Reflectional Symmetry

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K-12: Materials at high school level.

If points of a figure are equally positioned about a line, then we say the figure has reflection symmetry, or sometimes mirror symmetry. The line is called the reflection line, the mirror line, or the axis of symmetry. The axis of symmetry separates the figure into two parts, one of which is a mirror image of the other part.

The simplest case of reflection symmetry is known as bilateral symmetry. For example, each of the following figures exhibits bilateral symmetry:


The heart and smiley each have a vertical axis of symmetry, and the lobster has a horizontal axis of symmetry. The arrow has an axis of symmetry at an angle. If you draw the reflection line though any one of these figures, you will notice that for every point on one side of the line there is a corresponding point on the other side of the line. If you connect any two corresponding points with a segment, that segment will be perpendicular to the axis of symmetry and bisected by it (cut into two equal length segments):


Bilateral symmetry is the most common type of symmetry found in nature, occurring in almost all animals and many plants. Congnitive research has shown that the human mind is specially equipped to detect bilateral symmetry [1]. In fact, humans are especially good at detecting bilateral symmetry when the axis of symmetry is oriented vertically. As you proceed through this course, you will look for symmetry in all sorts of complicated images. Remember that your eyes are hard wired to do this well when the axis is vertical, and so it will be a tremendous help to rotate the images (or your head) as you look for symmetries.

Some objects or images can have more than one axis of reflection symmetry. Here are some examples, with the reflection axes shown as dotted red lines:


Pay special attention to the diagonal reflection axes in the cross. These are easy to overlook, and occur frequently.