# What is one method for proving the Pythagorean Theorem?

Nov 26, 2015

There are numerous ways but the most simple one is this

#### Explanation:

I really enjoyed this proof when I learnt it for the first Time .there is plenty of history behind it (;

So let me give you a timeline of the various mathematician's proof of this theorem

He provided 2 proofs;

1st proof Consider the above figures;
In the above diagrams, the blue triangles are all congruent and the yellow squares are congruent. First we need to find the area of the big square two different ways. First let's find the area using the area formula for a square.

$A = {c}^{2.}$

Area of the blue triangles$= 4 \left(\frac{1}{2}\right) a b$

Area of the yellow square $= {\left(b - a\right)}^{2}$

Area of the big square $= 4 \left(\frac{1}{2}\right) a b + {\left(b - a\right)}^{2}$

$= 2 a b + {b}^{2} - 2 a b + {a}^{2}$

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

$A = {c}^{2} = {a}^{2} + {b}^{2} ,$

What??? We are there already we have arrived at the Pythagorean theorem

Now The second way involves similarity which I am not sure you are exposed to but if you want it ..Just comment (;)

Now Another method is the James Garfield method ;

I may suggest a video for the same but anyhow i will explain if you have any difficulties;

James Garfield Proof