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
Jennifer Beddoe

Jennifer has an MS in Chemistry and a BS in Biological Sciences.

Expert Contributor
Dawn Mills

Dawn has taught chemistry and forensic courses at the college level for 9 years. She has a PhD in Chemistry and is an author of peer reviewed publications in chemistry.

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 mentioned before is an example of 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.

Image with reflection symmetry

images with reflection symmetry

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Additional Activities


In this activity, we will consider the three basic types of symmetry and will apply them to different shapes, objects or letters to gain a better understanding.


graphing paper



banana (can use any piece of fruit if a banana is not available)


shoe (can be wearing)


1. Start by drawing the letter A on your graphing paper. Does the letter A have point symmetry? If not, determine two letters from the alphabet that do have point symmetry.

2. Draw a triangle on your graphing paper. Does the triangle have rotational symmetry? If so, demonstrate this by drawing the rotational symmetry and noting the degree of rotation(s) used.

3. Examine the banana. Does it have rotational symmetry, reflection symmetry or point symmetry? Explain why or why not for each instance.

4. Examine the paperclip. Does it have rotational symmetry, reflection symmetry or point symmetry? Explain why or why not for each instance.

5. Draw a kite on your graphing paper. Does a kite have rotational symmetry? Does it have reflection symmetry or point symmetry?

6. Draw two different shapes that have point symmetry on your graphing paper.

7. Examine your shoe. Is it symmetrical or asymmetrical? Explain the difference between the two and provide support for which category your shoe falls in to.

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