a)
[tex]\it \left.\begin{aligned} \it FG||BC\ \stackrel{T.f.a.}{\Longrightarrow} \Delta AFG\sim\Delta ABC\\ \\ \it FH||AC\ \stackrel{T.f.a.}{\Longrightarrow} \Delta ABC\sim\Delta FBH \end{aligned}\right\} \stackrel{tranzitivitate}{\Longrightarrow}\ \ \Delta AFG\sim \Delta FBH[/tex]
b)
[tex]\it \Delta AFG\sim \Delta ABC \Rightarrow \dfrac{AG}{AC}=\dfrac{AF}{AB}\ \ \ \ (1)\\ \\ \\ \Delta FBH\sim \Delta ABC \Rightarrow \dfrac{BH}{BC}=\dfrac{FB}{AB}\ \ \ \ (2)\\ \\ \\ (1),\ (2) \Rightarrow \dfrac{AG}{AC}+\dfrac{BH}{BC}=\dfrac{AF}{AB}+\dfrac{FB}{AB}=\dfrac{AF+FB}{AB}=\dfrac{AB}{AB}=1[/tex]
