>>14085996I found a way to prove that it's not in the middle. Remove the lower diagonal side of the triangle. Then move the lower end of the vertical line to the right (the upper end stays where it is) in such a way that the line now divides the bottom side of the pentagon into the same ratio as the line marked with "x" does with the right lower diagonal side of the pentagon. If the upper-left corner of the triangle was coincident with the middle of the upper-left side of the pentagon, by symmetry the line that you moved would have the same length as the line marked with "x" but this is not the case because by moving the lower end of the line you made that line longer.
