∵∠C=90°∠B=45° ∴AC=BC
做AB上的高（如图）∵DE⊥AB ∴∠AED=90°
∵AD平分∠CAB
∴CD=ED在△ACD和△AED中
AD=AD
CD=ED
∠C=∠AED
∴△ACD≌△AED∴AC=AE
∴∠B=45° ∠BED=90°∴EB=ED
∵AB=AE+EBAE=ACEB=ED ED=CD∴AB=AC+CD
∵∠C=90°∠B=45° ∴AC=BC
做AB上的高（如图）∵DE⊥AB ∴∠AED=90°
∵AD平分∠CAB
∴CD=ED在△ACD和△AED中
AD=AD
CD=ED
∠C=∠AED
∴△ACD≌△AED∴AC=AE
∴∠B=45° ∠BED=90°∴EB=ED
∵AB=AE+EBAE=ACEB=ED ED=CD∴AB=AC+CD