# Pythagorean Theorem and Slope Wheel

## Phytagthagorean Theorem

 Years ago, a man named Pythagoras found an amazing fact about triangles: If the triangle had a right angle (90°) … … and you made a square on each of the three sides, then … … the biggest square had 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? Slope Wheel

Write it down as an equation:

 a2 + b2 = c2

Now you can use algebra to find any missing value.

## Slope Wheel

In the last chapter, we learned about slopes (gradient), and to help us do the slopes activity, our teacher, Mr. Jared, told us to make a slope wheel. I think the slope wheel helped me a lot in doing my homeworks.
I have a improvement idea for the slope wheel : the sate stick which represent the line, is to thick and sometimes it touches 2 lines at a time, so, its better if the tool to represent the line is subtituded to a thinner tool than the sate stick!