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## Are all right triangles Pythagorean triples?

The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula a2 + b2 = c2; thus, Pythagorean triples describe the three integer side lengths of a right triangle. However, right triangles with non-integer sides do not form Pythagorean triples.

## How do you identify Pythagorean triples?

A Pythagorean triple is a list of three numbers that works in the Pythagorean theorem — the square of the largest number is equal to the sum of the squares of the two smaller numbers. The multiple of any Pythagorean triple (multiply each of the numbers in the triple by the same number) is also a Pythagorean triple.

## Is there a pattern to Pythagorean triples?

Yes. You can obtain any Primitive Pythagorean Triple (PPT) , where is double the square of a positive integer, is the square of an odd integer, and . You can then multiply these through by positive integers to obtain the families of Pythagorean Triples originating with each PPT.

## What is a set of Pythagorean triples?

A set of three integers that can be the lengths of the sides of a right triangle is. called a Pythagorean triple. The simplest Pythagorean triple is the set “3, 4, 5.”

## How do you solve Pythagorean triples?

Pythagorean Triples

1. Pythagorean triples are a2+b2 = c2 where a, b and c are the three positive integers.
2. The integer solutions to the Pythagorean Theorem, a2 + b2 = c2 are called Pythagorean Triples which contains three positive integers a, b, and c.
3. 32 + 42 = 52
4. a2+b2=c2
5. (i.e.,) 32 + 42 = 52
6. Similarly,62 + 82 = 102

## Is 72 and 75 part of a Pythagorean triple?

no; They can be part of a Pythagorean triple if 75 is the hypotemse, because 752=212+722.

## Can two of the numbers in a Pythagorean Triple be 2 apart?

A Pythagorean Triple can never be made up of all odd numbers or two even numbers and one odd number. This is true because: The square of an odd number is an odd number and the square of an even number is an even number.