Symmetric Property: Definition & Examples

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  • 0:00 The Symmetric Property…
  • 0:20 Why Is It Important?
  • 1:07 Examples
  • 2:04 When This Property…
  • 3:04 Lesson Summary
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Lesson Transcript
Instructor: Karin Gonzalez

Karin has taught middle and high school Health and has a master's degree in social work.

In this lesson, you will learn the definition of the symmetric property of equality and why this property is so important in mathematics. You will also be given examples to illustrate.

The Symmetric Property of Equality

The symmetric property of equality, one of the eight properties of equality, states that if y = x, then x = y. Let's look at a quick and simple example:

If we know that 5y = 2x, then we know that 2x = 5y

You're probably thinking: is it really that easy? Yes, the symmetric property of equality really is that simple!

Why is it Important?

The symmetric property of equality is important in mathematics because it tells us that both sides of an equal sign are equal no matter which side of the equal sign they are on. If we did not have this property in mathematics, we would not be able to write 56 + x = y as y= 56 + x. Therefore, there is no need to worry if an equation is flipped, as it will remain equal either way.

Also, if we are writing an answer on a math test or quiz, it won't matter if we say 9 = x or x = 9. Both answers would be correct because they are exactly the same.


Let's look some examples that demonstrate the symmetric property of equality.

Example 1:

We have the equation:

56y + x = 9y - 6x

We can flip flop this equation and the symmetric property of equality states that they would still be equal. Therefore, this would be a true statement:

9y - 6x = 56y + x

Example 2:

2 + 3 = 5


5 = 2 + 3

Example 3:

2 + 3 + 5 - 8 - 1 x 4 x 5 = x


x = 2 + 3 + 5 - 8 - 1 x 4 x 5

As you can see, it doesn't matter how complicated or long an equation is, you can always switch the left and right sides of the equal sign and you will have an equal equation.

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