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What is Symmetry in Math? - Definition & Concept

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  • 0:01 Definition of Symmetry
  • 1:06 Reflection Symmetry
  • 1:31 Rotational Symmetry
  • 1:53 Point Symmetry
  • 2:29 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe
Symmetry occurs in many areas of mathematics. This lesson explains symmetry in math and explores the three basic types of symmetry: rotational symmetry, reflection symmetry, and point symmetry.

Definition of Symmetry

Symmetry comes from a Greek word meaning 'to measure together' and is widely used in the study of geometry. Mathematically, symmetry means that one shape becomes exactly like another when you move it in some way: turn, flip or slide. For two objects to be symmetrical, they must be the same size and shape, with one object having a different orientation from the first. There can also be symmetry in one object, such as a face. If you draw a line of symmetry down the center of your face, you can see that the left side is a mirror image of the right side. Not all objects have symmetry; if an object is not symmetrical, it is called asymmetric.

When working with symmetry, the initial image is called the pre-image, and the second image is called the image because it is the final step in the process. Just like the answer to a math problem is the final step in that process, the image is what is created when you rotate something 90 degrees or flip it about the x-axis. There are three basic types of symmetry: rotational symmetry, reflection symmetry, and point symmetry.

Reflection Symmetry

Sometimes called line symmetry or mirror symmetry, reflection symmetry is when an object is reflected across a line, like looking in a mirror. The face from before shows you reflection symmetry. Here are some more examples of reflection symmetry. The line of symmetry does not have to be vertical; it can go in any direction. Also, certain objects, like a square or a circle, can have many lines of symmetry.

Rotational Symmetry

Rotational symmetry occurs when an object is rotated about a fixed point. The object can be rotated more than once. The number of rotations is called the order of rotation. This image has been rotated three times and, therefore, has 'order four' (the pre-image is counted when determining the order of symmetry).

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