证明:
∵AD⊥BC,DE⊥AB∴∠ADB=∠AED=90°又∵∠DAB=∠EAD(公共角)∴△ADB∽△AED(AA)∴AB/AD=AD/AE∴AD²=AE×AB同理:△ADC∽△AFD∴AC/AD=AD/AF ∴AD²=AF×AC∴AE×AB=AF×AC【1证毕】∴AE/AC=AF/AB又∵∠EAF=∠CAB(公共角)∴△AEF∽△ACB(AA)
证明:
∵AD⊥BC,DE⊥AB∴∠ADB=∠AED=90°又∵∠DAB=∠EAD(公共角)∴△ADB∽△AED(AA)∴AB/AD=AD/AE∴AD²=AE×AB同理:△ADC∽△AFD∴AC/AD=AD/AF ∴AD²=AF×AC∴AE×AB=AF×AC【1证毕】∴AE/AC=AF/AB又∵∠EAF=∠CAB(公共角)∴△AEF∽△ACB(AA)