Proofs of Pythagorean Theorem

Proof #1
Now take a good look at the picture below.

The picture above shows 4 identical right-triangle. Each of them has an area of A. Area A is given by:

Now, if we put the four triangle together to form the square below:

The square above has a hole inside it. The total area of the square is given by:

Proof #2

The polygon below is a trapezoid. 

The area of the trapezoid is given by:

.

The area of the trapezoid can also be calculated in:

There are lots of proofs for Pyth Thm. The above are just the two of them. The Pyth Thm is so useful that even Einstein uses it in his calculations on Time Dilation in Special Relativity. On my next post, I will give an introduction on Time Dilation.