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First prove that both triangles are congruent.
In triangles ABO and CDO,
AO=DO [given]
angle A=angle D [given]
angle AOB=angle COD [vertically opposite angles]
Therefore both triangles are equal by ASA axiom.
BO=CO [Corresponding Parts Of Congruent Triangles Are Congruent ]
Therefore AD bisects BC at O.
In triangles ABO and CDO,
AO=DO [given]
angle A=angle D [given]
angle AOB=angle COD [vertically opposite angles]
Therefore both triangles are equal by ASA axiom.
BO=CO [Corresponding Parts Of Congruent Triangles Are Congruent ]
Therefore AD bisects BC at O.
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