a/ \(\Delta ABC\) cân tại A
\(\Leftrightarrow\widehat{ABC}=\widehat{ACB}=\dfrac{180^0-\widehat{A}}{2}\) \(\left(1\right)\)
\(\Delta AED\) có \(AE=ED\)
\(\Leftrightarrow\Delta AED\) cân tại A
\(\Leftrightarrow\widehat{AED}=\widehat{EDA}=\dfrac{180^0-\widehat{EAD}}{2}\left(2\right)\)
Từ \(\left(1\right)+\left(2\right)\Leftrightarrow\widehat{ABC}=\widehat{AED}\)
Mà đây là 2 góc đồng vị
\(\Leftrightarrow DE\backslash\backslash BC\left(d.h.n.b\right)\)
b/ Xét \(\Delta ABD;\Delta ACE\) có :
\(\left\{{}\begin{matrix}AB=AC\\\widehat{A}chug\\AD=AE\end{matrix}\right.\)
\(\Leftrightarrow\Delta ABD=\Delta ACE\left(c-g-c\right)\)
\(\Leftrightarrow\widehat{ADB}=\widehat{ACE}\)
Mà \(\widehat{ADB}=90^0\)
\(\Leftrightarrow\widehat{ADB}=90^0\)
