\begin{exercice}
On considère un tétraèdre régulier $ABCD$ comme ci-dessous avec $I$, $J$ et $K$ les milieux respectifs des segments $[BC]$, $[AB]$ et $[AD]$.
\begin{enumerate}
\item Reproduire la figure. 
\item Construire en justifiant la section du tétraèdre par le plan $(IJK)$.
\item Quelle est la nature de cette section ? Justifier.
\end{enumerate}

\begin{center}
\begin{tikzpicture}[general,x=1.0cm,y=1.0cm,scale=.7]
%\clip(-3.12,-1.2) rectangle (3.66,5.32);
\draw [color=Noir] (0.,4.)-- (1.,0.);
\draw [color=Noir] (1.,0.)-- (-1.42,0.98);
\draw [color=Noir] (-1.42,0.98)-- (0.,4.);
\draw [color=Noir] (0.,4.)-- (2.04,1.74);
\draw [color=Noir] (2.04,1.74)-- (1.,0.);
\draw [color=Noir] (1.,0.)-- (0.,4.);
\draw [dashed,color=J1] (-1.42,0.98)-- (2.04,1.74);
\begin{scriptsize}
\draw [fill=Noir] (0.,4.) circle (1.5pt);
\draw[color=Noir] (0.14,4.28) node {$A$};
\draw [fill=Noir] (1.,0.) circle (1.5pt);
\draw[color=Noir] (1.3,0.06) node {$B$};
\draw [fill=Noir] (-1.42,0.98) circle (1.5pt);
\draw[color=Noir] (-1.58,1.32) node {$C$};
\draw [fill=Noir] (2.04,1.74) circle (1.5pt);
\draw[color=Noir] (2.18,2.02) node {$D$};
\draw [color=J1] (-0.21,0.49)-- ++(-1.5pt,-1.5pt) -- ++(3.0pt,3.0pt) ++(-3.0pt,0) -- ++(3.0pt,-3.0pt);
\draw[color=J1] (-0.62,0.4) node {$I$};
\draw [color=J1] (0.5,2.)-- ++(-1.5pt,-1.5pt) -- ++(3.0pt,3.0pt) ++(-3.0pt,0) -- ++(3.0pt,-3.0pt);
\draw[color=J1] (0.64,2.28) node {$J$};
\draw [color=J1] (1.02,2.87)-- ++(-1.5pt,-1.5pt) -- ++(3.0pt,3.0pt) ++(-3.0pt,0) -- ++(3.0pt,-3.0pt);
\draw[color=J1] (1.16,3.16) node {$K$};
\end{scriptsize}
\end{tikzpicture}  
\end{center}
\end{exercice}

