If the three straight lines joining the corresponding vertices of two triangles perspector ), then the three intersections of pairs of corresponding sides lie on a straight line (the perspectrix ). Equivalently, if two triangles are perspective from a point , they are perspective from a line .
The 10 lines and 10 3-line intersections form a configuration sometimes called Desargues' configuration .
Desargues' theorem is self-dual .
See also Desargues' Configuration ,
Duality Principle ,
Pappus's Hexagon Theorem ,
Pascal Lines ,
Pascal's Theorem ,
Perspector ,
Perspective Triangles ,
Perspectrix ,
Self-Dual Explore with Wolfram|Alpha References Coxeter, H. S. M. The Beauty of Geometry: Twelve Essays. Coxeter, H. S. M. and Greitzer, S. L. "Perspective Triangles; Desargues's Theorem." §3.6 in Geometry Revisited. Durell, C. V. Modern Geometry: The Straight Line and Circle. Eves, H. "Desargues' Two-Triangle Theorem." §6.2.5 in A Survey of Geometry, rev. ed. Graustein, W. C. Introduction to Higher Geometry. Ogilvy, C. S. Excursions in Geometry. Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. Referenced on Wolfram|Alpha Desargues' Theorem Cite this as: Weisstein, Eric W. "Desargues' Theorem." From MathWorld https://mathworld.wolfram.com/DesarguesTheorem.html
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all meet in a point (the perspector), then the three intersections of pairs of corresponding sides lie on a straight line (the perspectrix). Equivalently, if two triangles are perspective from a point, they are perspective from a line. 
configuration sometimes called Desargues' configuration. 