Giải thích các bước giải:

a.Xét $\Delta AMD,\Delta ABD$ có:

Chung $\hat A$

$\widehat{AMD}=\widehat{ADB}(=90^o)$

$\to \Delta AMD\sim\Delta ADB(g.g)$

$\to \dfrac{AM}{AD}=\dfrac{AD}{AB}$

$\to AM.AB=AD^2$

Tương tự: $AN.AC=AD^2$

$\to AM.AB=AN.AC$

$\to \dfrac{AM}{AC}=\dfrac{AN}{AB}$

$\to \Delta ANM\sim\Delta ABC(c.g.c)$

b.Xét $\Delta AFH,\Delta ADB$ có:

Chung $\hat A$

$\hat F=\hat D(=90^o)$

$\to \Delta AFH\sim\Delta ADB(g.g)$

$\to \dfrac{AF}{AD}=\dfrac{AH}{AB}$

$\to AF.AB=AH.AD$

Tương tự: $AH.AD=AE.AC$

$\to AF.AB=AE.AC$

$\to \dfrac{AF}{AC}=\dfrac{AE}{AB}$

$\to \Delta AEF\sim\Delta ABC(c.g.c)$

c.Từ a $\to \widehat{AFE}=\widehat{ACB}$

         b $\to \widehat{AMN}=\widehat{ACB}$

$\to \widehat{AFE}=\widehat{AMN}$

$\to EF//MN$