jacky
∵∠BAC=90°，AC=AB，AD⊥BC，∴∠ABC=∠C=45°，AD=BD=CD，∠ADN=∠ADB=90°，∴∠BAD=45°=∠CAD，∵BE平分∠ABC，∴∠ABE=∠CBE=$\frac{1}{2}$∠ABC=22.5°，∴∠BFD=∠AEB=90°-22.5°=67.5°，∴∠AFE=∠BFD=∠AEB=67.5°，∴AF=AE，故①正确；∵M为EF的中点，∴AM⊥EF，∴BE⊥AN，故④正确；∵AM⊥EF，∴∠AMF=∠AME=90°，∴∠DAN=90°-67.5°=22.5°=∠MBN，在△FBD和△NAD中，$\left\{\begin{array}{l}{∠FBD=∠DAN}\\{BD=AD}\\{∠BDF=∠ADN}\end{array}\right.$，∴△FBD≌△NAD（ASA），∴DF=DN，故②正确；在△AFB和△△CNA中，$\left\{\begin{array}{l}{∠BAF=∠C=45°}\\{AB=AC}\\{∠ABF=∠CAN=22.5°}\end{array}\right.$，∴△AFB≌△CAN（ASA），∴AF=CN，∵AF=AE，∴AE=CN，故③正确；即正确的有4个，故选：A．
