A student claims that a rotation of 180°

Question

180
°
about the center of a regular polygon carries the polygon onto itself. Which statement BEST describes the student's claim?(1 point)
Responses

The student's claim is not true for any regular polygons.
The student's claim is not true for any regular polygons.

The student's claim is true for regular polygons with an even number of sides.
The student's claim is true for regular polygons with an even number of sides.

The student's claim is true for regular polygons with an odd number of sides.
The student's claim is true for regular polygons with an odd number of sides.

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

Answer 1

The best description of the student's claim is:

The student's claim is true for regular polygons with an even number of sides.

For regular polygons with an even number of sides, rotating 180° about the center will map each vertex onto another vertex, so the polygon is carried onto itself. However, for regular polygons with an odd number of sides, a 180° rotation will not carry the polygon onto itself, as it will not map vertices to vertices in the same way.