Pythagorean Theorem

Step 3: Pythagorean Triples

Picture of 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.

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