∵∠BAC=90°
∴∠BAD+∠DAC=90°
∵∠AEC=90°
∴∠AEC+∠DAC=90°
∴∠AEC=∠BAD
∵AB=AC
∴Rt△BAD全等于Rt△ACE
∴AE=BD,AD=EC
∵AD=AE+ED
∴AE+ED=EC
∴BD+ED=EC
∵∠BAC=90°
∴∠BAD+∠DAC=90°
∵∠AEC=90°
∴∠AEC+∠DAC=90°
∴∠AEC=∠BAD
∵AB=AC
∴Rt△BAD全等于Rt△ACE
∴AE=BD,AD=EC
∵AD=AE+ED
∴AE+ED=EC
∴BD+ED=EC