Given: ABCD is a parallelogram with diagonals AC and BD intersecting at M. Prove: Segment DB and Segment AC bisect each other.

Please complete the proof by providing the reasons for each statement ABCD is a parallelogram with diagonals AC and BD intersecting at M.
Segment AB||Segment CD,
Segment BC||Segment AD
Segment AD ≅ Segment CB, Segment AB ≅ DC
∠DBA and∠BDC are alternate interior angles
∠DBA≅∠BDC
∠CMD and∠AMB are vertical angles
∠CMD ≅ ∠AMB
ΔCMD ≅ ΔAMB
Segment AM ≅ Segment MC
M is the midpoint of Segment AC