Perspective (geometry)

Although stated here for figures in a plane, the concept is easily extended to higher dimensions.

[2] An important special case occurs when the figures are triangles.

[4] Desargues' theorem states that a central couple of triangles is axial.

The converse statement, that an axial couple of triangles is central, is equivalent (either can be used to prove the other).

[5] When this happens, the nine associated points (six triangle vertices and three centers) and nine associated lines (three through each perspective center) form an instance of the Pappus configuration.