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.

Move any of the six points, P1, P2, P3, P4, P5, P6. What do you notice about points E, F, and G? Is this always true? Are there exceptions?