a student claims that a rotation of 180 degree about the center of a regular polygon carries the ploygon onto itself. Which statement BEST describes the student's claim?

Question

a. he student's claim is true for regular polygons with an odd number of sides
b. he student's claim is not true for any regular polygons
c. he student's claim is true for all regular ploygons
d. The student's claim is true for regular polygon with an even number of sides

Answer 1

The student's claim that a rotation of 180 degrees about the center of a regular polygon carries the polygon onto itself is indeed true. A rotation of 180 degrees will position opposite vertices to be in the same location, effectively mapping the polygon onto itself regardless of the number of sides it has.

Thus, the best statement that describes the student's claim is:

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

This is because both even and odd regular polygons exhibit the same rotational symmetry at a 180-degree rotation about their center.