延长AC、BE相交于点F；在△ABE和△AFE中,∠BAE = ∠FAE ,AE 为公共边,∠AEB = 90°= ∠AEF ,所以,△ABE ≌ △AFE ,可得：BE = FE ；在△ACD和△BCF中,∠CAD = 90°-∠F = ∠CBF ,AC = BC ,∠ACD = 90° = ∠BCF ,所以,△ACD ≌ △BCF ,可得：AD = BF = BE+FE = 2BE .
