# pythagorean theorem

pythagoreon theorem

## pythagorean theorem

Over 2000 years ago there was an amazing discovery about triangles:

* When a triangle has a right angle (90°) ...*

*... and squares are made on each of the three sides, ...*

*... then the biggest square has the exact same area as the other two squares put together!*

It is called "Pythagoras' Theorem" and can be written in one short equation:

a2 + b2 = c2

Note:

**c**is the**longest side**of the triangle**a**and**b**are the other two sides

Definition

The longest side of the triangle is called the "hypotenuse", so the formal definition is:

In a right angled triangle:

the square of the hypotenuse is equal to

the sum of the squares of the other two sides.

Sure ... ?

Let's see if it really works using an example.

Example: A "3,4,5" triangle has a right angle in it.

Let's check if the areas **are** the same:

32 + 42 = 52

Calculating this becomes:

9 + 16 = 25

*It works ... like Magic! *

Why Is This Useful?

If we know the lengths of **two sides** of a right angled triangle, we can find the length of the **third side**. (But remember it only works on right angled triangles!)

How Do I Use it?

Write it down as an equation:

a2 + b2 = c2

Now you can use algebra to find any missing value, as in the following