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## Pythagorean Theorem Worksheet

48 pythagorean theorem worksheet with answers [word + pdf].

The simplicity of the Pythagorean Theorem worksheet is the best thing about it. What is the Pythagorean Theorem? Formulated in the 6th Century BC by Greek Philosopher and mathematician Pythagoras of Samos, Pythagorean Theorem is a mathematic equation used for a variety of purposes. Over the years, many engineers and architects have used Pythagorean Theorem worksheet to complete their projects .

Table of Contents

- 1 Pythagorean Theorem Worksheet
- 2 Knowing Pythagoras of Samos and how he came up with the Pythagorean equation
- 3 Understanding Pythagorean Theorem
- 4 Pythagorean Theorem Word Problems Worksheet
- 5 Using Pythagorean Theorem worksheet
- 6 Conclusion

A simple equation, Pythagorean Theorem states that the square of the hypotenuse (the side opposite to the right angle triangle) is equal to the sum of the other two sides . Following is how the Pythagorean equation is written:

In the aforementioned equation, c is the length of the hypotenuse while the length of the other two sides of the triangle are represented by b and a. Though the knowledge of the Pythagorean Theorem predates the Greek Philosopher, Pythagoras is generally credited for bringing the equation to the fore. This is the reason the Pythagorean equation is named after him. Before we discuss the Pythagorean Theorem and the Pythagorean Theorem worksheet in detail, let’s take a look at who Pythagoras of Samos was and how he came up with the Pythagorean equation.

## Knowing Pythagoras of Samos and how he came up with the Pythagorean equation

A 6 th century BC Greek philosopher and mathematician, Pythagoras of Samos is widely credited for bringing the Pythagorean equation to the fore. Though others used the relationship long before his time, Pythagoras is the first one who made the relationship between the lengths of the sides on a right-angled triangle public. This is why he’s regarded as the inventor of the Pythagorean equation.

Apart from being a philosopher and mathematician, Pythagoras founded the Pythagoreanism movement. Born in Croton, Italy, Pythagoras travelled to many different countries including Greece, Egypt, and India. After moving back to Croton in 530 BC, Pythagoras established some kind of school. He returned to Samos in 520 BC. It was in late 6 th Century BC that Pythagoras started to make important contributions to philosophy and math. The Pythagorean equation was one of those contributions.

Though he revealed the Pythagorean equation to the world in the late 6 th Century BC while living in Samos, many historians believe that Pythagoras first thought about the equation during his time in Egypt. In fact, according to many historians, Pythagoras learned geometry, the Phoenicians arithmetic and other branches of mathematics from the Egyptians.

Though he has made many important contributions to philosophy, Pythagoras is widely known as the founder of the Pythagorean Theorem. As previously mentioned, the Pythagorean Theorem is a mathematical equation that states that the square of the hypotenuse (the side opposite to the right angle triangle) is equal to the sum of the other two sides .

Today the aforementioned equation bears Pythagoras’s name but it’s important to know that he wasn’t the first one to use the equation. Before Pythagoras’s time, the Indians and the Babylonians utilized the Pythagorean Theorem or equation. Since they constructed the first proof of the theorem, Pythagoras and his disciples are regarded as the inventors of the equation.

Many historians say that Pythagoras worked in a very secretive manner. This is the reason little evidence is available that the Greek Philosopher/ mathematician himself worked on and proved the Pythagorean Theorem. It is important to note that the first time Pythagoras was given credit for the Theorem was five centuries after his death. This makes Pythagoras’s contribution to the Theorem even more debatable. Nonetheless, since Pythagoras is the only one connected to the Pythagorean Theorem known today, we have to give him due credit. Now that we’ve discussed who Pythagoras of Samos was and how he came up with the Pythagorean equation, it’s time to take a detailed look at the Pythagorean Theorem and the Pythagorean Theorem worksheet.

## Understanding Pythagorean Theorem

According to Pythagorean Theorem, the sum of the squares on the right-angled triangle’s two smaller sides is equal to the side opposite to the right angle triangle (the square on hypotenuse). Using a Pythagorean Theorem worksheet is a good way to prove the aforementioned equation. An amazing discovery about triangles made over two thousand years ago, Pythagorean Theorem says that when a triangle has a 90° angle and squares are made on each of the triangle’s three sides, the size of the biggest square is equal to the size of the other two squares put together! A short equation, Pythagorean Theorem can be written in the following manner:

In Pythagorean Theorem, c is the triangle’s longest side while b and a make up the other two sides. The longest side of the triangle in the Pythagorean Theorem is referred to as the ‘hypotenuse’. Many people ask why Pythagorean Theorem is important. The answer to this is simple: you’ll be able to find the length of a right-angled triangle’s third side if you know the length of the other two sides. This equation works like magic and can be used to find any missing value. Following is an example that uses the Pythagorean Theorem to solve a triangle.

In this equation, the longest side of the triangle ‘c’ is missing. By finding out the sum of the squares of the two other sides, we were able to find the missing value. The most famous mathematical contribution of Pythagoras, the Pythagoras Theorem was one of the earliest documented theorems. Though Pythagoras is given most of the credit for the theorem, a major contribution to the theorem was made by his students.

When you look at a Pythagoras Theorem worksheet, you’ll notice that the theorem enables you to find the length of any right angle triangle side provided you know the length of the other two sides. Also, using the theorem, you can check whether a triangle is a right triangle. The Pythagoras Theorem is extremely useful in solving many math problems. Further, you can use it in many real life situations. This is illustrated by a Pythagoras Theorem worksheet.

## Pythagorean Theorem Word Problems Worksheet

## Using Pythagorean Theorem worksheet

A good way to review the Pythagoras Theorem and expand the mathematical equation is using a Pythagoras Theorem worksheet. By using the worksheet, you’ll be able to get a good understanding of geometry. Additionally, the worksheet will give you an opportunity to review the knowledge related to the different types of triangles. Finally and most importantly, you’ll be able to practice the ancient equation invented by the Greek mathematician and philosopher, Pythagoras. Before you start using the Pythagoras Theorem worksheet, just remember that ‘c’ is the hypotenuse while the shorter sides of the triangle are represented by ‘a’ and ‘b’.

A Pythagoras Theorem worksheet presents students with triangles of various orientations and asks them to identify the longest side of the triangle i.e. the hypotenuse. As you know by now, the formula used in Pythagoras Theorem is a²+b²=c². Regardless of what the worksheet asks the students to identify, the formula or equation of the theorem always remain the same. Though, the students could be presented with different challenges including solving triangles:

- Labeled in different order
- With a different set of letters
- By using vertices to name the sides

The symbols used in the Pythagoras Theorem are something students will find on their calculators. Figuring out how to use these functions is what students need to establish. There is involvement of the Babylonians and the Egyptians in the invention of the Pythagoras Theorem but the earliest known proof of the theorem was produced by the school of Pythagoras.

Many Pythagorean triples were known to the Babylonians while the Egyptians knew and used the (3, 4, 5) triple. The Chinese and Indians also played a role in the invention of the Pythagoras Theorem. The first diagrammatic proof of the theorem was produced by the Chinese while the Indians discovered many triples. In 1995, the theorem became part of the Guinness Book of Records as the most proved theorem of all time.

The triples used in the Pythagoras Theorem include (3, 4, 5), (6, 8, 10), (5, 12, 13), (8,15,17), (7,24,25), (20,21,29), (12,35,37), (9,40,41), (28,45,53), (11,60,61), (16,63,65), (33,56,65) and (48,55,73). The aforementioned triples aren’t multiples of a smaller triple and the name given to them is ‘primitive’ triples. To solve a particular problem, the Pythagoras Theorem can be arranged. For example, if you’re asked to find b which is one of the two smaller sides of the right-angled triangle, you can rearrange the theorem to b²=c²-a². By doing this, you’ll be able to easily find the missing value.

The Pythagoras Theorem has many different proofs. However, when checking your answers, following are the two things that you must always remember:

- The side opposite to the right angle or simply the hypotenuse is always the longest side of the triangle
- Though it is the longest side of the triangle, the size of the hypotenuse can never exceed the sum of the other two squares

To understand this better, take a look at a Pythagoras Theorem worksheet. Today, you can get easy access to Pythagorean Theorem worksheet with answers. Nonetheless, we’re going to try and understand the Pythagoras Theorem as much as we can.

As mentioned earlier, if you know the size of the other two sides, you will be able to find out the length of the third side of the right angle triangle. Also, after being squared, the shorter length is subtracted from the square of the hypotenuse when the hypotenuse is one of the two known lengths. As seen earlier, the lengths of each side of the triangle in the Pythagoras Theorem are whole numbers. Such triangles are known as Pythagorean triangles.

Though there are many different proofs of the Pythagoras Theorem, only three of them can be constructed by students and other people on their own. The first proof starts off as rectangle and is then divided into three triangles that individually contain a right angle. To see first proof, you can use a computer or something as straight forward as an index card cut up into right triangles.

Beginning with a rectangle, the second proof of the Pythagoras Theorem starts off by constructing rectangle CADE with BA=DA. This is followed by the construction of the <BAD’s angle bisector. Once constructed, the bisector is allowed to intersect ED at point F. This makes <BAF and <DAF congruent, BA=DA, and AF=AF. This in turn makes the triangle DAF equal to triangle BAF which means that since ADF is a right angle, ABF will also be a right angle. The third and final proof of the Pythagorean Theorem that we’re going to discuss is the proof that starts off with a right angle. In this proof, triangle ABC is right angle and its right side is angle C.

The three proofs stated above are just few of the many Pythagoras Theorem. You’ll come across these proofs when you take a look at the Pythagorean Theorem worksheet with answers. Learning and understanding the Pythagorean concept is extremely important for students and other people who’ll use this theorem in their practical life.

It is important that you understand the algebraic representation of the Pythagoras Theorem as well as the geometric concepts behind it. You can accomplish this by using proofs, manipulatives, and computer technology. By using these methods to learn Pythagorean Theorem, you’ll be able to see the connections and benefit greatly.

Formulated in the 6th Century BC by Pythagoras of Samos, Pythagoras Theorem is widely used today. If you want to practice Pythagoras Theorem then you can do that easily. Pythagoras Theorem worksheets with answers are easily available and you can use these worksheets to get a good grip of the Theorem.

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## 20 Pythagorean Theorem Worksheet with Answers (Word & PDF)

If you are familiar with the Pythagorean Theorem, then you know that it is one of the simplest and most useful tools in geometry. The theorem was formulated by Pythagoras of Samos, a Greek mathematician, and philosopher, in the 6th century. Today, it has many applications in different areas of study, from simple elementary and high school geometry to complex engineering and architecture calculations. Below, we take a closer look at the theorem and how you can master it through a worksheet.

## What Is a Pythagorean Theorem Worksheet?

Simply put, the Pythagorean Theorem states that the square of the longest side of a right angle (the hypotenuse) is equal to the sum of the squares of the other two sides. A Pythagorean Theorem Worksheet is a workbook containing different triangle orientations requiring a student to fill in the missing values using the Pythagorean Theorem. It is a great study tool for geometry students.

## Pythagorean Theorem Worksheet Templates & Examples

## Understanding How Pythagoras of Samos Came Up with the Pythagorean Equation

Pythagoras of Samos was a Greek mathematician and philosopher of the 6th century who is widely credited with bringing the Pythagorean Theorem to the attention of the public. While there are other people who used the Pythagorean equation earlier than Pythagoras – most notably the Egyptians – he was the first person to make the connection between the lengths of a right angle triangle’s sides public. This explains why he is widely recognized as the originator and inventor of the equation and why it is named after him – the Pythagorean Equation.

Pythagoras of Samos shared information about the Pythagorean equation with the world in the late 6th century when he resided in Samos. However, many historians maintain that he first made the discovery during his visit to Egypt, where historians believe he learned several branches of mathematics, including Phoenicians arithmetic and geometry.

According to Historians, Pythagoras was very secretive about his work. There is very limited evidence that he even worked on the Theorem or proved it, and credit is often given to his students. Additionally, Pythagoras of Samos was only credited with proving the Theorem over 5 centuries after his demise – the fact that fuels a lot of debate on whether he was behind the theorem at all.

That said, however, Pythagoras of Samos is the most popular figure connected to the Pythagorean Theorem as it is known today. Therefore, it is only fair to give him credit for this amazing equation that has grown to have numerous real-life applications.

## Understanding Pythagorean Theorem

As mentioned, the Pythagorean Theorem states that, in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the two shorter sides. The theorem basically says that if you make squares on each side of a triangle with a 90° angle, the two smaller squares put together will be the same size as the largest square.

The Pythagorean Theorem can be represented mathematically as follows:

a² + b² = c²

Here, c represents the length of the hypotenuse (the longest side), while b and a are the lengths of the other two sides. From the equation, you can easily find the value of one side if you have the values of the other two. Here is an example to demonstrate:

Q. Consider a right-angled triangle with a base of 3cm and a height of 4cm. What is the hypotenuse of the triangle?

A: Using the Pythagorean Theorem to solve, we can assign the base ‘a’ and the height ‘b.’ Substituting in the equation, we have:

a² + b² = c² 3² + 4² = c² 9 + 16 = c² 25 = c² c = √25 c = 5

The hypotenuse of the triangle is 5 cm long.

As you can see, the hypotenuse was missing from the equation, and we used the relation to find its value. Such questions can be framed differently so that you either have to calculate the value of the base or height. All you have to do is use the Pythagorean Theorem to substitute the missing value. Additionally, you can use the equation to determine whether a triangle is a right triangle.

## How to Use Pythagorean Theorem Worksheet

The Pythagorean Theorem Worksheet is an excellent way to expand your understanding of the Pythagorean Theorem. As you use the worksheet, it is important to remember that ‘a’ and ‘b’ represent the shorter lengths on the triangle while c represents the hypotenuse, which is the longest side.

Pythagoras Theorem worksheets present you with different triangle orientations from which you must determine the value of the missing side. This could be the base, height, or hypotenuse. Regardless of the value you are asked to find; you can use the formula (a²+b²=c²) to solve for the answer. Remember, you can rearrange the equation, but it never changes. Several variations you could use include:

a² + b² = c² (standard) a² = c² – b² (finding the value of a) b² = c² – a² (finding the value of b)

Because the worksheet is designed to help familiarize you with the Pythagorean Theorem, the practice questions can be arranged differently to create a challenge. Some examples include:

- Questions using a different set of letters, e.g. (q, r, s) or (x, y, z)
- A question where the triangle sides are labeled in a different order.
- Questions where the sides are named as vertices.

You can also use the worksheet to prove the Pythagorean Theorem and determine whether a triangle is right-angled. As you check your answers, you should always remember:

- The hypotenuse is the longest side of the triangle and the side opposite to the 90° angle.
- While it is the longest side of the triangle, its size can never surpass the sum of the squares of the other 2 sides.

Pythagoras of Samos formulated the Pythagorean Theorem in the 6th century and, since then, it has been applied to several areas of Mathematics and Geometry. Students can use a Pythagorean Theorem Worksheet to understand the theorem and apply it to solving different questions. Depending on the student’s needs, some of these worksheets have answers, but you can set these pages aside and use them to confirm your answers.

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The Pythagorean Packet Everything Pythagorean Theorem Directions: Fill in each blank for the right triangle by using the words in the Vocab Box. A Right Triangle These sides are called the ____________ of the triangle.

Math4020 Pythagorean Theorem Assignment Complete these exercises about Pythagoras and his famous theorem. (Note: This work can be put directly into your portfolio after this, if done neatly and well. You might want to have a separate copy in addition to what you turn in since I'll likely write some comments on what you turn in.)

6) a = 2.1, b = 7.2, c = 7.5. Find each missing length to the nearest tenth.

Read simple Pythagorean Theorem explanation and download FREE Pythagorean Theorem Worksheet with Answers in Word and PDF.

Yes. Yes. State if each triangle is acute, obtuse, or right. 15) Obtuse Acute. 18) 4.8 km, 28.6 km, 29 km. Obtuse. Right. Create your own worksheets like this one with Infinite Geometry.

Pythagorean Theorem Assignment Identify whether the following triangle side lengths are from a right triangle using Pythagorean Theorem.

PYTHAGOREAN THEOREM - WORKSHEET. For each triangle find the missing length. Round your answer to the nearest tenth. Then find the area and the perimeter. 10. Find a third number so that the three numbers form a right triangle: 11. Ms. Green tells you that a right triangle has a hypotenuse of 13 and a leg of 5.

12 Answer: x = √288. x x =. x ≈ 16.97 12√2. #2. 30 x Answer: x. x = √675. 15 =. x ≈ 25.98 15√3. #3.

Pythagoras' theorem Pythagoras' theorem is well-known from schooldays. In this unit we revise the theorem and use it to solve problems involving right-angled triangles. We will also meet a less-familiar form of the theorem.

Question 2: Shown is a square with side length 5cm. Find the length of the diagonal, x. Question 3: Shown is a right angle triangle. Calculate: the perimeter of the triangle. the area of the triangle. Question 4: A rectangle is 20cm long and 8cm wide. Find the length of the diagonal of the rectangle. Question 5: An airplane is Ylying from ...

These Pythagorean Theorem Worksheets will produce colorful and visual pages that contain definitions and examples for the Pythagorean Theorem and the Distance Formula. These worksheets are great resources for the 6th Grade, 7th Grade, and 8th Grade. These Pythagorean Theorem Worksheets are perfect for providing children a fun way to practice ...

Pythagorean Theorem Assignment. A) Calculate the measure of x in each. Where necessary, round you answer correct to one decimal place. Complete on a separate piece of paper. B) A ladder is leaning against the side of a 10m house. If the base of the ladder is 3m away from the house, how tall is the ladder? Draw a diagram and show all work. PDF ...

The Pythagorean theorem is one of the most beautiful theorems in mathematics. It is simple to state, easy to use, and highly accessible - it doesn't require a huge amount of mathematical machinery to prove. We'll be able to prove it (in numerous ways!) with what we've learned so far.

19) Did you know that the area relationship in the Pythagorean Theorem holds true for shapes other than squares? For example, show that the sum of the two smaller semicircles add up to the area of the hypotenuse semicircle in the diagram on the left.

This document contains an assignment on the Pythagorean theorem. It instructs the student to calculate the measure of x for several triangles, either using the Pythagorean theorem or by rounding answers to one decimal place.

The theorem was named after Pythagoras, a Greek mathematician. It was believed that he was the first one to present a proof for the relationship. Other's proofs were presented after his time. PYTHAGOREAN THEOREM In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the length of the legs.

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PYTHAGOREAN THEOREM PYTHAGOREAN THEOREM #5 e is called c TRIANGLE. The two sides that form the right angle, a e, c, is call b HYPOTENUSE.

6.2 The Pythagorean Theorem STATE STANDARDS MA.8.G.2.4 MA.8.A.6.4 How are the lengths of the sides of a right triangle related? Pythagoras was a Greek mathematician and philosopher who discovered one of the most famous rules in mathematics. In mathematics, a rule is called a theorem.

The Pythagorean Theorem Worksheet is an excellent way to expand your understanding of the Pythagorean Theorem. As you use the worksheet, it is important to remember that 'a' and 'b' represent the shorter lengths on the triangle while c represents the hypotenuse, which is the longest side. Pythagoras Theorem worksheets present you with ...

This is followed by explaining a proof of the converse of the Pythagorean Theorem: For a triangle with side lengths a, b, and c if !+"!=#!, then the triangle is a right triangle. Using this theorem, students determine whether three given side lengths form a right triangle.

Pythagorean Theorem Assignment Answer Key - Free download as PDF File (.pdf) or read online for free. 2022-2023 Academic Year, Semester 1. L'Anse Creuse High School - North. Geometry Instructor: Lauren Wilson.