Pappus' Theorem
If the vertices P1, P2, P3, P4, P5, P6 of a hexagon P1P2P3P4P5P6 lie alternately on a pair of lines, then the three intersections E, F, and G of the opposite sides P1P2 and P4P5, P2P3 and P5P6, P3P4 and P6P1 of the hexagon are collinear.