Question

Why are two regular polygons that have the same number of sides similar?

Answer 1

because the degree of each angle is the same as the corresponding angle on the other polygon does this help?

Answer 2

in other words they both have the same shape though their size might be different

Answer 3

Because of the following properties:
1. ANY \(regular\) polygon of any number of sides has equal sides and equal interior angles.
2. So ALL polygons of the same number of sides have equal interior angles.
3. and ALL polygons of the same number of sides have sides that are equal within each polygon, proportional with others.