Transitive Property of Equality: Definition & Example

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  • 0:01 Definition
  • 0:54 Formula
  • 1:21 Example 1
  • 2:18 Example 2
  • 2:59 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you will understand how the transitive property of equality works when you have two equations that are equal to each other. Learn the formula for this property and how you can use it to help you solve problems.

Definition

In this video lesson, we talk about the transitive property of equality. This property tells us that if we have two things that are equal to each other and the second thing is equal to a third thing, then the first thing is also equal to the third thing.

You can think about it in terms of identical toy trucks. Say you have two identical toy trucks. They are both blue. Now, if the second truck is the same as a third blue toy truck, then we can also say that the first truck is also the same as the third blue toy truck. This is because we know that the first toy truck is equal to the second toy truck, so if either of those toy trucks is equal to a third, then they both are equal to that third truck. It's like a chain. They are all linked to each other.

Formula

In math, we have a formula for this property. It says that if a = b and b = c, then a = c. This is telling us that if two things are equal and the second thing is equal to a third, then because the first two things are equal, it also means that the first is equal to the third as well. They are all equal to each other. Let's look at a couple of examples to see how this transitive property of equality works in action.

Example 1

In this example, we look at how true the transitive property of equality is. We begin with our two equations:

5 = 3 + 2 and 3 + 2 = 5

We can label these two equations with our letters. Or, we can use our toy trucks. The first 5 is our letter a, or our first toy truck. The following 3 + 2 is our letter b, or our second toy truck. The last 5 is our letter c, or our third toy truck. By applying the transitive property of equality, we can say that the first 5 is equal to the last 5, that letter a is equal to letter c, or that the first toy truck is equal to the third toy truck. Is this true? Let's see.

5 = 5

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