If a 2-D 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

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