Prove the sum the projections of the sides of a polygon on any line is zero.
I've been trying to learn trigonometry on my own and to develop my math skills when I can across this problem.
I can visualize how the polygon can be constructed from vectors that follow along its perimeter.
These vectors, because they are changing direction and are projected onto a line that has a single direction, would result in the sums of the projections on a line to be zero (I think).
How do I come up with a convincing proof for this problem.