If a 2D figure or shape is rotated (or turned) around a point by a certain angle and looks the same as the original figure or shape then it has a rotation symmetry.
In this tutorial you will explore the rotation symmetry of regular polygons.
Interactive Tutorial (Answers to questions in this tutorial are located at the bottom of this page).
1  Press the button above to start the applet.
2  Use the top slider to set n, the number of sides of the regular polygon, to 3 to have an equilateral triangle. Use the slider " angle of rotation" to rotate the triangle. Note the smallest angle for which the two triangles, the blue which is the original one and the red (after rotation) are in the same position.
3  Repeat activity 3 above for n = 4, 5, 6 ....
4  What is the smallest angle of rotation for which two regular polygons with sides n have the same position? Find a formula.
Answers to Above Questions
Answer to question in part 2: angle of rotation for equilateral triangle is equal to 120 degrees.
Answer to questions in part 3:
n   angle of rotation

4   90 degrees 
5   72 degrees 
6   60 degrees 
Answer to questions in part 4: angle of rotation = 360 / n.
More geometry references
Geometry Tutorials, Problems and Interactive Applets.