a/ Xét \(ΔABC\) và \(ΔEAC\):
\(\widehat{BAC}=\widehat{AEC}(=90^\circ)\)
\(\widehat{C}:chung\)
\(→ΔABC\backsim ΔEAC(g-g)\)
\(→\dfrac{AB}{BC}=\dfrac{EA}{AC}\)
\(↔AB.AC=AE.BC\)
\(\\\)
b/ Xét \(ΔABC\) và \(ΔEBA\):
\(\widehat{BAC}=\widehat{BEA}(=90^\circ)\)
\(\widehat{B}:chung\)
\(→ΔABC\backsim ΔEBA(g-g)\)
\(→\dfrac{AB}{BC}=\dfrac{EB}{BA}\)
\(↔AB^2=BC.EB\)
\(\\\)
c/ \(BF\) là đường phân giác \(\widehat{B}\)
\(→\dfrac{FA}{FC}=\dfrac{BA}{BC}\)
\(BI\) là đường phân giác \(\widehat{B}\)
\(→\dfrac{IA}{IE}=\dfrac{BA}{BE}\)
\(ΔABC\backsim ΔEBA→\dfrac{BA}{BE}=\dfrac{BC}{AB}→\dfrac{IA}{IE}=\dfrac{BC}{AB}\)
\(→\dfrac{IA}{IE}.\dfrac{FA}{FC}=\dfrac{BA}{BC}.\dfrac{BC}{AB}=1\)
\(→\) ĐPCM