a. \(\left\{{}\begin{matrix}\widehat{D}=\widehat{E}=90^o\\\widehat{C}.chung\end{matrix}\right.\Rightarrow\Delta ADC\sim\Delta BEC\left(gg\right)\)
b. \(\left\{{}\begin{matrix}\widehat{HDB}=\widehat{BEC}=90^o\\\widehat{B}.chung\end{matrix}\right.\Rightarrow\Delta BDH\sim\Delta BEC\left(gg\right)\)
\(\Rightarrow\frac{BD}{DH}=\frac{BE}{EC}\Leftrightarrow BD\cdot EC=DH\cdot BE\)
c. \(\left\{{}\begin{matrix}\widehat{IAE}=\widehat{EBD}\left(phu_.\widehat{BHD}=\widehat{AHE}\right)\\\widehat{AEI}=\widehat{BED}\left(gt\right)\end{matrix}\right.\Rightarrow\Delta EBD\sim\Delta EAI\left(gg\right)\)
\(\Rightarrow\frac{BD}{BE}=\frac{AI}{AE}\Leftrightarrow AE\cdot BD=AI\cdot BE\) (1)
Tương tự: \(\Delta ABE\sim\Delta IDE\)
\(\Rightarrow AB\cdot DE=ID\cdot BE\) (2)
Cộng (1), (2) theo vế ta có đpcm
