$\Delta ABC$ đều
$=>AB=BC=CA;\widehat{A_1}=\widehat{B_1}=\widehat{C_1}=60^o\\ \widehat{DAF}=180^o-\widehat{A_1}=120^o\\ \widehat{FCE}=180^o-\widehat{C_1}=120^o\\ \widehat{EBD}=180^o-\widehat{C_1}=120^o\\ AB=BC=CA;AD=BE=CF\\ =>BD=CE=AF$
Xét $\Delta DAF$ và $\Delta FCE$
$\widehat{DAF}=\widehat{FCE}=120^o\\ AD=CF\\ AF=CE\\ => \Delta DAF = \Delta FCE\\ =>DF=FE$
CM tương tự$=>FE=ED$
$=>DF=FE=ED$
$=>\Delta DEF$ đều