Pythagorean Theorem

Algebra 1 Tutorial

Pythagorean Theorem

Intro

Pythagorean Theorem is over complicated in most class rooms and I want to simplify it. Originally Pythagoras, the guy who is credited with this theorem, was not doing “math” at all. He needed to find distance’s between two points and he stumbled across this proof. Pythagoras found that if he went 3 steps to the right, and 4 steps forward than he traveled 5 steps from his original position. Let me show you how and why this is.

Sample Problem

Try this: Let’s do the problem. Get a piece of paper, a pencil and a ruler.

Mark any point on the paper, this will be the origin (the place we start from). When the point is marked, move three inches in any direction you like. When that line is complete, move either straight up from that line, or straight down, by four inches. You have reached your ending point.

Now measure from the ending point to the origin. You should get 5 inches!

Pythagoras found that 3*3+4*4=5*5 (or 3^2+4^2=5^2)!

Solution

Remember the original theorem: a^2+b^2=c^2

Now we know a=3 and b=4

So
a^2=3^2=9
and
b^2=4^2=16

The theorem says to add the two numbers together AFTER they are squared
So

9+16=25

But that is not 5! Why isn’t it 5? Because we did not find c yet, we found c^2.

Lets look again: a^2+b^2=c^2 and we have 9+16=25 thus 25=c^2.

If we take the square root of 25 we get c=5! Sound familiar?

You can now successfully find any distance between two points if you know two of the sides!



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