
\bigskip

\exercice[style=R,N=3,verif]{Tétraèdre \& parallélogramme}

\begin{minipage}{0.5\linewidth}
Soit un tétraèdre quelconque ABCD. I, J, K et L sont les milieux respectifs de [AB],[BC], [CD] et [AD].

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Prouver que le quadrilatère IJKL est un parallélogramme
\end{minipage}
\begin{minipage}{.5\linewidth}
\begin{center}
\begin{tikzpicture}[scale=0.9,every node/.style={scale=0.9}]
\coordinate (A) at (4,0);
\coordinate (B) at (0,2);
\coordinate (C) at (-1,-1);
\coordinate (D) at (2,-2);
\coordinate (I) at ($0.5*(A)+0.5*(B)$);
\coordinate (J) at ($0.5*(B)+0.5*(C)$);
\coordinate (K) at ($0.5*(C)+0.5*(D)$);
\coordinate (L) at ($0.5*(A)+0.5*(D)$);
\fill[purple!20] (I) -- (J) -- (K) -- (L);
\draw[dashed] (I) -- (J);
\draw[dashed] (L) -- (K);
\draw (I) -- (L);
\draw (K) -- (J);
\draw (A) node[right] {A} -- (B) node[above] {B} -- (C) node[left] {C} -- (D) node[below] {D} -- cycle;
\draw (B) -- (D);
\draw[dotted] (A) -- (C);
\node[below right] at (L) {L};
\node[above right] at (I) {I};
\node[above left] at (J) {J};
\node[below] at (K) {K};
\end{tikzpicture}
\end{center}
\end{minipage}