证明：过C作CF⊥AD于F，∵AC平分∠BAD，∴∠FAC=∠EAC，∵CE⊥AB，CF⊥AD，∴∠DFC=∠CEB=90°，∴△AFC≌△AEC，∴AF=AE，CF=CE，∵∠ADC+∠B=180°∴∠FDC=∠EBC，∴△FDC≌△EBC∴DF=EB，∴AB+AD=AE+EB+AD=AE+DF+...