Bonjour,

Ex 25)

MN = MA + AN

= -AM + AC + CN

= -(5AB + CA) + AC + 2AB + AC - 3BC

= -5AB + AC + AC + 2AB + AC + 3(CA + AB)

= -3AB + 3AC + 3CA + 3AB

= 0

M et N sont confondus.

EX 26)

ABCD parallélogramme de centre E

1) AB + AD

= AB + BC   (car AD = BC)

= AC

E milieu de [AC] donc AC = 2AE = 2EC

⇒ AB + AD = AC = 2EC

2) EC + ED

= (1/2)AC + (1/2)BD

= (1/2)(AC + BD)

= (1/2)(AB + BC + BC + CD)

= (1/2)(2BC)   car AB + CD = 0   (AB = DC)

= BC

= AD