A Taste of Geometry

Pythagorean Triples: Certain sets of numbers have a very special property in connection to the Pythagorean Theorem.

Not only do these numbers satisfy the Pythagorean Theorem, but any multiples of these numbers also satisfy the Pythagorean Theorem.

For example: the numbers 3, 4, and 5 satisfy the Pythagorean Theorem. If you multiply all three numbers by 2 (you will get 6, 8, and 10), these new numbers ALSO satisfy the Pythagorean theorem.

The special sets of numbers that possess this property are called Pythagorean Triples. The most common Pythagorean Triples are: (3, 4, 5) and (5, 12, 13), and (8, 15, 17).

The first two numbers are the sides of a triangle and the third number is the hypotenuse. Thus 3^2+4^2=5^2.

These are important numerical relationships to remember, as they occur frequently on the SAT.

The key is that if you see any triangle with two sides that are proportional to say a 3, 4, 5 then you can quickly predict the other side. So if you are given a triangle that has a hypotenuse measuring 20, and a side measuring 12, you can tell that it is similar to a 3,4,5 triangle and the third side must be 16. Knowing this saves the time of running the numbers through the Pythagorean theorem. And that saves you time for more difficult questions.