\documentclass[a4paper,11pt]{article}
\usepackage{francois_meria}
\usepackage[dvips]{graphicx}
\usepackage[dvips]{epsfig}
\setlength{\parindent}{0mm}
    \lhead{\textsf{Collège Château Forbin} - \textit{Mathématiques} - \textsf{6\ieme}}
    \chead{}
    \rhead{\textit{Année} 2005/2006}
    \pagestyle{fancy}
  \renewcommand{\headrulewidth}{0.5pt}
%
\begin{document}
\begin{center}
\begin{tabularx}{\textwidth}{|X|}
\hline

\vskip 0.3cm

\begin{center}
   {\Large\textbf{Construction géométrique et symétrie - 1}}\\
\end{center}\\
\hline
\end{tabularx}
\end{center}
%
\vskip 1cm

\begin{enumerate}[(a)]
    \item
    \begin{multicols}{2}
        \begin{itemize}
            \item [$\circ$] Tracer au centre de la feuille un carré $ABCD$ de
            $6$~cm de côté ainsi que ses deux diagonales
            d'intersection $O$.
            \item [$\circ$] Construire les trois bissectrices du
            triangle $ABD$. elles se coupent en $I$.
            \item [$\circ$] Tracer le cercle de centre $I$ et de
            rayon $IO$. On obtient la figure 1.
        \end{itemize}
    \begin{center}
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            \pstGeonode[PointSymbol=none,PosAngle={225,-45,45,135}](0,0){D}(6,0){C}(6,6){B}(0,6){A}
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            \pstLineAB{C}{B}
            \pstLineAB{A}{D}
            \pstLineAB{D}{C}
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            \pstInterLL[PointSymbol=none,PosAngle=-90]{D}{B}{A}{C}{O}
            \pstBissectBAC[PointName=none,PointSymbol=none,linestyle=dotted]{A}{B}{D}{M}
            \pstBissectBAC[PointName=none,PointSymbol=none,linestyle=dotted,nodesepB=2.5]{B}{D}{A}{N}
            \pstInterLL[PointSymbol=+]{A}{C}{B}{M}{I}
            \pstCircleOA{I}{O}
            \put(2,-0.7){Figure 1}
        \endpspicture
    \end{center}
    \end{multicols}
    \item Compléter cette figure par symétrie par rapport à la
    droite $(BD)$, faire de même avec la nouvelle figure par
    rapport à la droite $(BC)$ et enfin par rapport à la droite
    $(DC)$.
    \item Colorier la figure avec deux couleurs différentes que l'on alternera afin d'obtenir la figure 2.
\end{enumerate}

\vskip 1cm

\begin{center}
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        \pspicture(0,-6)(12,6)
            \pstGeonode[PointSymbol=none,PointName=none](0,0){D}(6,0){C}(6,6){B}(0,6){A}
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            \pstLineAB{C}{B}
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            \pstLineAB{D}{C}
            \pstLineAB{A}{C}
            \pstLineAB{D}{B}
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            \pstBissectBAC[PointName=none,PointSymbol=none,linestyle=none]{A}{B}{D}{M}
            \pstBissectBAC[PointName=none,PointSymbol=none,linestyle=none]{B}{D}{A}{N}
            \pstInterLL[PointSymbol=none,PointName=none]{A}{C}{B}{M}{I}
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            \pstCircleOA{L}{O'}
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            \pstOrtSym[PointName=none,PointSymbol=none]{D}{C}{J}{T}
            \pstOrtSym[PointName=none,PointSymbol=none]{D}{C}{I}{Q}
            \pstOrtSym[PointName=none,PointSymbol=none]{D}{C}{O}{P}
            \pstOrtSym[PointName=none,PointSymbol=none]{D}{C}{O'}{S}
            \pstOrtSym[PointName=none,PointSymbol=none]{D}{C}{L}{H}
            \pstOrtSym[PointName=none,PointSymbol=none]{D}{C}{K}{H'}
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            \pstCircleOA{H}{S}
            \pstCircleOA{H'}{S}
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            \pstLineAB{C}{Y}
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            \pstLineAB{Z}{X}
            \pstLineAB{C}{Z}
            \pstLineAB{D}{Y}
            \pstLineAB{Y}{E}
            \put(5.4,-6.7){Figure 2}
        \endpspicture
\end{center}

\newpage
\begin{center}
\begin{tabularx}{\textwidth}{|X|}
\hline

\vskip 0.3cm

\begin{center}
   {\Large\textbf{Construction géométrique et symétrie - 2}}\\
\end{center}\\
\hline
\end{tabularx}
\end{center}

\vskip 1cm

\begin{multicols}{2}
À partir de la figure 1 ci-contre, on veut obtenir la figure 2
puis la figure 3, uniquement à l'aide de la symétrie axiale.
\begin{center}
    \psset{unit=1cm}
        \pspicture(-2,-0.5)(5,2.2)
            \rput{25}{
            \pstGeonode[PointSymbol=none,PosAngle={-45,-45,-45,-45,-45,-45,90}](0,0){O}(1,0){I}(2,0){J}(3,0){K}(4,0){L}(5,0){M}(0,2){A}
            \pstSegmentMark[SegmentSymbol=pstslashh]{O}{I}
            \pstSegmentMark[SegmentSymbol=pstslashh]{I}{J}
            \pstSegmentMark[SegmentSymbol=pstslashh]{J}{K}
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            }
            \put(2,0){Figure 1}
        \endpspicture
\end{center}
\end{multicols}

\begin{enumerate}[(a)]
    \item Reproduire la figure 1 en prenant $OA=2$~cm et
    $OI=1$~cm.
    \item Quels sont les axes de symétrie de la figure 2 ?
    Compléter la figure 1 afin d'obtenir la figure 2.
    \item Décrire avec précision les axes de symétrie de la figure
    3. Compléter la figure 2 pour obtenir la figure 3.
    \item Colorier la figure 3 à l'aide de deux couleurs en
    alternant les couleurs.
    \item Combien d'axes de symétrie possède la figure 3 ? Et la
    figure coloriée ?
\end{enumerate}

\begin{center}
    \psset{unit=1cm}
        \pspicture(-5,-3)(5,2.5)
          \rput{25}{
            \pstGeonode[PointSymbol=none,PosAngle={-40,-40,-40,-40,-40,-40,90}](0,0){O}(1,0){I}(2,0){J}(3,0){K}(4,0){L}(5,0){M}(0,2){A}            \pstLineAB{A}{O}
            \pstLineAB{A}{I}
            \pstLineAB{A}{J}
            \pstLineAB{A}{K}
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            \pstLineAB{O}{M}
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            \pstLineAB{B}{I}
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            \pstOrtSym[PointSymbol=none,PointName=none]{A}{B}{L}{L_1}
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            \pstLineAB{B}{L_1}
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        \put(2,-2){Figure 2}
        \endpspicture
\end{center}

\begin{center}
    \psset{unit=1cm}
        \pspicture(-5,-5)(6,2.5)
        \rput{25}{
            \pstGeonode[PointSymbol=none,PointName=none](0,0){O}(1,0){I}(2,0){J}(3,0){K}(4,0){L}(5,0){M}(0,1.4){A}
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            \pstOrtSym[PointSymbol=none,PointName=none]{B}{C}{J_2}{J_3}
            \pstOrtSym[PointSymbol=none,PointName=none]{B}{C}{K_2}{K_3}
            \pstOrtSym[PointSymbol=none,PointName=none]{B}{C}{L_2}{L_3}
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            \pstLineAB{B}{J_3}
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            \pstLineAB{C}{J_3}
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            \pstLineAB{C}{L_3}
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        \put(3,-4){Figure 3}
        \endpspicture
\end{center}

\newpage
\begin{center}
\begin{tabularx}{\textwidth}{|X|}
\hline

\vskip 0.3cm

\begin{center}
   {\Large\textbf{Construction géométrique et symétrie - 3}}\\
\end{center}\\
\hline
\end{tabularx}
\end{center}

\vskip 1cm

\begin{enumerate}[1.]
\begin{multicols}{2}
    \item
        \begin{enumerate}[(a)]
            \item Tracer un carré $ABCD$ de $15$~cm de côté et ses quatre axes de symétrie.
            Appeler $O$ leur point d'intersection.
            \item Placer le point $I$, milieu du segment $[AB]$ et
            le point $J$, milieu du segment $[BC]$.
            \item Construire les bissectrices des angles $\widehat{OAD}$, $\widehat{OAB}$,
            $\widehat{IOB}$ et $\widehat{JOB}$.
            \item Compléter la construction pour obtenir la figure 1.
        \end{enumerate}

    \begin{center}
    \psset{unit=0.4cm}
        \pspicture(15,15)
            \pstGeonode[PointSymbol=none,PosAngle={235,-45,45,135,0,90}](0,0){D}(15,0){C}(15,15){B}(0,15){A}(15,7.5){J}(7.5,15){I}
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            \put(6.2,-1){Figure 1}
        \endpspicture
\end{center}
\end{multicols}
    \item
        \begin{enumerate}[(a)]
            \item Compléter la figure 1 par symétrie par rapport aux
            deux diagonales du carré $ABCD$.
            \item Colorier la figure 2 à l'aide de deux couleurs
            que l'on alternera.
        \end{enumerate}
\end{enumerate}

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            \pspolygon[fillstyle=solid,fillcolor=lightgray](O)(T_1)(S)
            \pspolygon[fillstyle=solid,fillcolor=lightgray](A)(J_1)(T_1)
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            \pspolygon[fillstyle=solid,fillcolor=lightgray](O)(P_1)(I)
            \pspolygon[fillstyle=solid,fillcolor=lightgray](O)(S_1)(P_2)
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            \pstInterLL[PointName=none,PointSymbol=none]{R_1}{R_2}{O}{D}{U}
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            \pspolygon[fillstyle=solid,fillcolor=lightgray](O)(U_1)(Q_2)
            \pspolygon[fillstyle=solid,fillcolor=lightgray](Q_2)(J)(C)
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        \endpspicture
\end{center}
\end{document}

— Syracuse — Dernière modification : 31 mai 2006 (0.08s - 3953529 - 10 janvier 2009)

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