证明：过C作CF垂直AD于F，∵AC平分∠BAD，∴∠FAC=∠EAC，∵CE⊥AB，CF⊥AD，∴∠DFC=∠CEB=90°，∴△AFC≌△AEC，∴AF=AE，CF=CE，∵2AE=AB+AD，又∵AD=AF-DF，AB=AE+BE，AF=AE，∴2AE=AE+BE+AE-DF，∴BE=DF，∵∠...