Verified answer

1) a. DM    b. CM   c. BM

Appliquons le théorème de PYTHAGORE

AM² = AD² + DM² ⇒DM² = AM² - AD²

                                        = 32² - 19.2²

                                        = 1024 - 368.64

                                        = 655.36

DM = √655.36 = 25.6 cm

b) DC = DM + MC ⇒ MC = DC - DM       (DC = AB)   

                                         = 40 - 25.6 = 14.4 cm 

MC = 14.4 cm

c) on applique PYTHAGORE

BM² = BC² + MC²       (BC = AD)

       = 19.2² + 14.4²

       = 368.64 + 207.36

       = 576

BM = √576 = 24 cm

2) Réciproque du théorème de PYTHAGORE

AM² + MB² = 32² + 24²

                  = 1024 + 576

                  = 1600

AB = 40  et  AB² = 40² = 40 x 40 = 1600

Donc le triangle AMB est rectangle en M