applying the pythagorean theorem homework 3 answer key

• $ 0.00 0 items

Unit 8 – The Pythagorean Theorem

The Pythagorean Theorem

LESSON/HOMEWORK

LECCIÓN/TAREA

LESSON VIDEO

EDITABLE LESSON

EDITABLE KEY

SMART NOTEBOOK

The Pythagorean Theorem and Its Converse

Applying the Pythagorean Theorem

Distance in the Coordinate Plane

Understanding the Pythagorean Theorem

Unit Review

Unit 8 Review

UNIT REVIEW

REPASO DE LA UNIDAD

EDITABLE REVIEW

Unit 8 Assessment Form A

EDITABLE ASSESSMENT

Unit 8 Assessment Form B

Unit 8 Exit Tickets

Unit 8 Mid-Unit Quiz – Form A

Unit 8 Mid-Unit Quiz – Form B

U08.AO.01 – Practice with the Pythagorean Theorem and Its Converse

EDITABLE RESOURCE

U08.AO.02 – Practice Finding Distance in the Coordinate Plane

Thank you for using eMATHinstruction materials. In order to continue to provide high quality mathematics resources to you and your students we respectfully request that you do not post this or any of our files on any website. Doing so is a violation of copyright. Using these materials implies you agree to our terms and conditions and single user license agreement .

The content you are trying to access  requires a membership . If you already have a plan, please login. If you need to purchase a membership we offer yearly memberships for tutors and teachers and special bulk discounts for schools.

Sorry, the content you are trying to access requires verification that you are a mathematics teacher. Please click the link below to submit your verification request.

• TemplateLab

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.

More Templates

Law School Letters Of Recommendation

Community Service Forms

Genogram Templates

Permission Slip Templates

Story Map Templates

Unit Circle Charts

You are now being redirected to bestq.info....

Child Login

• Kindergarten
• Number charts
• Skip Counting
• Place Value
• Number Lines
• Subtraction
• Multiplication
• Word Problems
• Comparing Numbers
• Ordering Numbers
• Odd and Even
• Prime and Composite
• Roman Numerals
• Ordinal Numbers
• In and Out Boxes
• Number System Conversions
• More Number Sense Worksheets
• Size Comparison
• Measuring Length
• Metric Unit Conversion
• Customary Unit Conversion
• Temperature
• More Measurement Worksheets
• Writing Checks
• Profit and Loss
• Simple Interest
• Compound Interest
• Tally Marks
• Mean, Median, Mode, Range
• Mean Absolute Deviation
• Stem-and-leaf Plot
• Box-and-whisker Plot
• Permutation and Combination
• Probability
• Venn Diagram
• More Statistics Worksheets
• Shapes - 2D
• Shapes - 3D
• Lines, Rays and Line Segments
• Points, Lines and Planes
• Transformation
• Quadrilateral
• Ordered Pairs
• Midpoint Formula
• Distance Formula
• Parallel, Perpendicular and Intersecting Lines
• Scale Factor
• Surface Area
• Pythagorean Theorem
• More Geometry Worksheets
• Converting between Fractions and Decimals
• Significant Figures
• Convert between Fractions, Decimals, and Percents
• Proportions
• Direct and Inverse Variation
• Order of Operations
• Squaring Numbers
• Square Roots
• Scientific Notations
• Speed, Distance, and Time
• Absolute Value
• More Pre-Algebra Worksheets
• Translating Algebraic Phrases
• Evaluating Algebraic Expressions
• Simplifying Algebraic Expressions
• Algebraic Identities
• Quadratic Equations
• Systems of Equations
• Polynomials
• Inequalities
• Sequence and Series
• Complex Numbers
• More Algebra Worksheets
• Trigonometry
• Math Workbooks
• English Language Arts
• Summer Review Packets
• Social Studies
• Holidays and Events
• Worksheets >
• Geometry >

Pythagorean Theorem Worksheets

These printable worksheets have exercises on finding the leg and hypotenuse of a right triangle using the Pythagorean theorem. Pythagorean triple charts with exercises are provided here. Word problems on real time application are available. Moreover, descriptive charts on the application of the theorem in different shapes are included. These handouts are ideal for 7th grade, 8th grade, and high school students. Kick into gear with our free Pythagorean theorem worksheets!

Identifying Right Triangles

Apply Pythagorean theorem to identify whether the given triangle is a right triangle. Each printable worksheet consists of six problems.

• Download the set

Pythagorean Theorem Chart

These descriptive charts explain the Pythagorean theorem with an illustration. These pdfs emphasize the relation of the theorem derived as an equation.

Pythagorean Triple

A set of three numbers is given in each problem. Grade 7 and grade 8 students need to apply the theorem and identify whether the set of numbers forms a Pythagorean triple.

Pythagorean Triple Chart

This section comprises of Pythagorean triple sets up to 100. Besides, Pythagorean triple formulas with examples are provided in the charts.

Unknown Side of a Right Triangle

Apply Pythagorean theorem to find the unknown side of the right triangle. Round the answer to the nearest tenth.

Unknown Length: Shapes

Apply the Pythagorean theorem to find the unknown length of each shape in these printable worksheets. Round the answer to the nearest tenth.

Word Problems | Level 1

Brighten your math class with this bundle of real-life word problems based on the Pythagorean Theorem. Solve each word problem by finding the missing hypotenuse of the right triangle and rounding off the answer to the nearest tenth.

Word Problems | Level 2

Presenting word problems with clear illustrations, these pdf worksheets require high school students to plug in the known values into the equation form of the Pythagorean Theorem and figure out the unknown side of the right triangle.

Related Worksheets

» Pythagorean Inequality Theorem

» Triangle

» Triangle Inequality Theorem

» Trigonometry

Become a Member

Membership Information

Privacy Policy

What's New?

Printing Help

Testimonial

Copyright © 2024 - Math Worksheets 4 Kids

This is a members-only feature!

Pythagorean Theorem Exercises

Pythagorean theorem practice problems with answers.

There are eight (8) problems here about the Pythagorean Theorem for you to work on. When you do something a lot, you get better at it. Let’s get started!

Here’s the Pythagorean Theorem formula for your quick reference.

Note: drawings not to scale

Problem 1: Find the value of [latex]x[/latex] in the right triangle.

[latex]10[/latex]

Problem 2: Find the value of [latex]x[/latex] in the right triangle.

[latex]4\sqrt 7 [/latex]

Problem 3: Find the value of [latex]x[/latex] in the right triangle.

[latex]3[/latex]

Problem 4: The legs of a right triangle are [latex]5[/latex] and [latex]12[/latex]. What is the length of the hypotenuse?

[latex]13[/latex]

Problem 5: The leg of a right triangle is [latex]8[/latex] and its hypotenuse is [latex]17[/latex]. What is the measure of its other leg?

[latex]15[/latex]

Problem 6: Suppose the shorter leg of a right triangle is [latex]\sqrt 2[/latex]. The longer leg is twice the shorter leg. Find the hypotenuse.

[latex]\sqrt {10} [/latex]

Problem 7: The hypotenuse of a right triangle is [latex]4\sqrt 2[/latex]. If the longest leg is half the hypotenuse, what is the length of the shortest leg?

[latex]2\sqrt 6[/latex]

Problem 8: Find the value of [latex]x[/latex] of the right isosceles triangle.

[latex]\sqrt 6[/latex]

You might also like these tutorials:

• Pythagorean Theorem
• Pythagorean Triples
• Generating Pythagorean Triples

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Unit 9: Pythagorean theorem

About this unit.

The Pythagorean theorem describes a special relationship between the sides of a right triangle. Even the ancients knew of this relationship. In this topic, we’ll figure out how to use the Pythagorean theorem and prove why it works.

Pythagorean theorem

• Intro to the Pythagorean theorem (Opens a modal)
• Pythagorean theorem example (Opens a modal)
• Pythagorean theorem intro problems (Opens a modal)
• Use Pythagorean theorem to find right triangle side lengths 7 questions Practice
• Use Pythagorean theorem to find isosceles triangle side lengths 7 questions Practice
• Right triangle side lengths 4 questions Practice
• Use area of squares to visualize Pythagorean theorem 4 questions Practice

Pythagorean theorem application

• Pythagorean theorem word problem: carpet (Opens a modal)
• Pythagorean theorem word problem: fishing boat (Opens a modal)
• Pythagorean theorem in 3D (Opens a modal)
• Use Pythagorean theorem to find perimeter 4 questions Practice
• Pythagorean theorem word problems 4 questions Practice
• Pythagorean theorem in 3D 4 questions Practice
• Pythagorean theorem challenge 4 questions Practice

Pythagorean theorem and distance between points

• Distance formula (Opens a modal)
• Distance formula review (Opens a modal)
• Distance between two points 7 questions Practice

Pythagorean theorem proofs

• Garfield's proof of the Pythagorean theorem (Opens a modal)
• Bhaskara's proof of the Pythagorean theorem (Opens a modal)
• Pythagorean theorem proof using similarity (Opens a modal)
• Another Pythagorean theorem proof (Opens a modal)

Pythagorean Theorem Worksheets

Related Topics: More Math Worksheets More Printable Math Worksheets 7th Grade Math

There are five sets of triangle worksheets:

• Triangle Sum Theorem
• Exterior Angle Theorem
• Area of Triangle

Area of Triangle using Sine

• Pythagorean Theorem

Examples, solutions, videos, and worksheets to help grade 7 students learn how to use the Pythagorean Theorem.

How to use the Pythagorean Theorem?

There are five sets of Pythagorean Theorem worksheets:

• Find the length of the hypotenuse
• Find the length of a side
• Find the length in two steps
• Check for right triangle
• Pythagorean Theorem Word Problems

The Pythagorean Theorem also called the Pythagoras’ Theorem is a fundamental principle in geometry that relates the sides of a right triangle.

It states that in a right triangle (a triangle with one 90-degree angle), the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Mathematically, the Pythagorean Theorem can be expressed as: c² = a² + b²

• c represents the length of the hypotenuse.
• a and b represent the lengths of the other two sides.

The Pythagorean Theorem is widely used to calculate the length of any one side of a right triangle when the lengths of the other two sides are known. It is an essential tool in geometry and has applications in various fields, including trigonometry, engineering, physics, and architecture.

The Pythagorean Theorem can be used in various ways, including:

• Finding length of any one side of a right triangle when the lengths of the other two sides are known.
• Checking if a Triangle is Right: You can use the theorem to check if a triangle is a right triangle by verifying if the relationship a² + b² = c² holds.
• Solving Problems Involving Right Triangles: The theorem is used to solve problems involving right triangles, such as finding distances, heights, or angles in various real-world situations.

For example, if you have a right triangle with one side (a) measuring 3 units and the other side (b) measuring 4 units, you can use the Pythagorean Theorem to find the length of the hypotenuse (c):

c² = a² + b² c² = 3² + 4² c² = 9 + 16 c² = 25

To find c, take the square root of both sides:

c = √25 c = 5

So, the length of the hypotenuse (c) is 5 units. This illustrates how the Pythagorean Theorem can be used to solve for side lengths in a right triangle.

Click on the following worksheet to get a printable pdf document. Scroll down the page for more Pythagorean Theorem Worksheets .

More Pythagorean Theorem Worksheets

Printable (Answers on the second page.) Pythagorean Theorem Worksheet #1 (find hypotenuse) Pythagorean Theorem Worksheet #2 (find a side) Pythagorean Theorem Worksheet #3 (2-step) Pythagorean Theorem Worksheet #4 (check for right triangle) Pythagorean Theorem Worksheet #5 (word problems)

Online Pythagorean Theorem Find the missing side Test for right triangle Pythagorean Theorem Word Problems Converse Pythagorean Theorem, Types of Triangles

Related Lessons & Worksheets

More Printable Worksheets

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

• Texas Go Math
• Big Ideas Math
• Engageny Math
• McGraw Hill My Math
• enVision Math
• 180 Days of Math
• Math in Focus Answer Key
• Math Expressions Answer Key
• Privacy Policy

Into Math Grade 8 Module 11 Lesson 3 Answer Key Apply the Pythagorean Theorem

We included  HMH Into Math Grade 8 Answer Key PDF   Module 11 Lesson 3 Apply the Pythagorean Theorem to make students experts in learning maths.

HMH Into Math Grade 8 Module 11 Lesson 3 Answer Key Apply the Pythagorean Theorem

I Can apply the Pythagorean Theorem to solve real-life problems involving the legs and hypotenuse of a right triangle, including problems in three dimensions.

Step It Out

Explaantion: Given the red team and blue team are playing capture the Flag. Each team places their flag at opposite corners of the field. The red team sends two players, Alfredo and Angelina, from the red flag to capture the blue flag. Alfredo must follow the white arrows to the flag so far does he runs is 150 m + 85 m = 235 meters, Alfredo runs 235 meters.

Explanation: Given Angelina must follow the black arrow to the flag. Using the Pythagorean Theorem to determine how far she runs. a 2  + b 2  = c 2 , 150 2 + 85 2  = c 2 , 22,500 + 7,225 = c 2 , c 2 = 29,725, So c is equal to sqaure root of 29,725 we get c = 172.4 round to the nearest tenth is 172. Therefore Angelina runs 172 meters.

Explanation: Farther does Alfredo run than Angelina as Alfredo runs 235 meters and Angelina runs 172 meters is 235 – 172 = 63 meters.

Turn and Talk Will the direct route always be shorter than a route between two points with a right angle? Why or why not? Answer: No,

Explanation: A direct route isn’t always the shortest distance between two points with a right angle, The shortest distance between two points with a right angle depends on the geometry of the object/surface in question.

The Pythagorean Theorem can be used to find lengths inside a three-dimensional object by finding right triangle relationships inside the object.

Explanation: As given the length of \(\overline{D C}\) is 30 inches.

Explanation: To know the length of \(\overline{A C}\). Looking at the bottom of the box. \(\overline{A C}\) is the hypotenuse of another right triangle, ∆ABC. Using the Pythagorean Theorem to find the length of \(\overline{A C}\) as a 2  + b 2  = c 2 , 12 2 + 12 2 = ac 2 , 144 + 144 = \(\overline{A C}\) 2 , \(\overline{A C}\) 2 = 288, So ac is equal to sqaure root of 288, we get \(\overline{A C}\) = 16.97, rounding to the nearest tenth we get \(\overline{A C}\) = 17.

Explanation: As we have \(\overline{A C}\) = 17 inches and the length of \(\overline{D C}\) is 30 inches, So the length of \(\overline{A D }\) is 17 2 + 30 2 = ad 2 , 289 + 900 = \(\overline{A D}\) 2 , \(\overline{A D}\) 2 = 1,189, So ad is equal to sqaure root of 1,189, we get \(\overline{A D}\) = 34.48, rounding to the nearest tenth we get \(\overline{A D}\) = 34 inches.

D. About how long is the longest rod that could fit in the box? ___________ inches Answer: About 34 inches,

Explanation: As we have the longest distance in the box is the diagonal AD between opposite corners. It forms the hypotenuse of ∆ACD. So we have \(\overline{A D}\) = 34 inches, therefore 34 inches is the longest rod that could fit in the box.

E. Can the curtain rod fit in the box? Why or why not? Answer: No,

Explanation: As Jada wants to ship a 3-foot curtain rod to a customer, 3 foot, as 1 foot is equal to 12 inches so 3 foot means 3 X 12 = 36 inches, As the longest rod that could fit in the box is only 34 inches and we the curtain rod is 36 inches which is greater, So the curtain rod will not fit in the box.

Explanation: Given Cara measured the radius and outside length of an ice cream cone. Identified the right triangle in the cone, then used Cara’s measurements to find the height of the cone let it be b so 2.5 2 + b 2 = 11.7 2 , 6.25 + b 2 = 136.89 2 , b 2 = 136.89 – 6.25 = 130.64, So b is equal to sqaure root of 130.64, we get b = 11.42 rounding to the nearest hundredth is 11 cm. Therefore the height of the cone is about 11 centimeters.

Turn and Talk Cara has another ice cream cone. The radius and the height of the second cone is known. Explain how to use these dimensions to find the outside length of the cone. Answer: Outside length of the cone is square root of square of radius plus square of the height of the second cone,

Explanation: Given Cara has another ice cream cone. The radius and the height of the second cone is known. Using these dimensions to find the outside length of the cone is sqaure root of square of radius plus square of the height of the second cone. Let the outside length of the cone be c and radius be a and the height of the second cone is b, So c = sqaure root of a 2 + b 2 .

Check Understanding

Explanation: Given computer monitors are measured diagonally from corner to corner. If the rectangular screen of a 40-inch monitor is 35 inches wide, So let the height of the monitor is h, so applying Pythagorean theorem we have 35 2 + h 2 = 40 2 , 1,225 + h 2 = 1,600, h 2 = 1,600 – 1,225 = 375, So h is equal to sqaure root of 375, we get h = 19.36 rounding to the nearest tenth is 19 inches.

Explanation: Given a 20-inch rod fits perfectly in a box 15 inches tall. So the measurement of x in the diagram applying Pythagorean theorem we have 15 2 + x 2 = 20 2 , 225 + x 2 = 400, x 2 = 400 – 225 = 175, So x is equal to sqaure root of 175, we get x = 13.22 rounding to the nearest tenth is 13 inches.

On Your Own

Explanation: The length of the sidewalk from the library to the school is78 m  + 13 m = 91 m and the length she can travel across the grass directly is let it be x, applying Pythagorean theorem we have 13 2 + 78 2 = x 2 , 169 + 6,084 = x 2 , x 2 = 6,253 , So x is equal to sqaure root of 6,253, we get x = 79.07 rounding to the nearest tenth is 79 m. as 91 m > 79 m so the longest route is the sidewalk from the library to the school.

B. What is the difference between the lengths of the two routes? Answer: 12 m,

Explanation: As sidewalk from the library to the school distance is 91 m and the length she can travel across the grass directly is 79 m, the difference between the lengths of the two routes is 91 m – 79 m = 12 m.

Question 4. Adam’s closet measures 36 inches by 24 inches by 96 inches. What is the longest distance between corners inside his closet? Round to the nearest tenth. Answer: The longest distance between corners inside his closet is 105 inches,

Explanation: Given Adam’s closet measures 36 inches by 24 inches by 96 inches. So the longest distance between corners inside his closet is square root of length 2 + width 2 + height 2 = sqaure root of 36 2 + 24 2 + 96 2 = sqaure root of 1,296 + 576 + 9,216 = sqaure root of 11,088 = 105.29 rounding to the nearest tenth is 105 inches.

Explanation: Given the top of a building is a cone 10 meters tall with a radius of 4 meters at the base. So the measurement of x in the diagram is applying Pythagorean theorem we have 10 2 + 4 2 = x 2 , 100 + 16 = x 2 , x 2 = 116 , So x is equal to sqaure root of 116, we get x = 10.77 rounding to the nearest tenth is 11 m.

Question 6. Open-Ended Brianne purchased a box with a base diagonal length that is 45 centimeters long. What are two possible pairs of dimensions for the length and width of the box? Round to the nearest tenth. Answer: One pair: Length = 31.82 cm and Width = 31.82 cm, Other pair: Length = 30 cm and Width = 33.54 cm,

Explanation: Given Brianne purchased a box with a base diagonal length that is 45 centimeters long. The two possible pairs of dimensions for the length and width of the box are the base of the box has a shape of a rectangle, and to find the length of the diagonal we can use the pythagoras theorem as follows: d 2 = l 2 + w 2 ,Where d is the diagonal, l is the length and w is the width. If we assume the base of the box to be a square, we can find one pair of dimension: as l = w, d 2 = l 2 + l 2 = 2l 2 , d 2 = 2 X 45 X 45 = 4,050, d is equal to square root of 4,050 is 63.63, d 2 = 2l 2 , l = 63.63/2  = 31.82 cm, So one pair is length = 31.82 cm and width = 31.82 cm, To find other pair, we can just assume a value for the length, so length = 30 cm then we can find the width as 45 2 = 30 2 + w 2 , w 2 = 2,025 – 900 = 1,125, w is eqaul to square root of 1,125 = 33.54 cm, So the other pair is Length = 30 cm and Width = 33.54 cm.

For Problems 7-9, find the value for the unknown measurement in each rectangular prism or right cone. Round to the nearest tenth.

Explanation: Given measurements as 24 in, 16 in and x in, applying Pythagorean theorem we have 24 2 + 16 2 = x 2 , 576 + 256 = x 2 , x 2 = 832 , So x is equal to sqaure root of 832, we get x = 28.84 rounding to the nearest tenth is 29 in.

Explanation: Given measurements as 40 mm, x mm and 90 mm applying Pythagorean theorem we have 40 2 + x 2 = 90 2 , 1,600 + x 2 = 8,100, x 2 = 8,100 – 1,600 = 6,500 , So x is equal to sqaure root of 6,500, we get x = 80.62 rounding to the nearest tenth is 81 mm.

Explanation: Given measurements as 54 cm, 40 cm and x cm, First finding the hypotenuse side length of 54 cm, 12 cm and y cm, applying Pythagorean theorem we have 54 2 + 12 2 = y 2 , 2,916 + 144 = y 2 , y 2 = 3,060, So y is equal to sqaure root of 3,060, we get y = 55.31 rounding to the nearest tenth is 55 cm. Now we have 55 cm, 40 cm and x cm, applying Pythagorean theorem we have 55 2 + 40 2 = x 2 , 3,025 + 1,600 = x 2 , x 2 = 4,625, So x is equal to sqaure root of 4,625, we get x = 68.0073 rounding to the nearest tenth is 68 cm.

Question 10. Use Structure The Maron Luggage Company claims they have a suitcase large enough to fit a 34-inch baseball bat inside. If the suitcase has height and depth 17 inches by 11 inches, what must its whole-number length be, at minimum? Answer: Its whole- number length will be 34 inches,

Explanation: Given the Maron Luggage Company claims they have a suitcase large enough to fit a 34-inch baseball bat inside. If the suitcase has height and depth 17 inches by 11 inches, Its whole-number length will be 34 inch only aslength will be the same, therefore it is 34 inches.

Explanation: Given cone A – x as 10 cm, y as 17 cm, let z be the height applying Pythagorean theorem we have 10 2 + z 2 = 17 2 , 100 + z 2 = 28, z 2 = 289 – 100 = 189, So z is equal to sqaure root of 189, we get z = 13.74 cm rounding to the nearest tenth is 14 cm, given cone B – x as 12 cm, y as 18 cm, let z be the htpotenuse, applying Pythagorean theorem we have 12 2 + z 2 = 18 2 , 144 + z 2 = 324, z 2 = 324 – 144 = 180, So z is equal to sqaure root of 180, we get z = 13.41 cm rounding to the nearest tenth is 13 cm, upon compairing the heights of Cone A and Cone B , cone A > cone B as 14 cm > 13 cm, therefore cone A is taller than cone B.

B. By how much? Round to the nearest hundredth. Answer: Almost 1 cm,

Explanation: Cone A has height 13.74 cm and cone B has 13.41 cm, So much taller is  13.74 cm – 13.41 = 0.33 cm, nearly 1 cm tall.

Explanation: Given 24 in and 38 in and x in applying Pythagorean theorem we have 24 2 + x 2 = 38 2 , 576 + x 2 =1,444, x 2 = 1,444 – 576 = 868, So x is equal to sqaure root of 868, we get x = 29.46 in rounding to the nearest tenth is 29 in. Therefore the value of x in the diagram is 29 in.

Explanation: Asking to find the length of the longest rod that can fit inside this cube is Length of a cube(l) = 2 m, Breadth of a cube(b) = 2 m, Height of a cube(h) = 2m, The length of the longest rod is the diagonal of the cube. So, We have to find the diagonal of the cube as Diagonal of a cube = √ 3 X side Diagonal of a cube = 1.732 X 2, Diagonal of a cube = 3.46 ≈ 4 m. So the length of the longest rod that can fit inside this cube is 4 m.

Lesson 11.3 More Practice/Homework

Explanation: Given geography the distances between Centerville, Springfield, and Capital City form a right triangle. The distance between Centerville and Springfield is 913 kilometers and the distance between Springfield and Capital City is 976 kilometers. Let x be the direct distance between Centerville and Capital City applying Pythagorean theorem we have 913 2 + 976 2 = x 2 , 833,569 + 952,576 = x 2 , x 2 = 17,86,145, So x is equal to sqaure root of 17,86,145, we get x = 1,336.46 rounding to the nearest tenth is 1,336 kilometers.

B. Anwell travels from Centerville to Springfield, then on to Capital City. Yue travels directly from Centerville to Capital City. How much farther does Anwell travel than Yue? Round to the nearest kilometer. Answer: 553 kilometers,

Explanation: Given Anwell travels from Centerville to Springfield, then on to Capital City. Yue travels directly from Centerville to Capital City. Centerville to Springfield then on to Capital City 913 kilometers + 976 kilometers = 1,889 kilometers, Yue travels directly from Centerville to Capital City is 1,336 kilometers, Anwell travel than Yue is 1,889 kilometers – 1,336 kilometers = 553 kilometers.

Explanation: Given the lengths of ice cup as height 4 in hypotenuse 4.5 in, let r be the radius of  ice cup, applying Pythagorean theorem we have 4 2 + r 2 = 4.5 2 , 16 + r 2 = 20.25, r 2 = 20.25 – 16, So x is equal to sqaure root of 4.25, we get r = 2.06 rounding to the nearest tenth is 2 in.

Explanation: Given a child has an empty box that measures 4 inches by 6 inches by 3 inches. The length of the longest pencil that will fit into the box is the diagonal of cuboid, which is   = √ l 2 + b 2 + h 2 , ∴ Diagonal of box = √ 4 2 + 6 2 + 3 2 , ​ ∴ Diagonal of box =√ 16 + 36 + 9, ∴ Diagonal of box = √61 = 7.81 on rounding it is 8 inches, therefore the lon gest pencil that will fit into the box is 8 inches.

Explanation: Given Mr. Johnston supports a young tree by using a stake and a string forming a right angle with the ground. Let l be the length of the string applying Pythagorean theorem we have 60 2 + 33 2 = l 2 , 3,600 + 1,089 = l 2 , l 2 = 4,689, So l is equal to sqaure root of 4,689, we get l = 68.47 rounding to the nearest tenth is 68 in.

Question 5. The state of Wyoming is almost rectangular, with an approximate width of 365 miles and an approximate height of 276 miles. If you fly across the state from opposite corners, what is the best approximation of the distance you travel? (A) 448 miles (B) 450 miles (C) 458 miles (D) 462 miles Answer: (C) 458 miles,

Explanation: Given the state of Wyoming is almost rectangular with an approximate width of 365 miles and an approximate height of 276 miles. If we fly across the state from opposite corners, the best approximation of the distance I travel is let it be d applying Pythagorean theorem we have 365 2 + 276 2 = d 2 , 132,225 + 76,176 = d 2 , d 2 = 209,401, So d is equal to sqaure root of 209,401 we get d = 457.60 rounding to the nearest tenth is 458 miles which matches with bit (C).

Explanation: Given a box measuring 100 centimeters by 130 centimeters by 400 centimeters The length of the longest rod that will fit into the box is the diagonal of cuboid, which is   = √ l 2 + b 2 + h 2 , ∴ Diagonal of box = √ 100 2 + 130 2 + 400 2 , ​ ∴ Diagonal of box =√ 10,000 + 16,900 + 160,000, ∴ Diagonal of box = √186,900= 432.31 on rounding it is 432 centimeters, therefore the longest rod that will fit into the box is 432 centimeters.

Explanation: The measurements that could possibly fit the given cone diagram as it is a right traingle we applying Pythagorean theorem and checking with bits as Bit (A) x = 3, y = 4, z = 5, 3 2 + 4 2 = 5 2 , 9 + 16 = 25   as 25 = 25 matches, checking with bit (B) x = 9, y = 6, z = 10, 9 2 + 6 2 = 81 + 36 = 117 ≠ 10 2 ≠ 100, So not form a right triangle, Checking with bit (C) x = 3, y = 8, z = 5, 3 2 + 8 2 = 9 + 64 = 73 ≠ 5 2 ≠ 25, So not form a right triangle, Checking with bit (D) x = 6, y = 10, z = 8, 6 2 + 10 2 = 36 + 100 = 136 ≠ 8 2 ≠ 64, So not form a right triangle, Therfore only bit (A) x = 3, y = 4, z = 5 measurements that could possibly fit.

Spiral Review

Question 8. A fun park charges $10 for admission and then $2 for every ride. Write a function that determines the amount of money spent, y, based on the number of rides ridden, x. Answer: y = 2x + 10,

Explanation: Given a park charges $10 for admission and then $2 for every ride. The function that determines the amount of money spent y based on the number of rides ridden x is y= 2x + 10.

Explanation: Reflected the triangle across the y-axis and drawn the image as shown above, Given A(-5,2), B(-7,6) and C(-3,8) so we get A(-5,-2), B(-7,-6) and C(-3,-8).

Leave a Comment Cancel Reply

You must be logged in to post a comment.

Math Worksheets Land

Math Worksheets For All Ages

• Math Topics
• Grade Levels

Pythagorean Theorem Worksheets

When a triangle has a right side (measuring ninety degrees) and you extend each side with a square, the biggest square has the same exact are as the sum of the squares of the other two sides. If we labelled the longest side c and the other two sides (legs) a and b, we could sum up that phenomena with the equation a 2 + b 2 = c 2 . We term the longest side, that opposite the right angle, the hypotenuse. As you gather by the algebra, if you know the measures of any two sides of a right triangle, you can use this theorem to determine the third side. Pythagorean Theorem lends itself to all form of building and construction because it allows you to easily determine the length of any material that we using as long as you have two materials that meet at a right angle. Sailors use this all the time to find the shortest route between two points. You will find many applications in the field of surveying when cartographers and engineers are constructing maps that indicate steepness and slopes of areas.

Aligned Standard: Grade 8 Geometry - 8.G.B.8

• Applying the Pythagorean Theorem Step-by-Step Lesson - The side that is missing is defined as the hypotenuse. We can tell this because it is directly opposite the right angle.
• In Action Guided Lesson - Example: Given a right triangle with a hypotenuse of 27 and a leg of 17, what is the measure of the missing leg?
• Guided Lesson Explanation - If this is a right triangle it will work out when the Pythagorean Theorem is applied to it. This means it will flow in the formula: leg 2 + leg 2 = hypotenuse 2
• Are They Right Triangles? - Determine the classification of these shapes.
• Skills Review - We explore every way this topic can be looked at.
• Answer Keys - These are for all the unlocked materials above.

Review Sheets

The coordinate graph makes it much more understandable than just labeling sides.

• Review 1 - We will look this from the diagram perspective and in word form.
• Review 2 - Another go at this series of skills.

Homework Sheets

• Homework 1 - We will see if these shapes will work for us.
• Homework 2 - Another approach at the first version.
• Homework 3 - All of these shapes are much more narrow.
• Homework 4 - You will find decimal lengths to work with.

Practice Worksheets

We start to find random distances between points.

• Practice 1 - You will work with some really scaled down sides.
• Practice 2 - We orientate these shapes from all directions.
• Practice 3 - This is a basic look at this skill.
• Practice 4 - More decimal lengths to work with.

Math Skill Quizzes

Here are more like problems to help you master this topic.

• Quiz 1 - Use the Pythagorean theorem to find the length of the missing side of the right triangle.
• Quiz 2 - Apply this formula to see if you can determine that missing side.
• Quiz 3 - Time break out the decimal form one more time.

How is the Pythagorean Theorem Used Every in Life?

The history behind how this theorem was conceived is almost fiction-like. Pythagoras was a Greek mathematician, among other things. He was born around 500 B.C. He founded a group called the Brotherhood of Pythagoreans which was devoted towards the study of mathematics. The theorem is credited to Pythagoras, but historians do strongly suggest that it was the effort of this group.

More than 2,500 years later this math still holds up and we use this theorem in our daily lives without even realizing it. It goes without saying that most forms of architecture and construction projects heavily rely on this to form straight lines in their buildings. It also is the foundation of how the angle of roofing is pitched on almost all structures. All the beams and materials used are dependent on this calculation. Something as simple as determining how to optimal position ladders against a wall for safety are calculated in this manner as well.

The Brotherhood of Pythagoreans probably never thought that large water vessels would depend on their math to circumnavigate the Earth's oceans. From very short distances to long, understanding the best path is often a product of this theorem. It also helps ships Captains determine how to interest or disrupt enemies in battle. Watch just about any war movie that involves a ship or a submarine and you will see mathematical compasses and rulers putting this to work.

Get Access to Answers, Tests, and Worksheets

Become a paid member and get:

• Answer keys to everything
• Unlimited access - All Grades
• 64,000 printable Common Core worksheets, quizzes, and tests
• Used by 1000s of teachers!

Worksheets By Email:

Get Our Free Email Now!

We send out a monthly email of all our new free worksheets. Just tell us your email above. We hate spam! We will never sell or rent your email.

Thanks and Don't Forget To Tell Your Friends!

I would appreciate everyone letting me know if you find any errors. I'm getting a little older these days and my eyes are going. Please contact me, to let me know. I'll fix it ASAP.

• Privacy Policy
• Other Education Resource

© MathWorksheetsLand.com, All Rights Reserved

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.

How did our templates helped you today?

Opps what went wrong, related posts.

23+ Business Travel Itinerary Templates

Restaurant Employee Evaluation Form

Peer Evaluation Form: Templates and Examples

Free Newspaper Templates

40 Free Event Program Templates

44 Open House Sign in Sheet Templates

22+ Free Packing Slip Templates

40+ Free Christmas Wish List Templates

Thank you for your feedback.

• Rating Count
• Price (Ascending)
• Price (Descending)
• Most Recent

Applying the pythagorean theorem

Resource type.

Applying the Pythagorean Theorem Word Problems Guided Notes Lesson

Applying the Pythagorean Theorem Foldable Notes - Fully Editable

Applying The Pythagorean Theorem Word Problems Differentiated Worksheets

8th Grade enVision Lesson Plan 7-3: Apply the Pythagorean Theorem

Applying the Pythagorean Theorem (set 1) Digital Math Activity | Google Slides

Applying the Pythagorean Theorem (set 2) Digital Math Activity | Google Slides

Applying the Pythagorean Theorem to Real-World Context with Answer Key

8th Grade Math - Understanding and Applying the Pythagorean Theorem

Grade 8 Math Task Card Activity - Apply the Pythagorean Theorem

Applying the Pythagorean Theorem to find the distance between two points

Applying the Pythagorean Theorem - Word Problems

Applying the Pythagorean Theorem Task Cards - 8.G.7

Using and Applying the Pythagorean Theorem

Understand and apply the Pythagorean Theorem

Apply the Pythagorean Theorem to Determine Unknown Side Lengths

Pythagorean Perimeters TASK CARDS Applying the Pythagorean Theorem

Applying the Pythagorean Theorem Foldable Notes SOL(2016) 8.9

Geometry - Applying the Pythagorean Theorem Activity Sheet

Applying the Pythagorean Theorem (CCSS 8.G.B.7)

Applying the Pythagorean Theorem Student Worksheet (distance learning)

Applying the Pythagorean Theorem Cornell Notes

The Pythagorean Theorem - Applied Practice

Applying the Pythagorean Theorem CC.8.G.7

• We're hiring
• Help & FAQ
• Privacy policy
• Student privacy
• Terms of service
• Tell us what you think

• Skip to main content

Maneuvering the Middle

Student-Centered Math Lessons

• All Products

Pythagorean Theorem Unit 8th Grade TEKS

Description, additional information.

• Reviews (0)

An 8 day Pythagorean Theorem TEKS-Aligned complete unit including: the Pythagorean Theorem, the Pythagorean Theorem converse, Pythagorean Theorem application.

Students will practice with both skill-based problems, real-world application questions, and error analysis to support higher level thinking skills.  You can reach your students and teach the standards without all of the prep and stress of creating materials!

Standards:   TEKS: 8.6C, 8.7C, 8.7D;  Looking for CCSS-Aligned Resources?  Grab the Pythagorean Theorem CCSS-Aligned Unit.  Please don’t purchase both as there is overlapping content.

Learning Focus:

• use the pythagorean theorem and its converse to solve problems
• use models of the pythagorean theorem
• determine the distance between points on a coordinate plane using the pythagorean theorem

What is included in the 8th grade teks pythagorean theorem unit?

1. Unit Overviews

• Streamline planning with unit overviews that include essential questions, big ideas, vertical alignment, vocabulary, and common misconceptions.
• A pacing guide and tips for teaching each topic are included to help you be more efficient in your planning.

2. Student Handouts

• Student-friendly guided notes are scaffolded to support student learning.
• Available as a PDF and the student handouts/homework/study guides have been converted to Google Slides™ for your convenience.

3. Independent Practice

• Daily homework is aligned directly to the student handouts and is versatile for both in class or at home practice.

4. Assessments

• 1-2 quizzes, a unit study guide, and a unit test allow you to easily assess and meet the needs of your students.
• The Unit Test is available as an editable PPT, so that you can modify and adjust questions as needed.

5. Answer Keys

• All answer keys are included.

***Please download a preview to see sample pages and more information.***

How to use this resource:

• Use as a whole group, guided notes setting
• Use in a small group, math workshop setting
• Chunk each student handout to incorporate whole group instruction, small group practice, and independent practice.
• Incorporate our  Pythagorean Theorem Activity Bundle  for hands-on activities as additional and engaging practice opportunities.

Time to Complete:

• Each student handout is designed for a single class period. However, feel free to review the problems and select specific ones to meet your student needs. There are multiple problems to practice the same concepts, so you can adjust as needed.

Is this resource editable?

• The unit test is editable with Microsoft PPT. The remainder of the file is a PDF and not editable.

Looking for more 8th Grade Math Material? Join our All Access Membership Community! You can reach your students without the “I still have to prep for tomorrow” stress, the constant overwhelm of teaching multiple preps, and the hamster wheel demands of creating your own teaching materials.

• Grade Level Curriculum
• Supplemental Digital Components
• Complete and Comprehensive Student Video Library 

Click here to learn more about All Access by Maneuvering the Middle®!

Licensing: This file is a license for ONE teacher and their students. Please purchase the appropriate number of licenses if you plan to use this resource with your team. Thank you!

Customer Service: If you have any questions, please feel free to reach out for assistance .  We aim to provide quality resources to help teachers and students alike, so please reach out if you have any questions or concerns. 

Maneuvering the Middle ® Terms of Use: Products by Maneuvering the Middle®, LLC may be used by the purchaser for their classroom use only. This is a single classroom license only. All rights reserved. Resources may only be posted online in an LMS such as Google Classroom, Canvas, or Schoology. Students should be the only ones able to access the resources.  It is a copyright violation to upload the files to school/district servers or shared Google Drives. See more information on our terms of use here . 

If you are interested in a personalized quote for campus and district licenses, please click here . 

©Maneuvering the Middle® LLC, 2012-present

This file is a license for one teacher and their students. Please purchase the appropriate number of licenses if you plan to use this resource with your team. Thank you!

Customer Service

We strive to provide quality products to help teachers and students alike, so contact us with any questions.

Maneuvering the Middle® Terms of Use

Products by Maneuvering the Middle, LLC may be used by the purchaser for their classroom use only. This is a single classroom license only. All rights reserved. Resources may only be posted online if they are behind a password-protected site.

Campus and district licensing is available please contact us for pricing.

©Maneuvering the Middle LLC, 2012-present

There are no reviews yet.

Only logged in customers who have purchased this product may leave a review.

This resource is often paired with:

Digital Math Activity Bundle 8th Grade

Pythagorean Theorem Activity Bundle 8th Grade

• Create a ShowMe
• Community Guidelines
• Edit Profile
• Edit ShowMes
• Students' ShowMes
• My Subscriptions
• ShowMe Ambassadors

You must be logged into ShowMe

Are you sure you want to remove this ShowMe? You should do so only if this ShowMe contains inappropriate content.