Symmetry and Transformations Question
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Grade 11 Symmetry and Transformations CCSS: HSG-CO.A.3
Liam notices that there seems to be a pattern when looking at regular polygons and the number of rotations each figure has that will carry it onto itself. For a regular triangle, these angles will map the shape onto itself: 120°, 240°, 360°. For a square, these angles will map the shape onto itself: 90°, 180°, 270°, 360°. For a pentagon, these angles will map the shape onto itself: 72°, 144°, 216°, 288°, 360°. If this pattern continues, what will the angles of rotation be for an n-sided polygon that map it onto itself?
- 360°n, (2⋅360°n), ..., (n⋅360°n)
- There is no pattern.
- (360°-60°⋅n), (360°-60°⋅(n2)),..., 360°
- n⋅60°, n⋅80°,..., 360°