## Desargues' Theorem

Two triangles are *point perspective*, if and only if, they are *line perspective*.

Desargues' Theorem

For a proof read my joint paper with Mary Garner *Problemsolving and proving via generalization*

With Desargues' theorem, one can easily prove the concurrency of the medians as shown at *Concurrency of medians with Desargues*

The theorem is also applied several times in Michael Fox's proof of the BMO-Brianchon corollary at *A British Math Olympiad problem and its dual*

Desargues' Theorem also beautifully displays the projective duality between "*points*" and "*lines*", and between "*collinearity*" and "*concurrency*". Do a Google search to read up more on "*projective duality*".

For a poem of mine written many years ago related to the topic of duality, go to *Duality*

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Last modified, Michael de Villiers, 31 October 2010.