∵BD⊥MN CE⊥MN
∴△ ABD和 △ACE是Rt△
∴∠DBA+∠DAB=90
∵∠BAC=90°
∴∠DAB+∠EAC=90
∴∠DBA=∠EAC
∵AB=AC
∠BDA=∠AEC
∴Rt△ABD≌Rt△ACE
∴BD=AE