Before we talk about the definition of the Pythagorean Theorem, we should remember two basic ideas from mathematics and specifically geometry:

1. The definition of a right triangle: in simple terms, a right triangle is a triangle that has one of its internal angles measuring 90°.
2. The sides of a right triangle have names. We call the longest side the hypotenuse, which is also always found opposite the 90° internal angle; the other two sides are known as legs and the intersection of these two sides creates the internal right angle that is characteristic of all right triangles.

Now that we remember these two basic theoretical premises about triangles, we are ready to analyze the question, “what is the Pythagorean Theorem?”

The Pythagorean Theorem is a mathematical proposal that can be demonstrated in different ways. This theorem states the relationship that exists between the legs and the hypotenuse of a right triangle in which, if we square each of the two legs and add them together, we have a measurement equal to the square of the hyptoenuse.

In other words, if we call the hypotenuse h and each of the legs a and b, we have:

a^2 + b^2 = h^2

There are many applications of the Pythagorean Theorem and they have been helping different civilizations ever since its discovery by Pythagoras of Samos many centuries ago, well before the Christian era. The fact that this mathematical formula is so easy to learn has caused it to be taught starting at basic educational levels, and then expanded upon and developed mainly in the classroom over the years.