[drizzleRomanceGirl]

Originally Posted by Crashfan3

A square has four equal sides and four equal 90deg angles. A rectangle has four equal 90deg angles, but not necessarily four equal sides. You can't take a rectangle that is 10cm in width and 2cm in height, and expect to come out with two square shapes with four equal sides when you divide it horizontally.

Dividing a hexagon from one vertex to the another directly across from it creates two trapezoids, which have four sides. But a trapezoid's vertices are not the same as a hexagon's, and to divide from one vertex to another will create triangles, because you will be down to three sides. Even if you create a dividing line between the vertexes (on the sides themselves), you will only end up with a four-sided polygon. There is no way to divide a trapezoid with a single line and have the end result be a six-sided shape.

Oh, I think I understand this reasoning. Thank you for explaining.