how to make geometry your best friend

How to Make Geometry Your Best Friend (Part 3)

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.

how to make geometry your best friend

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.

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