In this lesson, students will use the Pythagorean Theorem to solve for any side of a right triangle. Students will:. The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.

What do you see? They give form to things we use every day. The top of the desk you sit in is a rectangle. The base of a lamp is a circle. Look around the classroom and tell the person next to you what shapes you see. While students are looking around, take pieces from the jigsaw puzzle and place them on the overhead projector, document camera, or whiteboard.

Also take out a set of tangrams and place them next to the jigsaw puzzle pieces. Let students share their observations with the class. The objective is to use the seven pieces to replicate a picture without overlapping any pieces. Here is an example. What are we supposed to make with our seven pieces? The red square should be 3 inches x 3 inches, the blue square should be 4 inches x 4 inches, and the yellow square should be 5 inches x 5 inches.

The green square should be 5 cm x 5 cm, the purple square should be 12 cm x 12 cm, and the orange square should be 13 cm x 13 cm. Students should cut out the squares.

Your goal is to create a triangle with the three squares with no overlap. Some of you have three squares measured in inches, and some have three squares measured in centimeters. Students are going to struggle creating a triangle with the three squares, so after a few minutes give them a hint that the triangle is not going to be made of paper.

It will be created by the space between the squares. It could be about side lengths, perimeter, area, or the shapes in general. After students write down their individual findings, pair them so that one had the squares in inches, and the other had the squares in centimeters. They should share their ideas and compare and contrast. Then have the pairs share with the whole class. If anyone does, call this student Pythagoras for the day. However, a Greek philosopher and mathematician named Pythagoras is the one getting the credit.

Today we are going to learn what the Pythagorean Theorem is and how the areas of three squares actually help us find side lengths of right triangles.

There are two practice problems on the bottom for students to try on their own. Go over the answers once everyone has attempted the problems. Answers are located in the notes section of the PowerPoint. Divide students into groups of three or four.

They work one problem at a time, and when they finish, they pass the problem clockwise writing their work on a separate sheet of paper. When everyone is done, if there is time, have each group present one of the problems to the class. You are impersonating. Stop Impersonating. Pythagorean Theorem.

Lesson Plan. Options Printer Friendly Version Email. Grade Levels.The Pythagorean Theorem, named after the Greek mathematician Pythagoras, is a formula used to calculate the length of the sides of a right triangle. The theorem states:. A right triangle is a triangle containing a right angle 90 degrees. The hypotenuse is the longest side of a right triangle, the one opposite the right angle.

The legs are the two shorter sides, which meet at the right angle. By convention, the legs are usually labeled a and b and the hypotenuse is labeled c. Therefore, the Pythagorean theorem formula is as follows:. Pythagorean theorem problems start by giving you the length of two of the sides of a right triangle. Using the Pythagorean formula, it is possible to calculate the length of the third side.

Because you are using squares and square roots, you may need the help of a calculator.

Name the legs a and b and the hypotenuse c. Add these values to the formula and solve for c :. Now take the square root of both sides of the equation to solve for c. The square root of 25 is 5. A right triangle has a leg of length 5 and a hypotenuse of length What is the length of the other leg? Name the known leg athe unknown leg band the hypotenuse c. Add these values to the formula and solve for b :. Word problems using the Pythagorean theorem require you to draw or imagine a right triangle where two of the sides are of known length.

When solving these problems, remember the following:. How wide is the screen horizontally?

## Learn Pythagorean Theorem Problems: Solving Right Triangles

The problem gives us the length of the hypotenuse and one of the legs. Therefore, name the height athe width band the diagonal c. Now find the square root of both sides to solve for b use a calculator to find the square root of large numbers. The square root of is Page content. Learn the Theorem The Pythagorean Theorem, named after the Greek mathematician Pythagoras, is a formula used to calculate the length of the sides of a right triangle. Article authored by Robyn Broyles.The Pythagorean Theorem or Pythagoras' Theorem is a formula relating the lengths of the three sides of a right triangle.

If we take the length of the hypotenuse to be c and the length of the legs to be a and b then this theorem tells us that:. In any right triangle, the sum of the squared lengths of the two legs is equal to the squared length of the hypotenuse. Note : Pythagorean theorem only works for right triangles. Example 2: Find the length of one side of a right triangle if the length of the hypotenuse is 10 inches and the length of the other side is 9 inches.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page. The following diagram gives the formula for the Pythagorean Theorem, scroll down the page for more examples and solutions that use the Pythagorean Theorem.

What is the Pythagorean Theorem? A right triangle consists of two sides called the legs and one side called the hypotenuse. The hypotenuse is the longest side and is opposite the right angle.The Pythagorean theorem is one of the most famous equations, as it helps us to relate the angle and sides of a right triangle. So when we solve right triangles for the missing side length, all we do is plug our given values into the formula and solve the corresponding equation.

But did you know that we can determine whether or not a triangle is a right triangleacute triangleor obtuse triangle? The theorem states that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

And the corollary states, if a triangle with side lengths a, b, and c where c is the length of the longest side, we can determine if the triangle is acute or obtuse. We do this by comparing the sum of the squares of the legs is less than or greater than the square of the largest side, as Varsity Tutors accurately states.

In the video below, you are going to review the Pythagorean theorem and its properties, and then use the converse of the Pythagorean theorem to determine if a triangle is a right triangle, acute triangle, or obtuse triangle. Hint: Order Matters. Get access to all the courses and over HD videos with your subscription.

Get My Subscription Now. Not yet ready to subscribe? Please click here if you are not redirected within a few seconds. And as we know, a right triangle is comprised of two legs and a hypotenuse.

The hypotenuse is the longest side and is always opposite to the right angle. Right Triangle Diagram. Formula for Using the Pythagorean Theorem. Pythagorean Theorem Example.

Converse of Pythagorean Theorem Formula.Teachers Pay Teachers is an online marketplace where teachers buy and sell original educational materials. Are you getting the free resources, updates, and special offers we send out every week in our teacher newsletter?

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Other Digital Resources. Grades PreK. Other Not Grade Specific. Higher Education. Adult Education. Art History. Graphic Arts. Music Composition.Braining Camp Pythagoren Theorem. Discover how the Pythagorean Theorem describes the relationship between the lengths of the sides.

Demonstrate the Pythagorean Theorem. Hotmath Practice Problems. Interactive Maths - Pythagoras Theorem. Proof Without Words: Pythagorean Theorem. Can you explain the proof? Pythagorean Explorer. Related resources can be found under the learner tab. Pythagorean Theorem and Right Triangle Facts. Pythagorean Theorem Applets. Pythagorean Theorem Game. The Pythagorean Theorem takes place in a right triangle.

Pythagorean Theorem Jeopardy Game. Students must also be able to determine whether a given set of numbers could be the lengths of the sides in a right triangle. Pythagorean Theorem: Find the Hypotenuse.

## Pythagorean theorem word problems

Activity follows ad. Session 6 The Pythagoren Theorem. You will examine different formal proofs of the Pythagorean Theorem. Examine applications such as finding missing lengths. Learn how to derive and use the distance formula. Squaring the Triangle.

The Pythagoren Theorem: Interactive Puzzle. Tree of Mysteries. Click around to find them. As you find each answer, use the decoder grid below to find its matching letter.

Ultimate Pythagorean Theorem Test. Solve the problems inside.Now, that is not to say that nothing needs to be memorized. So read on to learn more about it and then grab the free set of Pythagorean Theorem Practice Pageswhich will help your kids see the relevance of it! Read our full disclosure here. Kids are usually exposed to the Pythagorean Theorem in middle school or Pre-Algebra.

Although reciting the theorem is not difficult:. To solve problems using Pythagorean Theorem, kids will need to understand squaring numbers and finding square roots. They also need to understand what a right triangle is and how to evaluate and solve equations.

**The hardest problem on the hardest test**

But even if you give kids all the necessary numbers and show them step by step how to solve an equation using Pythagorean Theorem, it will just be a bunch of meaningless numbers to them. It will seem like a pointless exercise, where once again math is completely irrelevant to their everyday life.

Especially not about a fundamentally important and useful theorem such as this. We can use the Pythagorean Theorem to find lengths and distances of all sorts of questions in our everyday life. And when we show kids that it is relevant, then practicing the Pythagorean Theorem will not feel pointless and boring!

This set of Pythagorean Theorem practice pages includes 3 problems for kids to visualize, think about and solve using the theorem. The first discusses the layout of a baseball diamond, and challenges kids to find the distance from second base to home.

### Pythagorean theorem word problems

Kids who love baseball will enjoy this challenge, and it will hopefully spark other math questions for them as they consider a game of baseball! The next problem is about television sets. This is important for anyone wanting to make the right decision about which t.

In this problem, kids learn that t. Finally, there is a slightly more challenging problem, which will really require kids to think about the whole situation. This problem involves a firetruck with a ladder of only feet long.

Because the truck is parked 25 feet away from the building, they have to determine how high the ladder can actually reach. Although this is often shocking and concerning news to people, there are other fire safety precautions in place, making those very high condos perfectly safe in the event of a fire.

Each problem in this download includes a one page snapshot for kids to learn and solve the problem.

It starts with relevant and interesting facts. They may or may not need these as they solve the problem. In the middle section, kids draw a sketch of the situation and label all the measurements.

Finally, in the bottom space kids write out an equation and solve it to answer the given question. Depending on your kids and your situation, you could put kids into 3 small groups and let them work together to solve one of these problems. Or you could assign everyone the same problem and let them work on it individually in class or at home. But I would certainly pick at least one of the problems to discuss as a class.

Take time to draw a sketch of the situation. Then have kids label everything they know. Finally, ask kids how the Pythagorean Theorem helped them to solve the problem. Another fun way to explore this theorem is to challenge kids to prove it. Further explaining and visualizing the theorem will help kids not only remember it, but deepen their understanding of it.