A student claims that a rotation of 180°

Question

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

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

Answer 1

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

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

In detail, a rotation of 180° around the center of a regular polygon will map the vertices onto themselves if the polygon has an even number of sides. For regular polygons with an odd number of sides, a 180° rotation does not map the vertices onto themselves; therefore, the claim is not true for those. However, it is true for those with an even number of sides.