Let P be a Convex hexagon that all is angles are on the same size. I want to show that every pair of opposing edges has the same difference (if one edge is in the size $x$ and it's opossing edge is of the size $y$, i want to show that $|x-y|$ is a constant).
Can someone give me a hint on how to do that?
Thanks.
If you set the parallel sides as a,A and b,B, etc, it is possible to reduce this to a pentagon by reducing the sides by a, b, c. The polygon remains closed, so one gets a hexagon whose opposite sides are a-a and A-a.
This is still a closed polygon with three non zero sides and equal angles, hence A-a= B-b =C-c.