Question

in ∆ABC, D€ (AC). Daca DE||AB, E€ (BC) si DF||BC, demonstreaza ca CE/BC=AF/AB=1 ("/" înseamnă fracție)

Answer 1

$\Delta CDE\sim\Delta CAB\Rightarrow \frac{CE}{BC}=\frac{CD}{CA}$ (1)
$\Delta AFD\sim\Delta ABC\Rightarrow \frac{AF}{AB}=\frac{AD}{AC}$ (2)
Din (1) + (2) rezultă
$\frac{CE}{BC}+\frac{AF}{AB}=\frac{CD}{CA}+\frac{AD}{AC}=\frac{AD+DC}{AC}=\frac{AC}{AC}=1$