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Understanding Numbers That Are Pythagorean Triples

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  • 0:03 The Pythagorean Theorem
  • 0:48 Pythagorean Triples
  • 1:09 Examples
  • 2:31 Interesting Properties
  • 2:52 Lesson Summary
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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.

The Pythagorean Theory

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?

Pythagorean Triples

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.

Examples

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.

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