Proofs of Pythagoras Theorem:

The following sketches provide ideas to formal proofs of Pythagoras Theorem.

　

1. Proof by transformation of area.
The main idea is:

Here are two demonstrations based on the above idea

Demonstration 1

Demonstration 2

Demonstration 3: You may also try to do the transformation of area yourself

　

2. Proof by algebraic argument.

Let's look at the following figures. They show the proof we want.
The figure consists of two regions, i.e. the white region and the blue region. In this figure, Area of white region = a^2 +b^2
After some transformations on the blue region, we have: Area of white region = c^2 However, the total area and the area of the blue region is unchanged. So, a^2 +b^2 = c^2
Demonstration 4 You may also try to do the transformation of triangles yourself

　

　

3. Proof by dissection.
Try to find out the argument behind this proof.

Demonstration 5

Suggested answer:
(Mouse select the following area)

　

△_{bottom right} ≡△ _{top left}

 △_{bottom left} ≡△ _{top right}

So, the area is preserved