The prove, D is the midpoint of AC. is achieved using SAS congruence theorem and CPCTC
How to complete the proof
The two column proof is written as follows
Statement Reason
AB ≅ BC given
DB bisects ∠ ABC given
∠ ABD ≅ ∠ CBD SAS congruence theorem
AD ≅ DC CPCTC (definition of midpoint)