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G-CO.3 Warmup M1-038-A10-V01

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

Find the smallest positive rotation of a regular polygon

Problem

Find the smallest positive rotation that maps a regular \(3\text{-}\text{gon}\) onto itself.

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What this problem is really about

The smallest positive rotational symmetry moves each vertex to the nearest next vertex position. Equal central sectors partition a full turn, so divide the full angle by the number of sides and verify that any smaller turn would leave every vertex between valid positions.

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Four variants of this problem type
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
Find the smallest positive rotation of a regular polygon