Ta có: \(\Delta ABC\) cân \(\Rightarrow AB=AC;\widehat{ACB}=\widehat{ABC}\)
Mà: \(\widehat{ABC}+\widehat{ABD}=180^o\)
\(\widehat{ACB}+\widehat{ACE}=180^o\)
\(\Rightarrow\widehat{ABD}=\widehat{ACE}\)
Xét \(\Delta ABD\) và \(\Delta ACE\)
\(AB=AC\)
\(\widehat{ABD}=\widehat{ACE}\)
\(BD=CE\)
\(\Rightarrow\Delta ABD=\Delta ACE\left(c-g-c\right)\)
\(\Rightarrow AD=AE\) (hai cạnh tương ứng)
\(\Rightarrow\Delta ADE\) cân