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!

 Pythagoras
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.

pythagoras theorem 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:

abc triangle 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!

One thought on “Pythagorean Theorem and Slope Wheel

  1. Good presentation on the Pythagorean Theorem and nice reflection on the Slope Wheel. Keep up the good work! 🙂

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