已知AB=AC,DF平行于AB.求证:①DF=DC二,②若DE⊥FC于E,那么EF=CE急························

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已知AB=AC,DF平行于AB.求证:①DF=DC二,②若DE⊥FC于E,那么EF=CE急························

已知AB=AC,DF平行于AB.求证:①DF=DC二,②若DE⊥FC于E,那么EF=CE急························
已知AB=AC,DF平行于AB.求证:①DF=DC二,②若DE⊥FC于E,那么EF=CE
急························

已知AB=AC,DF平行于AB.求证:①DF=DC二,②若DE⊥FC于E,那么EF=CE急························
证明:①∵AB=AC
∴∠B=∠C
∵DF∥AB
∴∠B=∠DFC
∵∠B=∠C
∴∠DFC=∠C
∴DF=DC
②∵AE⊥FC于E
∴∠DEC=∠DEF=90°
∵∠DFC=∠C,DE=DE
∴△DEF≌△DEC
∴EF=CE

证明②若DE⊥FC于E,那么EF=CE
连接FC,CD,做DE⊥FC,因为DF平行AB,所以角F等于角ABC,又因为AB=AC,所以又等于角C,所以角F等于角C,所以DF=DC,又因为DE垂直CF,所以EF=CE