Problem preview

G-CO.3 Warmup M1-038-A07-V04

Describe rotations and reflections that carry rectangles, parallelograms, trapezoids, or regular polygons onto themselves.

List all symmetries of a regular polygon

Problem

List every symmetry of a regular pentagon, counting the identity as the \(0°\) rotation. Give the rotations, reflection-axis types and counts, and total number of symmetries.

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rotations = 0°,72°,144°,216°,288°; reflection axes = 5 vertex-to-opposite-side-midpoint axes; total symmetries = 10

rotations = 72°,144°,216°,288°; reflection axes = 5; total = 9

rotations = 0°,72°,144°; reflection axes = 2; total = 5

rotations = 0°,60°,120°,180°,240°,300°; reflection axes = 6; total = 12

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Curriculum context

Course: Math I
Standard: G-CO.3
Category: Geometry
Domain: Congruence
Objective: Describe rotations and reflections that carry rectangles, parallelograms, trapezoids, or regular polygons onto themselves.
Problem type: List all symmetries of a regular polygon