来自孙洪生的问题
已知,△ABC中,AB=AC,在AB上取一点D,在AC延长线上取一点E,连接DE交BC于点F.若F是DE中点,求证:BD=CE.
已知,△ABC中,AB=AC,在AB上取一点D,在AC延长线上取一点E,连接DE交BC于点F.若F是DE中点,求证:BD=CE.
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2020-03-20 23:52
已知,△ABC中,AB=AC,在AB上取一点D,在AC延长线上取一点E,连接DE交BC于点F.若F是DE中点,求证:BD=CE.
已知,△ABC中,AB=AC,在AB上取一点D,在AC延长线上取一点E,连接DE交BC于点F.若F是DE中点,求证:BD=CE.
证明:过点D作DP∥AC交BC于P,∴∠DPB=∠ACB,∠DPF=∠ECF.∵F是DE中点,∴DF=EF.在△DPF和△ECF中∠DPF=∠ECF∠DFP=∠EFCDF=EF,∴△DPF≌△ECF(AAS),∴DP=EC.∵AB=AC,∴∠ABC=∠ACB,∴∠DPB=∠ABC,∴B...