\exercice[style=R,N=3,verif]{Section d'un cube par un plan}

On considère le cube ABCDEFGH suivant :

\begin{center}
\begin{tikzpicture}
\coordinate (A) at (0,0);
\coordinate (B) at (3,0);
\coordinate (C) at (3,3);
\coordinate (D) at (0,3);
\coordinate (E) at (1,1);
\coordinate (F) at (4,1);
\coordinate (G) at (4,4);
\coordinate (H) at (1,4);
\coordinate (I) at (1,3);
\coordinate (J) at ($0.33*(C)+0.66*(G)$);
\coordinate (K) at (3.5,1);
\shade[left color=purple!5,right color=purple!40] (I) node[below left,scale=0.7] {I} -- (J) node[below right,scale=0.7] {J} -- (K) node[below,scale=0.7] {K} -- cycle;
\draw[purple] (I) -- (J);
\draw[dashed,purple] (I) -- (K) -- (J);
\draw (A) node[below left] {A} -- (B) node[below right] {B} -- (C) node[below left] {C} -- (D) node[above left] {D} -- (H) node[above] {H} -- (G) node[above right] {G} -- (F) node[right] {F} -- (B);
\draw (A) -- (D);
\draw (C) -- (G);
\draw[dashed] (A) -- (E) -- (H);
\draw[dashed] (E) node[above right] {E} -- (F);
\end{tikzpicture}
\end{center}

$\rm K\in[EF]$, $\rm I\in[DC]$ et $\rm J\in[CG]$.

\medskip

Construire la section du cube ABCDEFGH par le plan (IJK).