WATCH: Symmetry Videos

Line/Reflectional Symmetry

Example 1

Rotational Symmetry

Example 1

Point Symmetry

Point Symmetry

A plane (two-dimensional) figure has point symmetry if the reflection (in the center) of every point on the figure is also a point on the figure.

A figure with point symmetry looks the same right side up and upside down; it looks the same from the left and from the right. Therefore if you can rotate the image 180^o and it is the same image, it has point symmetry.

The figures below have point symmetry.

Note that all segments connecting a point of the figure to its image intersect at a common point called the center.

Point symmetry is a special case of rotational symmetry.

• If a figure has point symmetry it has rotational symmetry.
• The converse is not true. If a figure has rotational symmetry it may, or may not, have point symmetry.

Many flowers have petals that are arranged in point symmetry. (Keep in mind that some flowers have petals. They do not have point symmetry. See the next example.)

Here is a figure that has rotational symmetry but not point symmetry.