## Step 3: Pythagorean Triples

A **Pythagorean triple **is any group of three** integer** values that satisfies the equation a2 + B2 = C2 is called a Pythagorean triple. therefore any triangle that has sides that form a Pythagorean triple must be a right triangle. When all three sides are **whole numbers** you have a Pythagorean triple*.* For example A = 3 B = 4 C = 5 this can also be called a 3,4,5 triangle. Here is how you do the equation for example 3 squared plus 4 squared = 5 squared, in other words 9 + 16 = 25 therefor because these are all whole numbers the triangle must be a Pythagorean triple.

There are four main **Pythagorean triples families** there is the 3,4,5, the 6,8,10, the 5,12,13, and the 8,15,17 triangles. If you multiply any of the three integers by the same amount you will still have a Pythagorean triple. For example 3,4,5, multiplied by two will give you 6,8,10, witch is a Pythagorean triple.

**Review- **The integers represent the lengths of the sides of the triangles in a,b,c, order. If you do the equation and you don't come out with a whole number the integers are not a Pythagorean triple. Remember when multiplying Pythagorean triples families multiply all three numbers by the same amount.

Key words...

**Pythagorean triple-**A right triangle where the sides are in the ratio of integers. (Integers are whole numbers like 3, 12 etc)

**integer-**Includes the counting numbers {1, 2, 3, ...}, zero {0}, and the negative of the counting numbers {-1, -2, -3, ...}

**Whole numbers-**There is no fractional or decimal part. And no negatives.

Example: 5, 49 and 980 are all whole numbers.

**Pythagorean triples families-**every triple is a whole number multiple of the base triple.