等腰直角△
连结AC
∵M是AD的中点,AB= AD
∴AM = AB/2
∵AB = BC/2
∴AM:AB = AB:BC
∵∠A = 90°,AD//BC
∴△ABM∽△ABC
∴BM :AC =1:2
∴∠BAC = ∠AMB
∵∠BAC + ∠CAD = 90°
∴∠CAD + ∠AMB = 90°
∴AC⊥BM
∵M,N是AD,CD的中点
∴MN//AC,MN= AC/2
∴MN⊥BM,MN=BM
∴△BMN是等腰直角三角形
等腰直角△
连结AC
∵M是AD的中点,AB= AD
∴AM = AB/2
∵AB = BC/2
∴AM:AB = AB:BC
∵∠A = 90°,AD//BC
∴△ABM∽△ABC
∴BM :AC =1:2
∴∠BAC = ∠AMB
∵∠BAC + ∠CAD = 90°
∴∠CAD + ∠AMB = 90°
∴AC⊥BM
∵M,N是AD,CD的中点
∴MN//AC,MN= AC/2
∴MN⊥BM,MN=BM
∴△BMN是等腰直角三角形