(i) D is the mid-point of AC
Considering ∆ABC
We observe that M is the mid point of side AB and DM || BC [Given]
This implies, DC= AD ……….. (NCERT Theorem 8.10)
Hence, D is the mid-point of AC.
(ii) MD ⊥ AC
We know that MD || BC and AC is transversal
This implies, ∠ACB = ∠ADM = 90°
Hence, MD ⊥AC
(iii) CM = MA = ½ AB
Considering ∆ADM and ∆CDM
AD = CD (D is the mid point of AC (Proved))
∠CDM = ∠ADM (proved, MD ⊥AC)
DM = DM (common)
∆ADM ≅ ∆CDM (By SAS congruency)
CM = AM (By C.P.C.T.)
CM = AM = ½ AB (M is the mid point of AB)