exo7 7268

Soit $\mathcal{T}$ un triangle rectangle dont les côtés adjacents à l'angle droit mesurent $a$ et $b$, et l'hypoténuse $c$. On construit dans un carré $ABCD$ de côté $a+b$ les points $A'B'C'D'$ sur les côtés aux distances indiquées des extrémités.

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Montrer que $A'B'C'D'$ est un carré. En déduire une démonstration du théorème de Pythagore.