Question

△ABC为等边三角形,D,E分别在AC,AB的延长线上,且CD=AE,求证:DB=DE

Answer 1

延长AE至F,使 EF=AB,连结DF,∵AE=CD,（已知）,EF=AB,AB=AC,∴AC+CD=AE+CF,∴AD=AF,∵△ABC是正△,∴〈A=60度,∴△ADF是含顶角60度的等腰△,∴△ADF是正△,∴AD=DF,∴〈A=〈F=60°,∵AB=EF,∴△DAB≌△DFE（SAS）∴DB=DE