来自高济的问题
如图,△ABC中,点D在AB上,E是AC延长线上一点,BD=CE,DE交BC于点F,DF=EF,DP∥AE交BC于点P,求证:AB=AC.
如图,△ABC中,点D在AB上,E是AC延长线上一点,BD=CE,DE交BC于点F,DF=EF,DP∥AE交BC于点P,求证:AB=AC.
1回答
2020-03-20 21:21
如图,△ABC中,点D在AB上,E是AC延长线上一点,BD=CE,DE交BC于点F,DF=EF,DP∥AE交BC于点P,求证:AB=AC.
如图,△ABC中,点D在AB上,E是AC延长线上一点,BD=CE,DE交BC于点F,DF=EF,DP∥AE交BC于点P,求证:AB=AC.
证明:∵DP∥AE,
∴∠FDP=∠FEC,
在△DFP和△EFC中,
DF=EF∠DFP=∠EFC∠PDF=∠CEF