
\begin{center}
\begin{tikzpicture}
\coordinate (A) at (0,0);
\coordinate (B) at (6,0);
\coordinate (C) at (2,2);
\coordinate (E) at (2,0);
\coordinate (G) at (barycentric cs:A=1,C=-2);
\coordinate (F) at (barycentric cs:C=1,G=-2);
\draw (A) node[left] {A} -- (B) node[right] {B} -- (C) node[above] {C} -- cycle;
\fill (E) circle (2pt) node[below] {E};
\draw (C) -- (F);
\fill (F) circle (2pt) node[right] {F};
\draw[red] (C) -- (E);
\draw[red] (F) -- (B);
\draw ($(G)+({-0.1*cos(45)},{0.1*sin(45)})$) -- ($(G)+({0.1*cos(45)},{-0.1*sin(45)})$);
\draw (4,0.1) -- (4,-.1);
\end{tikzpicture}
\end{center}

\medskip

On sait que $\vv{AE}=\dfrac{1}{3}\vv{AB}$ et que $\vv{AC}=\dfrac{1}{3}\vv{AF}$ par construction. Ainsi, $\dfrac{AC}{AF}=\dfrac{AE}{AB}=\dfrac{1}{3}$.

\bigskip

Donc, d'après la réciproque du théorème de Thalès, (CE) et (BF) sont parallèles.