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# Perspective Triangles

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.

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

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## References

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.

## Referenced on Wolfram|Alpha

Perspective Triangles

## Cite this as:

Weisstein, Eric W. "Perspective Triangles." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PerspectiveTriangles.html