Desargues' Theorem
If the three straight Lines joining the corresponding Vertices of twoTriangles 
and 
all meet in a point (the Perspective Center), then the threeintersections of pairs of corresponding sides lie on a straight Line (the Perspective Axis). Equivalently,if two Triangles are Perspective from a Point, they arePerspective from a Line.
Desargues' theorem is dual to Pappus's Hexagon Theorem according to the Duality Principle of ProjectiveGeometry.
See also Duality Principle, Pappus's Hexagon Theorem, Pascal Line, Pascal's Theorem,Perspective Axis, Perspective Center, Perspective Triangles
References
Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 70-72, 1967. Ogilvy, C. S. Excursions in Geometry. New York: Dover, pp. 89-92, 1990.
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