∠ADE=∠AFD、∠EDF=∠A
∵DE⊥AB,DF⊥AC
∴∠ADE+∠BDE=90°
∠AFD+∠BDE=90°
∴∠ADE=∠AFD
∵∠A+∠AFD=90°
∠ABF+∠EDF=90°
∴∠A=∠EDF