Le plan - 5e

Hauteurs, médiatrices

Exercice 1 : Déterminer par construction l'intersection des médiatrices

Nicolas, Florent et Louis souhaitent jouer à la bataille corse.
Ils s'asseoient autour d'une table aux positions A, B et C.
Ils souhaitent positionner la pile de cartes à égale distance entre eux.
Pour trouver ce point P, ils doivent chercher l'intersection de la médiatrice de [AB] et de [AC].
Déterminer, par construction, une approximation de la distance AP (AP = BP = CP).

On sait que: \[ AB = 56 cm \] \[ BC = 68 cm \] \[ AC = 89 cm \]

On pourra utiliser le fichier de géométrie dynamique suivant.

On arrondira la distance à 0,1cm près.

Exercice 2 : Reconnaître une hauteur de triangle

Parmi les figures suivantes, pour lesquelles la droite \((DC)\) est-elle la hauteur du triangle \(ABC\) ?

1.

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2.

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3.

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4.

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Suivant Valider

Exercice 3 : Démontrer l'équidistance entre un point sur la médiatrice et les deux sommets du triangle associés

Sachant que \((d)\) est la médiatrice de \([LN]\) et \(M \in (d)\)

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Prouver que \(LM = NM\).

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Suivant Valider

Exercice 4 : Reconnaître une médiatrice d'un triangle isocèle

Sachant que ME = MF, NE = NF et \( (d) \) est la médiatrice de [EF].

Prouver que la droite (MN) est la médiatrice du segment [EF].

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Exercice 5 : Construire la médiatrice du côté d'un triangle

Dans le triangle \(ABC\) suivant, tracer la médiatrice du segment \([AB]\).

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