Learn the Pythagorean Theorem with our Chart and Triple Examples

The Pythagorean Theorem is a fundamental concept in mathematics that has been used for centuries to solve a wide range of problems. It is a simple formula that helps us find the length of the sides of a right triangle, given the lengths of the other two sides. This theorem has many real-world applications, including in construction, navigation, and astronomy. In this article, we will discuss how you can use the Pythagorean Theorem to find triples with a chart.

The Pythagorean Theorem

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This can be written in the form of an equation:

a² + b² = c²

where a and b are the lengths of the two legs of the right triangle, and c is the length of the hypotenuse. To use this formula, you must know the values of two sides in the right triangle, and you can use it to find the length of the third side.

Finding Pythagorean Triples

A Pythagorean triple is a set of three positive integers a, b, and c that satisfy the Pythagorean Theorem. In other words, a² + b² = c² for these values. Here are some examples of Pythagorean triples:

• 3, 4, 5
• 5, 12, 13
• 8, 15, 17
• 7, 24, 25

You can use a chart to find Pythagorean triples. To make a chart, start by listing the square of each integer, starting with 1:

Number	Square
1	1
2	4
3	9
4	16
5	25
6	36
...	...

Then, look for sets of three square numbers that differ by 1, like this:

• 3² - 2² = 5
• 5² - 4² = 9
• 8² - 6² = 10
• ...

These sets of three numbers are Pythagorean triples. By dividing each number by the smallest one, you can generate other triples, like this:

• 3, 4, 5
• 5, 12, 13
• 4, 3, 5 (divided by 3)
• 15, 8, 17 (divided by 5)
• ...

Get Your Pythagorean Theorem Chart

If you want to find more Pythagorean triples or need a tool to help you learn the Pythagorean Theorem, download our Pythagorean Theorem Chart in DOCX format. It includes a list of squares up to 200 and highlights the sets of three numbers that form Pythagorean triples. Use it to study or as a reference for solving problems.

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