Question

数学！！在线等

如图,在△ABC中,∠C=60°,且高BE经过高AD的中点F.求证：BF=4EF

Answer 1

∵AD⊥BC，BE⊥AC
∠C=60°
∴RT△BCE和RT△ACD中
∴∠DBF=∠CBF=30°
∠FAE=∠CAD=30°
∴RT△AEF和RT△BDF中
DF=1/2BF即BF=2DF
EF=1/2AF即AF=2EF
∵F是AD中点，即AF=DF
∴BF=2DF=2AF=2×2EF=4EF

Answer 2

∠CAD=30°
AF=2EF
∠CBE=30°
BF=2FD
AF=FD
BF=4EF

Answer 3

观察△BEC △ADC 易得∠EBC=∠CAD=30° 则Rt △AEF中 AF=2EF Rt △BFD中 BF=2DF
又F为AD中点 AF=DF 即BF=2DF=2AF=4EF

Answer 4

sorry，I don not know.

追问

Okay. Thank you