Reflectional Symmetry

K-12: Materials at high school level.

If one side of the image is the mirror image of the other side, then we say the figure has reflectional symmetry. Sometimes we would say that the image has a mirror line. Here we have some images from real life that have such mirror lines. The image on the left is McCarren Park Pool in New York. The red line in the center was added to show you where the mirror line is located. You will have to ignore the man in the picture.

The next image is a piece of a Persian rug. Here again you can see that the left side is an exact mirror image of the right hand side. The bug right next to it also has a vertical mirror line, and the left side is a mirror image of the right side. The image of the ducks shows that the mirror line can also run in other directions. In the duck picture the mirror line runs from left to right.

McCarren Park Pool	A rug	A Beetle	Ducks

To make the idea of symmetry a bit more precise, we would say that if points of a figure are equally positioned about a line, then the figure has reflection symmetry. Note that mirror symmetry is just another word for reflection symmetry. You can use either one of these terms. The line is known by several different names. Sometimes it's called the reflection line, others may call it the mirror line, or the axis of symmetry. The important part to remember is that this line separates the figure into two parts, one of which is a mirror image of the other part.

Here are several more examples of this mirror symmetry:

The heart and smiley each have a vertical mirror line, and the lobster has a horizontal mirror line. The arrow has a mirror line at an angle. If you draw the mirror 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):

Mirror or reflection symmetry is the most common type of symmetry found in nature, occurring in almost all animals and many plants. Scientists have shown that our brain is rather good at recognizing this type of symmetry. [1]. In fact, people are especially good at detecting mirror symmetry when the mirror line is oriented vertically (up-down). 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 big help to turn the images (or your head) as you look for symmetries. Try this with the picture of the ducks for instance: turn your head to the right and the look at the picture again. Do you notice the mirror line even more?

Some objects or images can have more than one mirror line. Here are some examples, with the mirror lines shown as dotted red lines:

Pay special attention to the diagonal mirror lines in the cross. These are easy to miss, and do show up quite often.