Problem preview

G-CO.3 Warmup M1-038-A09-V04

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

Compare the symmetries of related quadrilaterals

Problem

Compare a square with a non-square rhombus. For each, identify reflection-axis count/types and nonzero rotation angles below \(360°\); then identify the square-only symmetries.

Clean source shape or proposed symmetry without the requested conclusion.

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square = 4 axes, rotations 180°; rhombus = 2 axes, rotations 180°; square-only = 2 diagonal axes

square = 2 diagonal axes, rotations 180°; rhombus = 4 axes, rotations 90°,180°,270°; square-only = none

square = 4 axes, rotations 90°,180°,270°; rhombus = 4 axes, rotations 90°,180°,270°; square-only = none

square = 4 axes (2 diagonals, 2 opposite-side-midpoint axes), rotations 90°,180°,270°; non-square rhombus = 2 axes (its diagonals), rotations 180°; square-only = 2 opposite-side-midpoint axes and rotations 90°,270°

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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: Compare the symmetries of related quadrilaterals