a, xét \(\Delta BAD\)và\(\Delta CAE\)có:
\(\widehat{BAD}=\widehat{CAE}\)(góc chung)
\(\widehat{BDA}=\widehat{CEA}\left(90^0\right)\)
\(\Rightarrow\Delta BAD~\Delta CAE\left(g.g\right)\)
\(b,\)xét \(\Delta EHB\)và\(\Delta DHC\)có:
\(\widehat{EHB}=\widehat{DHC}\)(đối đỉnh)
\(\widehat{HEB}=\widehat{HDC}\left(=90^0\right)\)
\(\Rightarrow\Delta EHB~\Delta DHC\left(g.g\right)\)
\(\Rightarrow\frac{HE}{HD}=\frac{HB}{HC}\Rightarrow HE.HC=HB.HD\)
c,\(HE.HC=HB.HD\Rightarrow\frac{HE}{HB}=\frac{HD}{HC}\)
xét\(\Delta EHD\)và\(\Delta BHC\)có
\(\frac{HE}{HB}=\frac{HD}{HC}\left(cmt\right)\)
\(\widehat{EHD}=\widehat{BHC}\)(đối đỉnh)
\(\Rightarrow\Delta EHD~\Delta BHC\left(c.g.c\right)\)
