\begin{exercice}
Soit $SABC$ un tétraèdre de tel que les triangles $ABC$ et $SBC$ soient isocèles respectivement en $A$ et $S$ :
\begin{center}
 %\includegraphics[scale=0.3]{./images/tetra_triangles_isoceles.eps}
 \begin{tikzpicture}[general, scale=3]
	%points
	\coordinate (A) at (0,0); \draw (A) node[below  left] {$A$};
	\coordinate (C) at (1,0); \draw (C) node[below right] {$C$};
	\coordinate (B) at (0.4,0.4); \draw (B) node[right] {$B$};
	\coordinate (S) at (0.6,1.17); \draw (S) node[above] {$S$};
	%segments
	\draw[color=D1] (C)--(A)--(B);
	\draw[color=J1] (B)--(S)--(C);
	\draw[color=B1, ->, thick] (B)--(C);
	\draw[color=B1, ->, thick] (A)--(S);
	%codage
	\draw[color=D1] (0.5,0) node {{\boldmath $\bullet$}};
	\draw[color=D1] (0.2,0.2) node {{\boldmath $\bullet$}};
	\draw[color=J1] (0.5,0.74) node {{\boldmath $\approx$}};
	\draw[color=J1] (0.8,0.59) node {{\boldmath $\approx$}};
	\end{tikzpicture}
\end{center}

Démontrer que $\vv{AS} \cdot \vv{BC} = 0$.
\end{exercice}

