Point Symmetry: Definition & Examples

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  • 0:01 What is Symmetry?
  • 1:16 Point Symmetry vs Reflection
  • 1:54 Examples of Point Symmetry
  • 2:37 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.

Symmetry is a common occurrence and concept of nature and life. In this lesson, we will look particularly at the characteristics of objects that have point symmetry.

What Is Symmetry?

Before we explore the definition of symmetry, let's complete an activity. Draw an uppercase X on a piece of paper. At the point where the lines cross, place a noticeable dot or point. What do you notice? Do you see two Vs, but one is upside down?

Now, draw an S. Is there a place on the S where you could place a point so that you have the same effect as with the X? If you chose right in the center of the S, then you are correct.

Point symmetry occurs when there exists a position or a central point on an object such that:

  1. The central point splits the object or shape into two parts.
  2. Every part on each has a matching part on the other that is the same distance from the central point.
  3. Both parts face different directions.

Let's test our definition with the X and S. Notice the point splits both letters into two similar shapes, but they face different directions.

If you walk up to a mirror and touch the mirror with your finger, you would have made an example of point symmetry. Right where your finger touches the mirror is the point. It's as if you're connected to your image. That is the most important concept of point symmetry: there has to be a connection.

Point Symmetry vs. Reflection

There is usually a misconception about symmetry and reflection. The difference is in the connection. It's as if you are connected to the image. If you stand three feet away from the mirror, you and your image are separate entities. However, with point symmetry, the object is not away from the image, it's onto the image.

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