a) Xét \(ΔBHA\) và \(ΔBED\):
\(\widehat B:chung\)
\(\widehat{BHA}=\widehat{BED}(=90^\circ)\)
\(→ΔBHA\backsim ΔBED(g-g)\)
\(→\dfrac{AH}{AB}=\dfrac{DE}{DB}\)
\(↔AH.DE=AB.DB\)
Xét \(ΔCFD\) và \(ΔCHA\):
\(\widehat C:chung\)
\(\widehat{CFD}=\widehat{CHA}(=90^\circ)\)
\(→ΔCFD\backsim ΔCHA(g-g)\)
\(→\dfrac{DF}{DC}=\dfrac{AH}{AC}\)
\(↔DF.AC=DC.AH\)
b) \(D\) là trung điểm \(BC\)
\(→DB=DC\)
\(→DB.AH=DC.AH\)
mà \(AB.DE=DB.AH,AC.DF=DC.AH\)
\(→AB.DE=AC.DF\)
\(↔\dfrac{DE}{DF}=\dfrac{AC}{AB}\)
c) \(AB.DE=DB.AH\)
\(AC.DF=DC.AH\)
\(→AB.DE=AC.DF=DB.AH+DC.AH=AH(DB+DC)=AH.BC\)
\(→\) ĐPCM
