Exploring rotational symmetry of regular polygons - Lesson+Exploration+Practice

A shape has rotational symmetry when it looks the same after some rotation by a partial turn about its center. The order of the rotational symmetry is the number of times a shape can “fit into itself” when it is rotated. Let's explore the order of rotational symmetry of some regular polygons! Use the sides slider to select the number of sides of the polygon, then rotate the polygon using the rotate slider, until the rotated shape overlaps the original one exactly. Complete the full rotation of your polygon, and count the number of times that it overlapped the original one.

How many times has your polygon overlapped the original one, after a full rotation of 360°? Can you relate the number of sides of the polygon and its order of rotational symmetry?

Food for thought...

Now imagine rotating a circle about its center, and consider the definition of rotational symmetry. What is the order of rotational symmetry for a circle?