S. L. "Perspective Triangles; Desargues's Theorem." §3.6 in Geometry
Revisited. Washington, DC: Math. Assoc. Amer., pp. 70-72, 1967.Lachlan,
R. "Triangles in Perspective" and "Relations Between Two Triangles
in Perspective." §160-180 in An
Elementary Treatise on Modern Pure Geometry. London: Macmillian, pp. 100-113,
1893.