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# Introduction to The Pythagorean Theorem

a²+ b² = c²

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.