A demonstration of the Pythagoras' theorem [Une démonstration du théorème de Pythagore].

Let's build the following polygons:

==> ==> ==>

• The big green quadrilateral is a square (one right angle and four sides equal to X+Y).
• The small red quadrilateral is a square (one right angle and four sides equal to Z).
• The four blue/red triangles are equal (they are right angled triangles with two equal small sides X and Y).

Then:
```  Surface(Green Square)    =      Surface(Red Square)     +   4.Surface(Blue Triangle)
```
= +

```             2                           2                             1
(X+Y)           =               Z               +          4.(---.X.Y)
2
```
```           ___          ___
2    2   /   \    2   /   \
X  + Y  + 2.X.Y = Z  + 2.X.Y
\___/        \___/
```

```  2    2    2
X  + Y  = Z
```

``` CQFD
```

(Z, X and Y denoting respectively the hypotenuse and the two other sides of the four right angled triangles)

(CMAP28 WWW site: this page was created on 04/26/2017 and last updated on 06/26/2020 18:56:31 -CEST-)

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