\exercice[style=R,N=4,verif]{Cube \& section}

ABCDEFHG est un cube. 

\medskip

I et J sont respectivement le milieu de [GH] et [EH].

\medskip

K est dans le plan (BCD).

\bigskip

Tracer la section du cube par le plan (IJK).


\begin{center}
\begin{tikzpicture}[scale=1.5]
\coordinate (A) at (0,0);
\coordinate (E) at (0,2);
\coordinate (F) at (2,2);
\coordinate (B) at (2,0);
\coordinate (C) at (2.7,.7);
\coordinate (G) at (2.7,2.7);
\coordinate (H) at (.7,2.7);
\coordinate (D) at (.7,.7);
\coordinate (I) at ($0.5*(H)+0.5*(G)$);
\coordinate (J) at ($0.5*(E)+0.5*(H)$);
\coordinate (K) at ($0.8*(B)+0.2*(D)$);
\fill (K) circle (1pt);
\fill (I) circle (1pt);
\fill (J) circle (1pt);
\draw (E) node[left] {E} -- (A) node[left] {A} -- (B) node[below] {B} -- (F) node[above] {F} -- (E) -- (H) node[above] {H} -- (G) node[right] {G} -- (C) node[below] {C} -- (B);
\draw (F) -- (G);
\draw[dashed] (A) -- (D) node[left] {D} -- (H);
\draw[dashed] (D) -- (C);
\node[above] at (I) {I};
\node[above left] at (J) {J};
\node[above left] at (K) {K};
\end{tikzpicture}
\end{center}