Giúp mình vớiiiiiiiii

Giải thích các bước giải:

a.Xét $\Delta ABD,\Delta ACE$ có:

$\widehat{DAB}=\widehat{CAE}$

$\widehat{ABD}=\widehat{ACE}$

$\to \Delta ABD\sim\Delta ACE(g.g)$

b.Từ a $\to \widehat{AEC}=\widehat{ADB}$

$\to \widehat{CED}=\widehat{ADB}=\widehat{CDE}$

$\to \Delta CDE$ cân tại $C$

c.Từ a $\to\dfrac{AB}{AC}=\dfrac{AD}{AE}$

Ta có: $BF//CE$

$\to \dfrac{DF}{DE}=\dfrac{DB}{DC}=\dfrac{AB}{AC}=\dfrac{AD}{AE}$

$\to DF.AE=AD.DE$

d.Ta có:

$\dfrac{AD}{AE}=\dfrac{AB}{AC}=\dfrac23$

$\to \dfrac{AD}{AE-AD}=\dfrac2{3-2}$

$\to \dfrac{AD}{DE}=2$

$\to AD=2DE$

$\dfrac{DF}{DE}=\dfrac{DB}{DC}=\dfrac23$

$\to 2DE=3DF$

$\to AD=3DF$

$\to AD-DF=2DF$

$\to AF=2DF$

$\to \dfrac{FA}{FD}=2$

Mà $xy//BC$

$\to \dfrac{FI}{FH}=\dfrac{FA}{FD}=2$

$\to FH=2FI$