A student claims that a rotation of 180° about the center of a regular polygon carries the polygon onto itself.

Question

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.

Answer 1

The correct statement that BEST describes the student's claim is:

A. The student's claim is true for all regular polygons.

A rotation of 180° about the center of a regular polygon will map every vertex of the polygon to the vertex directly opposite it. Since all sides and angles are congruent in regular polygons, the polygon will overlap with itself after the rotation, confirming that the claim holds true for any regular polygon, regardless of whether it has an odd or even number of sides.