垂直
∵△ACB和△ECD是等腰Rt三角形
∴∠ACB = ∠ECD = 90°
∴∠ACE =∠BCD
∵AC = CB,EC = DC
∴△ACE≌△BCD
∴∠CAE = ∠CBD,AE = BD
∵M是AE的中点,N是BD的中点
∴AM = BN
∵AC = BC
∴△AMC≌△BNC
∴∠ACM = ∠BCN
∵∠ACM + ∠MCB = 90°
∴∠BCN + ∠MCB = 90°
∴∠MCN = 90°
∴MC⊥NC