i) yes.
∠ACB = ∠DBC
BC = BC
∠ABC = ∠DCB (by angle sum property)
∴ ΔABC ≅ ΔDCB (A.S.A)
ii) yes
∠A = ∠D
∠ABO = ∠DCO (angle sum property)
AB = DC [From (i)]
∴ ΔAOB ≅ ΔDOC (A.S.A)
Otherwise ΔAOB and ΔDOC are similar by A.A.A. In congruent triangles corresponding parts are equal.