Question

Does a regular nonagon have point symmetry?

Answer 1

Yes, a regular nonagon (a nine-sided polygon with all sides and angles equal) does have point symmetry. Point symmetry means that for every point in the shape, there is a corresponding point that is equidistant from the center but in the opposite direction.

In a regular nonagon, if you draw a line through the center of the nonagon, you can find pairs of points (such as vertices and midpoints of edges) that are opposite each other. This property allows the nonagon to retain its shape even if rotated 180 degrees around its center.

Additionally, since it has an odd number of sides, every vertex corresponds with another point (which may be either a vertex or a mid-edge point) that lies directly opposite to it through the center, confirming the point symmetry property.