Consider the picture attached with the solution-
(1) AB and CD intersects at O.
(2) AD is parallel to BC
(3) AD is equal to BC

As AD is parallel to BC, this results-
(1) if angle AOD = a then angle BOC = a
(2) if angle DAO = b then angle CBO = b
(3) if angle ADO = c then angle BCO = c

Now ΔAOD and ΔBOC are congruent as all the three angles are equal to each other and AD = BC. So,
(1) AO = OB
(2) CO = OD

AB and CD bisects at O