Congruence in Geometric Shapes

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  • 0:01 Congruence
  • 1:01 Determining Congruence
  • 1:41 Two Congruent Shapes
  • 2:15 Two Non-Congruent Shapes
  • 3:26 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.

Watch this video lesson to learn how you can determine whether two shapes are congruent or not. You will learn what the one criterion is when determining congruency between two shapes.


In this lesson, we'll talk about congruence. Congruence is when something is equal to something else. For example, identical twins are congruent to each other because they look exactly the same. In math, when two geometric shapes are congruent, they are like identical twins. You can't tell them apart from each other.

Our geometric shapes are just shapes without any math attached to them, so any shape that you see is a geometric shape. Why would you want to learn whether two shapes are congruent or not? This is something that you will need to know for your math tests. It can help you determine the measurements of other shapes that are congruent to a shape you already know. And also if you become an architect or designer, then knowing whether two shapes are congruent will help you as you design a product or building. For example, the legs on a table need to be congruent so that the table won't wobble.

So let's see how you can determine whether two shapes are congruent.

Determining Congruence

We can rephrase our definition of congruence to say that to be congruent means to be equal to each other. If two shapes are congruent, then they are the same. This means that all of their critical dimensions are the same. If two circles are congruent, then it means that both circles have the same radius length. If two rectangles are the same, then they both have the same width and length. If any of these dimensions are different, then the two shapes are not congruent. Also, if the two shapes are completely different shapes, then obviously they are not congruent.

Let's look at a couple of examples to see how we can use this information.

Two Congruent Shapes

Jackie is working at his dad's construction company. His dad asks him to find an identical copy of a wheel that needs to be replaced. His dad tells him that the wheel has a radius of 10 inches. What is the radius of the identical copy that Jackie needs to find?

If something is identical to something else, then it means that they are congruent - they are the same. If they are congruent, then all the dimensions are also the same. So, if the original wheel has a radius of 10 inches, then the identical copy must also have a radius of 10 inches.

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