Back To Course

Math for Kids23 chapters | 325 lessons

{{courseNav.course.topics.length}} chapters | {{courseNav.course.mDynamicIntFields.lessonCount}} lessons | {{course.flashcardSetCount}} flashcard set{{course.flashcardSetCoun > 1 ? 's' : ''}}

Instructor:
*Allison Petrovic*

Allison has experience teaching high school and college mathematics and has a master's degree in mathematics education.

Did you know that we can use art and math together? In this lesson, we will use one picture to prove the famous Pythagorean Theorem! Join me to see how this Pythagorean Theorem Proof works with art.

Let's have some fun and combine art with math! But, before we can begin, let's review a couple of terms. The **Pythagorean Theorem** says that for right triangles, the sum of the squares of the leg measurements is equal to the hypotenuse measurement squared. The **legs** are the two shorter sides of a right triangle. The **hypotenuse** is the longest side of a right triangle. Let's look at the 'Definition of Pythagorean Theorem' picture to get a better understanding. Letter *a* represents the length of one leg. Letter *b* represents the length of the other leg, and letter *c* is the length of the hypotenuse!

Look at the 'Proof of Pythagorean Theorem' image which shows a right triangle outlined in orange. The two legs are 3 units and 4 units. The hypotenuse is 5 units. Each side of the triangle has a square that goes along with it. So the leg that is 3 units has a 3 x 3 square. This square is pink. The leg that is 4 units has a 4 x 4 square. This square is blue. The hypotenuse, which is 5 units, has a 5 x 5 square. This square is pink and blue.

This picture is showing us the Pythagorean Theorem! Let's break it down. First, we need to square each of the legs. For the leg that is 3 units, we can square 3 (32) and get 3 x 3 = 9. In the picture, the pink square is made up of 9 units. For the leg that is 4 units, we can square 4 (42) and get 4 x 4 = 16. In this picture, the blue square has 16 units! If we add those two squares together, we should get the square of the hypotenuse according to the Pythagorean Theorem! Adding the two squares together, we get 9 + 16 = 25 square units!

That means that the square that goes with the hypotenuse should have 25 units! It sure does in the picture! This square is both pink and blue and has a total of 25 units. If you were to cut out all units on the pink square and blue square, you can rearrange them to fill in each unit of the square that goes with the hypotenuse! This is really neat! You can also see how the hypotenuse is 5 units long. If you square 5 (52), you get 5 x 5 = 25!

OK. We just proved the Pythagorean Theorem for one size of a right triangle. But what about other sizes? Using grid paper, you could draw any size of a right triangle and use this same proof. All you have to do is draw squares to go along with each leg, with the side of each square being equal to the side of the triangle. The number of units in each square is equal to the square of the side length. Then, draw a square to go along with the hypotenuse. If you were to count all the units in the two squares that go with the two legs, that total number would be equal to the number of units in the square that goes with the hypotenuse!

Art can be used to prove the **Pythagorean Theorem**. If you were to draw squares to go along with each of the **legs** of any right triangle, the sum of those squares would be equal to the square of the **hypotenuse**!

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Log in here for access

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
24 in chapter 2 of the course:

Back To Course

Math for Kids23 chapters | 325 lessons

{{courseNav.course.topics.length}} chapters | {{courseNav.course.mDynamicIntFields.lessonCount}} lessons | {{course.flashcardSetCount}} flashcard set{{course.flashcardSetCoun > 1 ? 's' : ''}}

- Surface Area Lesson for Kids
- Types of Angles: Lesson for Kids
- Types of Triangles: Lesson for Kids
- Geometric Shapes: Lesson for Kids
- Isosceles Triangle Lesson for Kids
- How to Use a Protractor: Lesson for Kids
- 3-D Shapes: Lesson for Kids
- Pentagon Shapes: Lesson for Kids
- Polygon Shapes: Lesson for Kids
- Diamond Shapes: Lesson for Kids 2:42
- Measuring Angles: Lesson for Kids
- Circle Definition: Lesson for Kids 3:10
- Circumference Lesson for Kids: Definition & Formula
- Cubes: Lesson for Kids
- Properties of a Circle: Lesson for Kids
- Rectangle Definition: Lesson for Kids
- Triangle Lesson for Kids: Definition & Facts 3:06
- 2-D Shapes: Lesson for Kids
- How to Find the Area of a Triangle: Lesson for Kids
- How to Find the Volume of a Cylinder: Lesson for Kids
- Pentagon Shape Facts: Lesson for Kids 2:39
- Vertices: Lesson for Kids
- What is a Regular Polygon? - Lesson for Kids
- Pythagorean Theorem Proof: Lesson for Kids
- How to Find the Perimeter of a Regular Pentagon 2:43
- Is a Pentagon a Regular Polygon?
- Geometry Definition: Lesson for Kids
- Names of Polygons
- What is a Venn Diagram? - Lesson for Kids 3:32
- Triangle Sum Theorem Proof
- Facts About Right Angles
- Octagon Lesson for Kids: Definition & Facts
- Hexagon Lesson for Kids: Definition & Facts
- Perimeter Lesson for Kids: Definition & Examples
- 4-Sided Polygons 3:55
- Dodecahedron: Definition & Facts
- Special Right Triangles: 3-4-5 Triangle
- Triangle Sum Theorem: Definition & Examples
- Dodecahedron: Patterns & Properties
- Finding the Area of an Irregular Hexagon 3:38
- How to Divide an Angle into Two Equal Angles
- What is a Congruent Angle? - Lesson for Kids
- Go to Geometry for Elementary School

- 7th Grade Math: Homeschool Curriculum
- 8th Grade Math: Homeschool Curriculum
- 7th Grade Life Science: Homeschool Curriculum
- 8th Grade Language Arts: Homeschool Curriculum
- 6th Grade Math: Homeschool Curriculum
- History & Social Impacts of Computer Science
- Fundamentals of Computer Programming
- Resources for Computer Science Teachers
- SPED Curriculum Planning in New York State
- Instructing English Language Learners
- CEOE Test Retake Policy
- Study.com Customer Service FAQs: Login, Cost & Support Email
- Study.com Refund: How to Request a Refund from Study.com
- California Real Estate Exam Dates
- How to Study for the FSA Exam
- FSA Test Cost
- How to Pass the FSA Reading Test

- Mesopotamian Animals: Wild & Domesticated
- Ecocentrism in Environmental Ethics
- The Open Boat by Stephen Crane Summary
- What do Hawks Eat? - Lesson for Kids
- John Brown Discussion Questions
- Perfume River by Robert Olen Butler Discussion Questions
- Koala Adaptations: Lesson for Kids
- Quiz & Worksheet - Milk & Dairy Production
- Quiz & Worksheet - East of Eden Synopsis & Characters
- Quiz & Worksheet - Indicator Words
- Tornadoes vs. Hurricanes: Quiz & Worksheet for Kids
- Flashcards - Real Estate Marketing Basics
- Flashcards - Promotional Marketing in Real Estate
- Statistics Worksheets
- What is Summative Assessment? | A Guide to Summative Assessment

- SAT US History: Help and Review
- American Literature Textbook
- Introduction to Human Geography: Help and Review
- High School World History: Homework Help Resource
- High School Physical Science: Tutoring Solution
- CLEP Social Sciences and History: Macroeconomic Equilibrium
- AEPA Math: Summarizing Data
- Quiz & Worksheet - Mental Institutions in the 1950s
- Quiz & Worksheet - Seeing by Annie Dillard
- Quiz & Worksheet - Arab Trade & Merchants in the Middle Ages
- Quiz & Worksheet - Ethical Codes of Conduct
- Quiz & Worksheet - Modern Experimental Music

- Major River Systems of Mesopotamia & Egypt
- The Magnificent Ambersons: Book Summary & Characters
- What is Micro Credentialing?
- Grants for Field Trips
- How to Pass the NAPLEX
- How to Pass the MPRE Exam
- Best Free Online English Courses
- Global History & Geography Regents Exam Info
- The American Civil War Era: Assignment 1 - National Effects Essay
- How to Find an AP Environmental Science Released Exam
- How to Prep for the NYS Geometry Regents Exam
- How to Pass Statistics

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject