Named Pythagoras found an amazing fact about triangles:

f the triangle had a right angle (90°) …

… and you made a square on each of the three sides, then …

… the biggest square had theexact same areaas the other two squares put together!

It is called “Pythagoras’ Theorem” and can be written in one short equation:

a^{2} + b^{2} = c^{2}

## 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.

### Example: A “3,4,5” triangle has a right angle in it.

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

3^{2} + 4^{2} = 5^{2}

Calculating this becomes:

9 + 16 = 25

Nice explanation of the Pythagorean Theorem. What did you learn from it? How did the Slope Wheel help you learn in math class? Keep working hard! 🙂