Perspective Triangles


Two triangles DeltaABC and DeltaA^'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.

See also

Cevian Point, Cevian Triangle, Desargues' Theorem, Dilation, Homothetic Triangles, Paralogic Triangles, Perspector

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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.

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Perspective Triangles

Cite this as:

Weisstein, Eric W. "Perspective Triangles." From MathWorld--A Wolfram Web Resource.

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