已知三角形abc,ce,bf为高,求证ae*ab=af*ac

已知三角形abc,ce,bf为高,求证ae*ab=af*ac
已知三角形abc,ce,bf为高,求证ae*ab=af*ac

已知三角形abc,ce,bf为高,求证ae*ab=af*ac
连接EF
△AEC和△AFB中
∵∠A=∠A,∠AEC=∠AFB
∴△AEC∽△AFB
∴AE:AF=AC:AB
对△AEF和△ACB来说
∵∠A=∠A,AE:AF=AC:AB
∴△AFE∽△ABC
∴AE：AF=AC：AB
即AE*AB=AF*AC