bonsoir
exercice 16
a- les deux droites sont parallèles, on peut donc appliquer thalès. D'après Thalès, on a :
MN/BC = AN/AC = AM/AB
donc
[tex] \frac{6}{2} = \frac{AN}{3} = \frac{4.5}{AB} [/tex]
AN = 6*3/2 =9
AB = 2*4.5/6 = 1.5
b)
[tex] \frac{CB}{CS} = \frac{CA}{CT} = \frac{BA}{ST} [/tex]
donc
[tex] \frac{13}{5} = \frac{6.5}{CT} = \frac{BA}{3} [/tex]
CT = 5*6.5/13 = 2.5
BA = 3*13/5 = 7.8
c-
BA/BP = AC/AM = BC/PM
6/2 = AC/5 = BC/3
AC = 5*6/2 =15
BC = 3*6/2 = 9
d- IJ/IL = IK/IM = KJ/LM
10/8 = IK/5 = 7/ML
IK = 5*10/8 = 6.25
LM = 7*8/10 = 5.6
