Question

Please never try to tease me
Proof pythagoras theorem

Answer 1

We can show that a2 + b2 = c2 using Algebra

Take a look at this diagram ... it has that "abc" triangle in it (four of them actually):



Area of Whole Square

It is a big square, with each side having a length of a+b, so the total area is:

A = (a+b)(a+b)

Area of The Pieces

Now let's add up the areas of all the smaller pieces:

First, the smaller (tilted) square has an area of:c2


Each of the four triangles has an area of:ab2

So all four of them together is:4ab2 = 2ab


Adding up the tilted square and the 4 triangles gives:A = c2 + 2ab

Both Areas Must Be Equal

The area of the large square is equal to the area of the tilted square and the 4 triangles. This can be written as:

(a+b)(a+b) = c2 + 2ab

NOW, let us rearrange this to see if we can get the pythagoras theorem:

Start with:(a+b)(a+b) = c2 + 2ab

Expand (a+b)(a+b):a2 + 2ab + b2 = c2 + 2ab

Subtract "2ab" from both sides:a2 + b2 = c2

DONE!

Now we can see why the Pythagorean Theorem works ... and it is actually a proof of the Pythagorean Theorem.

This proof came from China over 2000 years ago!