What is the relationship between similar regular polygons?

[Miike012]

Homework Statement

I am reading this trig book and it is saying that if both are reg polygons ( I am assuming they would have to have the same sides) that they are ratios of one another...
I would like to read more on this so I understand it better... is there a link anywhere that someone can post in hjere? thank yoiu..

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

Saying that they are "regular polygons" means that all the sides of one (and all angles) are equal. It does NOT mean that the lengths of the sides of one polygon are equal to the lengths of sides of the other.

Yes, as you say, it is necessary that the two polygons have the same number of sides!

Now, divide the two polygons into triangles by drawing the lines from one vertex to all the other vertices. Even though the sides may have different lengths, the angles in the two polygons are equal so you will have divided the two polygons into triangles that have different length side but the same angles: "similar" triangles.

And, it is an important theorem of geometry that similar triangles have corresponding sides in a constant ratio.