If you haven’t discovered Pythagorean Triples yet, then prepare to have your mind blown. Basically, instead of having to use the Pythagorean Theorem to solve for the missing length of a hypotenuse, you can use Pythagorean Triples without doing any arithmetic!

### How it works

All right triangles are Pythagorean Triples. The most common triples, however, are {3,4,5} and {5,12,13}. What does this mean? Any right triangles with side lengths that are positive-integer multiples of these triples are also right triangles. Here’s the formal definition of Pythagorean triples.

##### If {a, b, c} is a Pythagorean triple, then so is {ka, kb, kc} for any positive integer k.

For example, if you see a right triangle that has leg lengths of 6 and 8, then the hypotenuse has to be 10 because that’s a positive-integer multiple of the Pythagorean Triple {3,4,5}. In other words, if you multiply the positive integer 2 with {3,4,5}, you’ll get {6,8,10}, therefore saving you from using the Pythagorean Theorem!

Memorize the two most common Pythagorean Triples, {3,4,5} and {5,12,13}, to save yourself time while doing geometry homework and tests. For more help with geometry, read the rest of this series and check out Brightstorm geometry.