Théorème de Thalès - 3e

Triangles emboîtés : longueur complémentaire

Exercice 1 : Calcul d'un côté dans une figure de Thales

Compléter le programme suivant permettant de trouver la longueur \( AE \) connaissant \( AB \), \( AC \) et \( AD \) dans la figure de Thales suivante :

Par exemple si l'utilisateur rentre \( AB=11 \), \( AC=8 \) et \( AD=5 \), votre programme doit afficher en sortie la valeur de \( AE \), soit \( 3,636 \)

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Exercice 2 : Thalès et Pythagore, cas simple

On considère la figure suivante :

Sachant que \( G, F, I \) sont alignés et que \( G, H, J \) sont alignés et que les droites \( (FH) \) et \( (IJ) \) sont parallèles et à l'aide des informations contenues dans la figure, trouver la longueur inconnue.
De plus, on vous rappelle que : \[ GH = 10 \] \[ FH = 8 \] \[ FI = 8 \]

On donnera la réponse sous la forme d'un entier ou d'une fraction simplifiée.

Exercice 3 : Reconnaître une situation d'utilisation du théorème de Thalès et l'appliquer

Exercice 4 : Théorème de thalès (peut être x / ( 3 + x) = 2/5)

On considère la figure suivante :

Sachant que S, X, T sont alignés, que S, W, V sont alignés et que les droites \((TV)\) et \((WX)\) sont parallèles et à l'aide des informations contenues dans la figure, trouver la longueur inconnue.
On donnera la réponse sous la forme d'un entier ou d'une fraction simplifiée.

Exercice 5 : Calcul d'un côté dans une figure de Thales

Compléter le programme suivant permettant de trouver la longueur \( AE \) connaissant \( AB \), \( AC \) et \( AD \) dans la figure de Thales suivante :

Par exemple si l'utilisateur rentre \( AB=18 \), \( AC=18 \) et \( AD=13 \), votre programme doit afficher en sortie la valeur de \( AE \), soit \( 13 \)

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