a)
a/ Xét ΔABC và ΔDEC ta có:
\(\widehat{C}\) \(chung\)
\(\widehat{ABC}=\widehat{DEC}\left(gt\right)\)
\(\Rightarrow\Delta ABC\) ∼ \(\Delta DEC\left(g.g\right)\)
b/ \(Vì\) \(\Delta ABC\) ∼\(\Delta DEC\left(g.g\right)\left(cmt\right)\)
\(\Rightarrow\dfrac{AB}{DE}=\dfrac{AC}{DC}\)
b)
a/\(Xét\Delta ABE\) \(và\) \(\Delta KBH\) \(ta\) \(có:\)
\(\widehat{BEA}=\widehat{KHB}\left(gt\right)\)
\(\widehat{HBK}=\widehat{EBA}\left(đđ\right)\)
\(\Rightarrow\Delta ABE\)∼\(\Delta KBH\left(g.g\right)\)
b/ \(Vì\) \(\Delta ABE\)∼\(\Delta KBH\left(g.g\right)\left(cmt\right)\)
\(\rightarrow\dfrac{AE}{KH}=\dfrac{AB}{KB}\)
\(\Rightarrow AE.KB=KH.AB\)
c)
a/\(Xét\) \(\Delta AHQ\) \(và\) \(\Delta FEQ\) \(ta\) \(có\):
\(\widehat{Q}\) \(chung\)
\(\widehat{HAQ}=\widehat{EFQ}=90^0\)
\(\Rightarrow\Delta AHQ\)∼\(\Delta FEQ\left(g.g\right)\)
b/ \(Vì\) \(\Delta AHQ\)∼\(\Delta FEQ\left(g.g\right)\left(cmt\right)\)
\(\rightarrow\dfrac{AH}{EF}=\dfrac{HQ}{EQ}\)
\(\Rightarrow AH.EQ=EF.HQ\)
d)
a/\(Xét\Delta DEF\) \(và\) \(\Delta DAE\) \(ta\) \(có:\)
\(\widehat{D}\) \(chung\)
\(\widehat{DEF}=\widehat{EAD}=90^0\)
\(\Rightarrow\Delta DEF\)∼\(\Delta DAE\left(g.g\right)\left(1\right)\)
b/\(Xét\Delta EAF\) \(và\) \(\Delta FED\) \(ta\) \(có\):
\(\widehat{F}\) \(chung\)
\(\widehat{EAF}=\widehat{DEF}=90^0\)
\(\Rightarrow\Delta EAF\)∼\(\Delta FED\left(g.g\right)\left(2\right)\)
\(Từ\left(1\right)và\left(2\right)suy\) \(ra\) \(\Delta DEF\)∼\(\Delta DAE\)∼\(\Delta AEF\)
\(\Rightarrow\Delta DAE\)∼\(\Delta EAF\)
c/\(Vì\Delta DAE\)∼\(\Delta EAF\left(cmt\right)\)
\(\rightarrow\dfrac{EA}{DA}=\dfrac{AF}{EA}\)
\(\rightarrow EA.EA=DA.AF\)
\(\Rightarrow EA^2=DA.AF\)
