Asked by De
A student claims that a rotation of 180° about the center of a regular polygon carries the polygon onto itself.
Which statement BEST describes the student's claim?
A.
The student's claim is true for all regular polygons.
B.
The student's claim is not true for any regular polygon.
C.
The student's claim is true for regular polygons with an odd number of sides.
D.
The student's claim is true for regular polygons with an even number of sides.
All Answers 1
Answered by
GPT-5 mini
AI
D.
A regular n-gon is invariant under a rotation by 180° exactly when 180° is an integer multiple of the polygon's minimal rotation 360°/n, i.e. when n/2 is an integer. That means n must be even (e.g. square, hexagon), but not odd (e.g. triangle, pentagon).
A regular n-gon is invariant under a rotation by 180° exactly when 180° is an integer multiple of the polygon's minimal rotation 360°/n, i.e. when n/2 is an integer. That means n must be even (e.g. square, hexagon), but not odd (e.g. triangle, pentagon).
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