Pythagorean Theorem Worksheets

Free Pythagorean Theorem Worksheets with Answer Keys

Are you in need of some Pythagorean Theorem worksheets to help you practice and learn one of the most famous math theorems ever known?

Learning how to correctly use the Pythagorean Theorem, which states that, for any right triangle with sides a, b, and c (where a and b are the legs and c is the hypotenuse), the following equation is always true: a² + b² = c².

The Pythagorean Theorem has been around for thousands of years and it remains as one of the most fascinating and well-known math theorems of all time. Learning how to use the Pythagorean Theorem to solve problems involving right triangles is a skill that every math student can learn with some consistent practice. And one of the best ways to consistently practice using the Pythagorean Theorem to solve right triangle problems is by working on a Pythagorean Theorem Worksheet or two assess your understanding and to keep your skills sharp!

If you are looking for effective Pythagorean Theorem Worksheets (that include both triangle diagram problems and word problems), then you’re in the right place! The next section of this page shares a free library of Pythagorean Theorem Worksheet PDF files that include a variety of practice problems as well as complete answer keys on the second page. These free worksheets will give you tons of practice opportunities to use the Pythagorean Theorem (a² + b² = c²) to solve a variety of right triangle problems (including word problems).

Every single Pythagorean Theorem worksheet pdf file is easy to download to your computer and/or print (with or without the answer key). You can download any of the worksheets in the free library below simply by clicking on any of the blue text links to open the PDF preview. From the preview page, you will have the option to save the file to your computer or to send it to your printer if you want a paper version of any of the worksheets.

All of the Pythagorean Theorem Worksheets below are samples from the Mashup Math K-12 Infinite Worksheet Libraries, where you can find hundreds more topic-specific math worksheets with answer keys for grades K-9, Algebra I, and Geometry.

Pythagorean Theorem Worksheets

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If so, please visit our Free Math Worksheets Library, where you can download hundreds of PDF math worksheets and answer keys for Grades K-9, Algebra I, and Geometry!

Quick Review: The Pythagorean Theorem

If you are struggling with any of the practice problems on any Pythagorean Theorem worksheet above, here is a short review of some key concepts related to the Pythagorean Theorem.

First, note that the Pythagorean Theorem applies only to right triangles. If a math problem is related to a triangle that does not have a 90-degree angle, then you likely can not use the Pythagorean Theorem to solve it.

However, in the case of all right triangles with the following properties:

• The legs of the right triangle (the two smaller sides) are a and b

• The hypotenuse of the right triangle (the longest side) is c

Then the following is always true: a² + b² = c²

In other words, the square of the length of the longest side, c, is equal to the sum of the squares of the two smaller sides, a and b.

To help you to visualize how the Pythagorean Theorem relates to a right triangle with side lengths a, b, and c (where c is the hypotenuse), take a look at Figure 01 below.

For example, let’s say that you have a triangle with side lengths 3, 4, and 5, and you wanted to confirm whether or not the triangle in question was a right triangle.

To verify whether or not the triangle is right, we would have to substitute the three side lengths into the Pythagorean Theorem, a² + b² = c², and see if the equation holds true. If it does, then we can conclude that the triangle is a right triangle.

In this case, the shorter sides a and b are 3 and 4, and the longest side is 5, so:

• a=3

• b=4

• c=5

Next, we just have to plug these values into the Pythagorean Theorem as follows:

• a² + b² = c²

• 3² + 4² = 5²

• 9 + 16 = 25

• 25 = 25 ✔️

What do you notice? The left side of the equation, 3² + 4² = 9 + 16 = 25, and the right side of the equation, 5² = 25, both equal 25. So, we can conclude that this triangle is a right triangle because it satisfies the Pythagorean Theorem, as illustrated in Figure 02 below.

If you or your students need a more in-depth review of how to use the Pythagorean Theorem to find the missing side of a right triangle, check out our free video tutorial linked below!