a/Xét \(ΔABC\) và \(ΔHAC\):
\(\widehat{C}\) chung
\(\widehat{BAC}=\widehat{AHC}(=90^\circ)\)
\(→ΔABC\backsim ΔHAC(g-g)\)
Xét \(ΔABC\) và \(ΔHBA\):
\(\widehat{B}\) chung
\(\widehat{BAC}=\widehat{BHA}(=90^\circ)\)
\(→ΔABC\backsim ΔHBA(g-g)\)
\(ΔABC\backsim ΔHBA→\dfrac{AB}{BC}=\dfrac{BH}{AB}\\→AB^2=BC.BH\)
\(ΔABC\backsim ΔHAC→\dfrac{AC}{BC}=\dfrac{CH}{AC}\\→AC^2=BC.CH\)
b/ \(ΔABC\backsim ΔHAC\) và \(ΔABC\backsim ΔHBA\)
\(→ΔHAC\backsim ΔHBA\)
\(→\dfrac{AH}{CH}=\dfrac{BH}{AH}\)
\(→AH^2=BH.CH\)
