Reflectional Symmetry: Definition & Examples

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  • 0:00 What Is Reflectional…
  • 1:31 Examples Of…
  • 2:10 Reflectional Symmetry…
  • 2:38 Symmetry In Graphs And Math
  • 2:55 Lesson Summary
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Lesson Transcript
Instructor: Beverly Maitland-Frett

Beverly has taught mathematics at the high school level and has a doctorate in teaching and learning.

Reflectional symmetry can be found in geometric figures, math, nature and the man-made world. In this lesson, we'll explore the characteristics that define reflectional symmetry, as well as some everyday examples.

What Is Reflectional Symmetry?

What if you took a picture of yourself, particularly a passport type photograph, and drew a line straight down the middle of your face, from your forehead down to your chin? What would you notice? Wouldn't it seem as if one side of your face was a reflection of the other? For example, there would be an eye on each side. Both halves of your lips would look nearly identical. Unless you'd suffered some type of injury, both halves of your nose would look the same.

Ideally, your hypothetical passport photo is just one example of reflectional symmetry, also known as bilateral, line, or mirror symmetry. The line you drew to divide your face is called the line of symmetry.

However, since humans have uncontrollable differences, our faces may not always count as examples of reflectional symmetry. For instance, some of us may have a beauty spot on one side; others may have a scar. If you look closely in a mirror, you may notice that one of your eyes is a little smaller than the other. Many aspects of human appearance may distort the notion of true reflectional symmetry; therefore, reflectional symmetry must satisfy certain conditions.

Reflectional symmetry occurs when a line is used to split an object or shape in halves so that each half reflects the other half. Sometimes objects or shapes have more than one line of symmetry. Take, for instance, the letter H. How many lines of symmetry does it have? If you answered two, you are correct. There are two ways to draw a line so that each half reflects the other half.

Examples of Reflectional Symmetry

Many letters of the alphabet have reflectional symmetry. Some use a vertical line; some use a horizonatal line. Geometric shapes can also demonstrate reflectional symmetry, such as circles and squares, which have four lines of symmetry. Depending on the type of triangle, one may have zero, one or three lines of symmetry.

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