Broken line, polygon and triangle

If we join segments A₁A₂, A₂A₃, …, Aₙ₋₁Aₙ so that each starts where the previous one ends, and no two neighbouring segments lie on one line, we get a broken line. A₁, …, Aₙ are its vertices and the segments are its links (sides); the sum of the link lengths is the length of the broken line. If a broken line comes back and joins its starting vertex, it is closed. If the links of a closed broken line do not cross one another, the figure is a polygon; with n vertices it is an n-gon (triangle, quadrilateral, pentagon, …). A polygon divides the plane into a bounded interior and an unbounded exterior. A polygon has as many vertices as sides.