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Exercice 2 :
a) AC/AN = AB/AM = BC/MN
3/AN = AB/4,5 = 2/6
3/AN = 2/6
AN = 3 x 6 / 2 = 9 cm
AB/4,5 = 2/6
AB = 4,5 x 2 / 6 = 1,5 cm
b) CS/CB = CT/CA = ST/BA
5/13 = CT/6,5 = 3/BA
5/13 = CT/6,5
CT = 6,5 x 5 / 13 = 2,5 cm
5/13 = 3/BA
BA = 13x3/5 = 7,8 cm
c) AP/AB = AM/AC = PM/BC
AC = AMxAB/AP = 5x6/4 = 7,5 cm
BC = PMxAB/AP = 3x6/4 = 4,5 cm
d) IL/IJ = IM/IK = LM/JK
IK = IMxIJ/IL = 5x10/8 = 6,25 cm
MK = IK-IM = 6,25 - 5 = 1,25 cm
LM = ILxJK/IJ = 8x7/10  = 5,6 cm

Exercice 3 :
1) (IJ)//(AP)
D'après Thalès :
IJ/AP = DI/DP = DJ/DA
IJ/32 = 15/20 = DJ/45
IJ = 32 x 15 / 20 = 24 mm
DJ = 45 x 15 / 20 = 33,75 mm
2) (JK)//(DR)
D'après Thalès :
AJ/AD = JK/DR
11,25/45 = JK/48
JK = 48x11,25 / 45 = 12 mm
IK = IJ + JK = 24 + 12 = 36 mm