Symmetric Property in Geometry: Definition & Examples

Symmetric Property in Geometry: Definition & Examples
Coming up next: Graphing Basic Functions

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
 Replay
Your next lesson will play in 10 seconds
  • 0:00 Symmetric Property of Equality
  • 1:40 Symmetric Property in Geometry
  • 2:24 Real-World Examples
  • 3:28 Lesson Summary
Add to Add to Add to

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Timeline
Autoplay
Autoplay
Speed

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Laura Pennington

Laura has taught collegiate mathematics and holds a master's degree in pure mathematics.

The symmetric property shows up often in the world around us, so it is useful to be familiar with this property. This lesson will allow us to become comfortable with, see examples of, and work with this neat property.

Symmetric Property of Equality

It's no secret that 2 + 2 = 4. Most of us know this from elementary school when we learned how to add. But what if I switched the order of this and told you that 4 = 2 + 2? This is probably still an obvious statement to you, right? This fact, that if 2 + 2 = 4, then 4 = 2 + 2, is actually an illustration of the symmetric property of equality. In mathematics, the symmetric property of equality is really quite simple. This property states that if a = b, then b = a. That is, we can interchange the sides of an equation, and the equation is still a true statement.

For example, all of the following are demonstrations of the symmetric property:

  • If x + y = 7, then 7 = x + y
  • If 2c - d = 3e + 7f, then 3e + 7f = 2c - d
  • If apple = orange, then orange = apple

In all of these, we see that the symmetric property just says that we can switch the sides of an equation, and the equation is still true.

A good way to remember the symmetric property is to think of it as the mirror property. When you look in the mirror, your mirror image is looking back at you, and you and your mirror image are the same regardless of which side of the mirror you are on. Thinking of the symmetric property this way brings us to the symmetric property in geometry.

Symmetric Property in Geometry

As we said, the symmetric property can be thought of as the mirror property. In geometry, an image or object is said to be symmetric if both of its sides are the same. That is, the sides of a symmetric image or object are mirror images of each other, so the image's sides are symmetric with respect to a line. This line is called the axis of symmetry. For example, a rectangle is symmetric.

symmetric property 1

We can see from this image that if we were to fold the rectangle in half along the axis of symmetry, both sides of the rectangle would line up with each other. This is because both sides of the rectangle are the same.

Let's consider some real world examples of symmetry.

To unlock this lesson you must be a Study.com Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back
What teachers are saying about Study.com
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create An Account
Support