Question

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

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

D.

A regular n-gon has rotational symmetries by multiples of 360°/n. A 180° rotation is one of those iff 180° = m·(360°/n) for some integer m, i.e. m = n/2, so n must be even. (Example: square works, regular pentagon does not.)