Pythagorean Triples and Similar Triangles

What is a Pythagorean triple?

To best understand Pythagorean triples, we had best talk briefly about the Pythagorean Theorem first. The Pythagorean Theorem says that if a right triangle has a hypotenuse of side length c, and legs of lengths a and b, then the following formula must be true:

Now, a Pythagorean triple is a set of three natural numbers (a, b, c) (called an ordered triple) such that they satisfy the Pythagorean Theorem. The order in which the numbers are listed matter. If a, b, and c are plugged into the above equation…