# Polygons defined by lengths of sides

Can a polygon be defined by the lengths of its sides?

In other words, if given the lengths of the sides of a polygon, is there a way to figure out what polygon has those lengths and show that there is only one such polygon?

I know that this is true for triangles because of the SSS Congruence Theorem. If two triangles can be proven congruent by having the same sides, there must be only one way to make a triangle if given side lengths.

It seems like this should work for every type of polygon, but it would be great if anyone could provide proof of this.

• Since the case of triangles is already understood (triangles are "rigid"), I'd suggest considering the next simplest case, that of quadrilaterals. – hardmath Dec 10 '18 at 5:36
• You can't do that even for a quadrilateral with all sides of length $1$. However, if we restrict ourself to cyclic polygons, there is at most one cyclic polygon with given side lengths in given order. – achille hui Dec 10 '18 at 5:41