
\begin{tabular}{l@{~}|@{~}l}
\begin{minipage}{\dimexpr\linewidth-5cm}
{\color{red}\bf \'Etape 1 : on prolonge la droite (IJ) car I et J sont sur la même face.}

\medskip

Nous trouvons ainsi l'intersection de (IJ) et (HG) : on nomme ce point L.

\medskip

Pourquoi chercher l'intersection de (IJ) avec (HG) ? Parce que le troisième point (K) est sur la face (EFGH) et que (HG) est aussi sur cette face.

(IJ) coupe aussi (DH), mais (DH) n'est pas incluse dans (EFGH).
\end{minipage}
&
\begin{minipage}{5cm}
\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);
%
\draw[dotted,gray] (J) -- ($(J)+(2.66,0.66)$);
\draw[dotted,gray] (G) -- ($(G)+(2,0)$);
\coordinate (L) at ($(G)+(1.1,0)$);
\fill[red] (L) circle (1.5pt) node[above] {L};
\end{tikzpicture}
\end{center}
\end{minipage}
\end{tabular}

\newpage

\begin{tabular}{l@{~}|@{~}l}
\begin{minipage}{\dimexpr\linewidth-5cm}
{\color{red}\bf \'Etape 2 : on trace la droite (LK).}

\medskip

Cette droite est dans le plan (EFG) mais aussi dans le plan (IJK) car L et K sont deux points de ces deux plans.

Ainsi, en prenant la partie de (LK) dans la face (EFGH), on aura une section du cube par (IJK) : c'est le segment [KM].
\end{minipage}
&
\begin{minipage}{5cm}
\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);
%
\draw[dotted,gray] (J) -- ($(J)+(2.66,0.66)$);
\draw[dotted,gray] (G) -- ($(G)+(2,0)$);
\coordinate (L) at ($(G)+(1.1,0)$);
\fill[red] (L) circle (1.5pt) node[above] {L};
%
\draw[dotted,gray] (L) -- (K);
\coordinate (M) at (4,1.9);
\fill[red] (M) circle (1.5pt) node[below right,scale=0.7] {M};
\end{tikzpicture}
\end{center}
\end{minipage}
\\
\begin{minipage}{\dimexpr\linewidth-5cm}
{\color{red}\bf \'Etape 3 : on trace [JM].}

\medskip

Ben ouais ! Parce que J et M sont sur la face (BFGC)... alors bon ! [JM] fait partie de la section du cube par (IJK)...
\end{minipage}
&
\begin{minipage}{5cm}
\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);
%
\draw[dotted,gray] (J) -- ($(J)+(2.66,0.66)$);
\draw[dotted,gray] (G) -- ($(G)+(2,0)$);
\coordinate (L) at ($(G)+(1.1,0)$);
\fill[red] (L) circle (1.5pt) node[above] {L};
%
\draw[dotted,gray] (L) -- (K);
\coordinate (M) at (4,1.9);
\fill[red] (M) circle (1.5pt) node[below right,scale=0.7] {M};
%
\draw[red] (J) -- (M);
\draw[red,dashed] (K) -- (M);
\end{tikzpicture}
\end{center}
\end{minipage}
\\
\begin{minipage}{\dimexpr\linewidth-5cm}
{\color{red}\bf \'Etape 4 : on trace les parallèles aux segments obtenus.}

\medskip

On trace la parallèle à (IJ) passant par K, car K est sur la face (ABCD) qui est parallèle à la face (DCGH). Elle coupe [AE] en un point que l'on nomme N.

\medskip

Ensuite, on trace la parallèle à (JM) passant par N car (JM) est incluse dans la face (BFGC) et que celle-ci est parallèle à la face (AEHD). Cette parallèle coupe [AD] en un point que l'on nomme P.
\end{minipage}
&
\begin{minipage}{5cm}
\begin{center}
\begin{tikzpicture}
\clip (-1,-1) rectangle (5.5,5);
\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);
%
\draw[dotted,gray] (J) -- ($(J)+(2.66,0.66)$);
\draw[dotted,gray] (G) -- ($(G)+(2,0)$);
\coordinate (L) at ($(G)+(1.1,0)$);
\fill[red] (L) circle (1.5pt) node[above] {L};
%
\draw[dotted,gray] (L) -- (K);
\coordinate (M) at (4,1.9);
\fill[red] (M) circle (1.5pt) node[below right,scale=0.7] {M};
%
\draw[red,thick] (J) -- (M);
\draw[red,dashed,thick] (K) -- (M);
%
\draw[dotted,gray] (K) -- ($(K)+(-8,-2)$);
\coordinate (N) at ($0.85*(A)+0.15*(E)$);
\fill[red] (N) circle (1.5pt) node[below,scale=0.7] {N};
\draw[dotted,gray] (N) -- (-0.33,1.76);
\coordinate (P) at (0,0.66);
\fill[red] (P) circle (1.5pt) node[left,scale=0.7] {P};
\draw[thick,red,dashed] (P) -- (N) -- (K);
\end{tikzpicture}
\end{center}
\end{minipage}
\\
\begin{minipage}{\dimexpr\linewidth-5cm}
Il ne reste plus qu'à joindre P et I et nous avons la section du cube par (IJK).
\end{minipage}
&
\begin{minipage}{5cm}
\begin{center}
\begin{tikzpicture}
\clip (-1,-1) rectangle (5.5,5);
\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);
\coordinate (L) at ($(G)+(1.1,0)$);
\coordinate (M) at (4,1.9);
\coordinate (N) at ($0.85*(A)+0.15*(E)$);
\coordinate (P) at (0,0.66);
\shade[left color=purple!5,right color=purple!40] (I) -- (J) -- (M) -- (K) -- (N) -- (P) 	 -- cycle;
\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);
%
\draw[dotted,gray] (J) -- ($(J)+(2.66,0.66)$);
\draw[dotted,gray] (G) -- ($(G)+(2,0)$);
\fill[red] (L) circle (1.5pt) node[above] {L};
%
\draw[dotted,gray] (L) -- (K);
\fill[red] (M) circle (1.5pt) node[below right,scale=0.7] {M};
%
\draw[red,thick] (J) -- (M);
\draw[red,dashed,thick] (K) -- (M);
%
\draw[dotted,gray] (K) -- ($(K)+(-8,-2)$);
\fill[red] (N) circle (1.5pt) node[below,scale=0.7] {N};
\draw[dotted,gray] (N) -- (-0.33,1.76);
\fill[red] (P) circle (1.5pt) node[left,scale=0.7] {P};
\draw[thick,red,dashed] (P) -- (N) -- (K) node[below,scale=0.7] {K};
\draw[thick,red] (P) -- (I) node[above right,scale=0.7] {I} -- (J) node[above left,scale=0.7] {J};
\end{tikzpicture}
\end{center}
\end{minipage}
\end{tabular}

\newpage