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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

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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.

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.

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.

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).

**Point symmetry** occurs when every part of an object has a matching part that is the same distance from the origin on a coordinate plane, but is in the opposite direction. Point symmetry is often called **origin symmetry** because the point is frequently the origin on the coordinate plane. Many playing cards have point symmetry - they look the same from top and bottom. Items with point symmetry look the same from other directions, too. If you were to cut a playing card in half at a 45 degree angle, the two sides would still look the same.

Objects are said to be symmetrical if their **pre-image** and **image** have the same size and shape, but are either mirror images of each other or one has been rotated to go in a different direction from the first. There are three basic types of symmetry: **reflection symmetry**, rotational symmetry, and **point symmetry**.

When you are done, you should be able to:

- State the mathematical definition for symmetry
- Describe the three types of symmetry in math

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8 in chapter 42 of the course:

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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

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