AD=BC且AD‖CB
设AC,BD交于O
∵AC垂直平分BD
∴△ABO≌△ADO
∴∠ABO=∠ADO,AB=AD
∵BD平分∠ABC
∴∠ABD=∠CBD
∴∠CBD=∠ADO
∴AD‖BC
∵BO=DO,∠ADO=∠CBO,∠AOD=∠COB
∴△AOD≌△COB
∴AD=BC
AD=BC且AD‖CB
设AC,BD交于O
∵AC垂直平分BD
∴△ABO≌△ADO
∴∠ABO=∠ADO,AB=AD
∵BD平分∠ABC
∴∠ABD=∠CBD
∴∠CBD=∠ADO
∴AD‖BC
∵BO=DO,∠ADO=∠CBO,∠AOD=∠COB
∴△AOD≌△COB
∴AD=BC