# 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