[tex]\it MN||BC \stackrel{T.Thales}{\Longrightarrow}\ \dfrac{AN}{AC}=\dfrac{AM}{AB}\ \ \ \ (1)\\ \\ \\ MP||AC \stackrel{T.Thales}{\Longrightarrow}\ \dfrac{BP}{BC}=\dfrac{MB}{AB}\ \ \ \ (2)\\ \\ \\ (1),\ (2) \Rightarrow \dfrac{AN}{AC}+\dfrac{BP}{BC}=\dfrac{AM}{AB}+\dfrac{MB}{AB}=\dfrac{AM+MB}{AB}=\dfrac{AB}{AB}=1[/tex]
