[tex]\it a)\ \ DF||BC\stackrel{T.f.a}{\Longrightarrow}\ \Delta ADF\sim\Delta ABC\ \ \ \ \ (1)\\ \\ DE||AC\stackrel{T.f.a}{\Longrightarrow}\ \Delta DBE\sim\Delta ABC\ \ \ \ \ (2)\\ \\ (1),\ (2) \Rightarrow \Delta ADF\sim\Delta DBE[/tex]
[tex]\it b)\ (1) \Rightarrow \dfrac{AF}{AC}= \dfrac{AD}{AB} \ \ \ \ \ \ (3)\\ \\ \\ (2) \Rightarrow \dfrac{BE}{BC}= \dfrac{DB}{AB} \ \ \ \ \ \ (4)\\ \\ \\ (3),\ (4) \Rightarrow \dfrac{AF}{AC}+\dfrac{BE}{BC} =\dfrac{AD}{AB} +\dfrac{DB}{AB} = \dfrac{AD+DB}{AB}=\dfrac{AB}{AB}=1[/tex]
