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 student's claim is that a rotation of \(180^\circ\) about the center of a regular polygon carries the polygon onto itself.

To analyze this claim, we can consider the properties of regular polygons:

1. A regular polygon is symmetric, meaning that rotating it by a certain angle will align it with its original shape.
2. For any regular polygon (whether it has an odd or even number of sides), rotating it by \(180^\circ\) will result in a configuration that overlaps perfectly with the original shape.

Thus, the rotation of \(180^\circ\) will always result in the same polygon, regardless of whether the polygon has an odd or even number of sides.

Therefore, the BEST statement that describes the student's claim is:

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