\(a,\left\{{}\begin{matrix}\widehat{B_1}=\widehat{B_2}=\dfrac{1}{2}\widehat{ABC};\widehat{C_1}=\widehat{C_2}=\dfrac{1}{2}\widehat{ACB}\\\widehat{ABC}=\widehat{ACB}\left(\Delta ABC.cân.tại.A\right)\end{matrix}\right.\Rightarrow\widehat{B_1}=\widehat{B_2}=\widehat{C_1}=\widehat{C_2}\\ \left\{{}\begin{matrix}\widehat{B_1}=\widehat{C_1}\\AB=AC\\\widehat{A}\end{matrix}\right.\Rightarrow\Delta AEB=\Delta AFC\left(g.c.g\right)\Rightarrow AE=AF\\ \Rightarrow\Delta AEF.cân\)
\(b,\left\{{}\begin{matrix}AE=AF\\AB=AC\end{matrix}\right.\Rightarrow AB-AF=AC-AE\Rightarrow BF=CE\\ \left\{{}\begin{matrix}BF=CE\\\widehat{ABC}=\widehat{ACB}\\BC.chung\end{matrix}\right.\Rightarrow\Delta BFC=\Delta CEB\left(c.g.c\right)\)
\(c,\widehat{AFE}=\dfrac{180^0-\widehat{A}}{2}\left(\Delta AEF.cân\right);\widehat{ABC}=\dfrac{180^0-\widehat{A}}{2}\left(\Delta ABC.cân\right)\\ \Rightarrow\widehat{AFE}=\widehat{ABC}\)
Mà 2 góc này ở vị trí đồng vị nên \(EF//BC\Rightarrow BFCE\) là hthang
Mà \(\widehat{ABC}=\widehat{ACB}\) nên BFCE là hthang cân
