# Symmetric Property of Equality: Definition & Examples

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• 0:01 Defining the Symmetric…
• 1:08 Examples and Non-Examples
• 2:59 Lesson Summary

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Lesson Transcript
Instructor: Elizabeth Often

Elizabeth has taught high school math for over 10 years, and has a master's in secondary math education.

Have you ever finished a math problem only to see that the teacher's answer was written backwards? Find out why your answer is correct in this lesson on the symmetric property of equality!

## Defining the Symmetric Property of Equality

Many times in class when I am reviewing homework answers, I will write something on the board that looks like this: x = 5. Then a student will ask me 'I have 5 = x. Is that still correct?' The answer, of course, is that it is still correct. The reason that it is correct is due to the symmetric property of equality, which we will discuss in this lesson.

The symmetric property of equality states: if a = b, then b = a. In short, with the symmetric property, we can take the left-hand side of the equation (a) and move it to the right-hand side, while taking the right-hand side of the equation (b) and moving it to the left-hand side.

The symmetric property may not seem like much, but it is important. This property allows you to write either x = 5 or 5 = x on your quiz and have either one be the correct answer. You may not have seen the symmetric property used often in arithmetic classes, but it is there as well. We'll look at arithmetic and algebra examples next.

## Examples and Non-Examples

In arithmetic, we can write 6 - 3 = 3, or we can write 3 = 6 - 3. We say that both these equations are equivalent, that is, they have the same solution. The symmetric property has been used here in exchanging the right-hand side and left-hand side of the equations.

In algebra, we can write y = x + 3, or we can write x + 3 = y. Again, the symmetric property has been used in exchanging the right-hand side and left-hand side.

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