来自聂林的问题
如图,在△ABC中,AB=AC,AD⊥BC,垂足为D,E为AD的中点,DF⊥BE,垂足为F,CF交AD于点G.求证:(1)∠CFD=∠CAD;(2)EG<EF.
如图,在△ABC中,AB=AC,AD⊥BC,垂足为D,E为AD的中点,DF⊥BE,垂足为F,CF交AD于点G.
求证:(1)∠CFD=∠CAD;
(2)EG<EF.


如图,在△ABC中,AB=AC,AD⊥BC,垂足为D,E为AD的中点,DF⊥BE,垂足为F,CF交AD于点G.求证:(1)∠CFD=∠CAD;(2)EG<EF.
如图,在△ABC中,AB=AC,AD⊥BC,垂足为D,E为AD的中点,DF⊥BE,垂足为F,CF交AD于点G.
求证:(1)∠CFD=∠CAD;
(2)EG<EF.
(1)证明:连接AF,并延长交BC于N,
∵AD⊥BC,DF⊥BE,
∴∠DFE=∠ADB,
∴∠BDF=∠DEF,
∵BD=DC,DE=AE,
∵∠BDF=∠DEF,∠EFD=∠BFD=90°,
∴△BDF∽△DEF,
∴BDDF