Desargues’ Theorem

https://commons.wikimedia.org/wiki/File:Desargues_theorem_alt.svg

If two triangles ABC and abc are oriented so that lines Aa, Bb, and Cc meet at a point, then the pairs of corresponding sides (AB and ab; BC and bc; and AC and ac) will meet in three collinear points.

The converse is also true: If the pairs of corresponding sides intersect in three collinear points, then the lines joining corresponding vertices will meet in a point.