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

For a regular polygon, when rotated 180° about its center, each vertex is moved to the position directly opposite it. This means that for regular polygons with an even number of sides, the vertices map onto other vertices, keeping the polygon invariant under this rotation.

In contrast, for regular polygons with an odd number of sides, a rotation of 180° will not carry the polygon onto itself because there is no vertex directly opposite any given vertex. Thus, the claim does not hold for odd-sided polygons.

So, the correct statement is: The student's claim is true for regular polygons with an even number of sides.