# Introduction to The Pythagorean Theorem

*(Cover Artist: Jada Moncur)*

** a**²

**+**²

*b***=**²

*c**The Pythagorean Theorem*.

We’ve all heard of it in one context or another. It’s the method we use to find the third leg of a right triangle, known as the *hypotenuse*.

If you are given any two legs of a right triangle (a triangle with one

right angle) you are able to find the third. *a *and *b* represent the legs of the

triangle, and *c* represents the hypotenuse. The *hypotenuse* is the leg of a right triangle that sits across from the right angle, and is also the longest side in a right triangle.

Let’s say you’re given triangle ABC. Angle B is a right angle, meaning side AC is the hypotenuse since it sits across from the right triangle. If you are given side AB = 3, side BC = 4, and side AC is unknown, you can find the unknown side using the Pythagorean Theorem. Knowing that side AC is the hypotenuse, we can make the equation:

32+ 42 = x²

So now, let’s solve for the unknown:

9 + 16 = x²

25 = x²

5 = x

Using the Pythagorean Theorem, you can actually solve for any of the three legs — not just the hypotenuse — as long as you know the values of the other two legs! Simply plug in the two values that you *do *know, and solve algebraically to find the unknown leg.

*Fun Facts About the Creator of the Pythagorean Theorem! *

- The Pythagorean Theorem was named after Pythagoras, an ancient Greek philosopher and mathematician.

- It is believed that Pythagoras had *synesthesia*, a condition where one associates multiple senses with each other. For example, individuals with synesthesia might match a smell to a color, or a sound to a color.

- Pythagoras didn’t allow his followers to eat beans.

- Pythagoras was most likely a vegetarian.

- Along with the Pythagorean Theorem, Pythagoras also discovered Pythagorean tuning, the five regular solids, the Theory of Proportions, and the sphericity of the Earth.

*Practice Problems with The Pythagorean Theorem:*

Solve for the variable.