Back To Course

Algebra II: High School23 chapters | 203 lessons

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Login here for access

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this video lesson, you will learn about numbers that form Pythagorean Triples. Learn why these are special numbers and what they have to do with triangles.

Before we can talk about Pythagorean triples, we need to talk about triangles and the Pythagorean Theorem. Yes, triangles, specifically, right triangles - you know, the triangle where one of the angles measures 90 degrees. According to the **Pythagorean Theorem**, the sides of a right triangle follow the rule that the square of the hypotenuse equals the sum of the squares of the other two sides. We can write this mathematically as *a*^2 + *b*^2 = *c*^2, where *c* is the hypotenuse, and *a* and *b* are the other two sides. This is a very popular formula in math and can be found virtually everywhere! What does this have to do with Pythagorean triples, you ask?

I'm glad you asked, and just in time, too. See, **Pythagorean triples** are the integers that fit the formula for the Pythagorean Theorem. These are whole numbers that can't be decimals. Because all Pythagorean triples solve the formula for the Pythagorean Theorem, you can take any Pythagorean triple and make a right triangle out of it.

You want to see? Let's look at the first Pythagorean triple of 3, 4 and 5. If we plug these numbers into the Pythagorean Theorem, we see that it works. 3^2 + 4^2 = 5^2 becomes 9 + 16 = 25, which is true. 3, 4 and 5 are also all integers; no decimals here. Also, if we took three sticks that are the same lengths as our numbers and we connected the ends of the sticks to each other, we would end up with a right triangle.

We can scale any Pythagorean triple by multiplying each number by the same factor. For example, 3, 4 and 5 scales to 6, 8 and 10. If you plugged this new set of numbers into the Pythagorean Theorem, you will see that it works as well. 6^2 + 8^2 = 10^2 becomes 36 + 64 = 100, which is true.

We can keep playing with different numbers to find even more Pythagorean triples. Playing around, we find that 5, 12 and 13 are Pythagorean triples. 7, 24 and 25 are also Pythagorean triples; so are 8, 15 and 17. There are actually an infinite amount of Pythagorean triples. Thinking about it, right triangles can be infinitely larger or smaller, so yes, there would be an infinite amount of Pythagorean triples.

Taking a closer look at our Pythagorean triples shows us some interesting properties. We find that either all of the numbers in a Pythagorean triple are even or we have two odd numbers with an even number. We never have all odd numbers or even one odd number with two even numbers.

So what have we learned? We've learned that **Pythagorean triples** are the integers that fit the formula for the Pythagorean Theorem. The **Pythagorean Theorem** says that the sides of a right triangle follow the rule that the square of the hypotenuse equals the sum of the squares of the other two sides. The formula for this is *a*^2 + *b*^2 = *c*^2, where *c* is the hypotenuse, and *a* and *b* are the two other sides. There are an infinite number of Pythagorean triples that fit the formula. The few that we've covered in this lesson are (3, 4, 5), (6, 8, 10), (5, 12, 13), (7, 24, 25) and (8, 15, 17). Our Pythagorean triples are either all even numbers or one even number with two odd numbers.

Display your ability to do the following after completing the lesson:

- State the Pythagorean Theorem
- Define Pythagorean triples
- Identify the properties of Pythagorean triples

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? Login here for access

Did you know… We have over 160 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
8 in chapter 1 of the course:

Back To Course

Algebra II: High School23 chapters | 203 lessons

- What are the Different Types of Numbers? 6:56
- Graphing Rational Numbers on a Number Line 5:02
- Notation for Rational Numbers, Fractions & Decimals 6:16
- The Order of Real Numbers: Inequalities 4:36
- Finding the Absolute Value of a Real Number 3:11
- How to Rationalize the Denominator with a Radical Expression 3:52
- Algebraic Numbers and Transcendental Numbers 6:23
- Understanding Numbers That Are Pythagorean Triples 3:41
- Go to Algebra II: Real Numbers

- AFOQT Information Guide
- ACT Information Guide
- Computer Science 335: Mobile Forensics
- Electricity, Physics & Engineering Lesson Plans
- Teaching Economics Lesson Plans
- FTCE Middle Grades Math: Connecting Math Concepts
- Social Justice Goals in Social Work
- Developmental Abnormalities
- Overview of Human Growth & Development
- ACT Informational Resources
- AFOQT Prep Product Comparison
- ACT Prep Product Comparison
- CGAP Prep Product Comparison
- CPCE Prep Product Comparison
- CCXP Prep Product Comparison
- CNE Prep Product Comparison
- IAAP CAP Prep Product Comparison

- What's the Difference Between Polytheism and Monotheism?
- Ethnic Groups in America
- What Are the 5 Ws in Writing? - Uses & Examples
- Phenol: Preparation & Reactions
- Plant Life Cycle Project Ideas
- Medieval Castle Project Ideas
- Samurai Project Ideas
- Quiz & Worksheet - Solvay Process
- Quiz & Worksheet - Kinds of Color Wheels
- Quiz & Worksheet - Understanding Abbreviations
- Quiz & Worksheet - Act & Rule Utilitarianism Comparison
- Analytical & Non-Euclidean Geometry Flashcards
- Flashcards - Measurement & Experimental Design
- Sentence Structure Worksheets
- Trigonometry Worksheets

- Classroom Management Strategies for Teachers
- NY Regents Exam - Global History and Geography: Test Prep & Practice
- CLEP College Composition: Study Guide & Test Prep
- TABE - Math: Practice & Study Guide
- Precalculus: Help and Review
- OAE Physics: Laboratory Safety
- Non-Euclidean Geometry
- Quiz & Worksheet - Impact of Contact & Exchange Between Societies
- Quiz & Worksheet - How Resources Drive Movement in Canada
- Quiz & Worksheet - Characteristics of Social Media Marketing
- Quiz & Worksheet - Fundamental Forces of Nature
- Quiz & Worksheet - Adding, Subtracting, Multiplying & Dividing Decimals

- Giving Directions in Spanish
- Strategies for Promoting Students' Communication Skills
- Oregon Science Standards for 5th Grade
- 504 Plans in Virginia
- Third Grade Georgia Science Standards
- 504 Plans in Illinois
- What is the TExES PPR Exam?
- South Dakota Science Standards for Kindergarten
- Texas Teacher Certification Renewal
- Special Education Certification in Texas
- WV Next Generation Standards for Math
- Animal Farm Lesson Plan

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

Browse by subject