\documentclass[a4paper]{article}
\usepackage[latin1]{inputenc}
\usepackage[LGR,T1]{fontenc}
\usepackage[francais,greek,frenchb]{babel}
\usepackage{array,multicol,multirow,enumerate}
\usepackage{graphicx,pst-all,pst-eucl}
\usepackage{lscape}
\usepackage{amsmath,amsfonts,amsthm,geometry}
\usepackage{frcursive}
\usepackage{fancyhdr}
\setlength{\parindent}{0mm}
\def\d{$\diamond \,$}
\def\*{\times}
\def\Euro{\textgreek{\euro}\ }
\def\m@th{\mathsurround=0pt}
\def\trou#1{
    \setbox0=\hbox{\textbf{#1}} \dp0=0pt \m@th
    \underline{\hbox{\hskip\wd0}}
}
\newcommand{\machine}[4]{
        \begin{pspicture}
        \rput(0,0){\rnode{A}{#1}}
        \rput(3,0.11){\rnode{B}{#2}}
        \psset{nodesep=5pt}
        \ncarc[arcangleA=25,arcangleB=25]{->}{A}{B}\mput*{\ovalnode{m}{#3}}
        \ncarc[arcangleA=25,arcangleB=25]{->}{B}{A}\mput*{\ovalnode{d}{#4}}
        \end{pspicture}
        \hskip 3.1cm}
\newcommand{\cylindre}[5]{
\pstGeonode[PointSymbol=*,PointName=#2](0,0){#1}
\pstGeonode[PointSymbol=none,PointName=none](10,0){Aamoi}
\pstGeonode[PointSymbol=none,PointName=none](#4,#3){HG}
\pstGeonode[PointSymbol=none,PointName=none](-#4,#3){HD}
\pstGeonode[PointSymbol=none,PointName=none](#4,0){BG}
\pstGeonode[PointSymbol=none,PointName=none](-#4,0){BD}
\pstLineAB{HG}{BG}
\pstLineAB{HD}{BD}

\psplot[linestyle=dashed]{-#4}{#4}{#4 2 exp x 2 exp sub .5 exp #5 mul}
\psplot{-#4}{#4}{#4 2 exp x 2 exp sub .5 exp -#5 mul}
\psplot{-#4}{#4}{#4 2 exp x 2 exp sub .5 exp #5 mul #3 add}
\psplot{-#4}{#4}{#4 2 exp x 2 exp sub .5 exp -#5 mul #3 add}
}

\newcommand{\cone}[7]{
\pstGeonode[PointSymbol=*,PointName=#2](0,0){#1}
\pstGeonode[PointSymbol=none,PointName=none](10,0){Aamoi}
\pstGeonode[PointSymbol=none,PointName=none](0,#3){Hsommet}
\pstMiddleAB[PointSymbol=none,PointName=none]{#1}{Hsommet}{Milieuu}
\pstInterCC[PointSymbol=none,PointName=none,RadiusA=\pstDistVal{#6}]{#1}{}{Milieuu}{Hsommet}{Ibidon}{Jbidon}
\pstProjection[PointSymbol=none,PointName=none]{#1}{Aamoi}{Jbidon}{Jbidon'}
\pstProjection[PointSymbol=none,PointName=none]{#1}{Aamoi}{Ibidon}{Ibidon'}

\psplot[linestyle=dashed]{-#6}{#6}{#6 2 exp x 2 exp sub .5 exp #7 mul}
\psplot{-#6}{#6}{#6 2 exp x 2 exp sub .5 exp -#7 mul}
\pstHomO[HomCoef=#7,PointSymbol=none,PointName=#5]{#1}{Hsommet}{#4}
\pstHomO[HomCoef=#7,PointSymbol=none,PointName=none]{Jbidon'}{Jbidon}{T1}
\pstHomO[HomCoef=#7,PointSymbol=none,PointName=none]{Ibidon'}{Ibidon}{T2}
\pstLineAB{#4}{T1}
\pstLineAB{#4}{T2}
}

\newcommand{\rapporteur}{
\SpecialCoor
\pscircle{5}
\multido{\i=0+1}{181}{\psline(5;\i)}
\pscircle[fillcolor=white,fillstyle=solid,linestyle=none]{4.5}
\multido{\i=0+10}{19}{\psline(5;\i)}
\pscircle[fillcolor=white,fillstyle=solid,linestyle=none]{4}
\pscircle[fillcolor=white,fillstyle=solid]{3}
\psframe[fillcolor=white,fillstyle=solid,linestyle=none](5,-5.1)(-5,-1.75)
\pscircle[fillcolor=white,fillstyle=solid]{.5}
\psframe[fillcolor=white,fillstyle=solid](-5,-1.75)(5,0)
\psline[linecolor=white](-.5,0)(.5,0)
\psline[linecolor=white](-3,0)(-4,0)
\psline[linecolor=white](3,0)(4,0)
\pscircle[fillcolor=white,fillstyle=solid]{.05}
\NormalCoor
}

\newcommand{\QCM}[4]{
    \begin{tabular}[t]{p{13cm}c}
    #1 & \psset{xunit=1 cm}
    \begin{pspicture}(-0.3,0)(1.5,0.5)
    \pspolygon(0,0)(1.5,0)(1.5,-.5)(0,-.5)
    \psline(.5,0)(.5,-.5) \psline(1,0)(1,-.5)
    \uput[90](0.25,0){A}  \uput[90](0.75,0){B} \uput[90](1.25,0){C}
    \end{pspicture} \\
    A: #2 \qquad B: #3 \qquad C: #4 & \\
    \end{tabular}}

\newcommand{\smallbox}{
    \begin{pspicture}(.5,.5)
    \pspolygon(0,0)(.25,0)(.25,.25)(0,.25)
    \end{pspicture}}

\renewcommand{\vec}[1]
{\mathord{\setbox0\hbox{$#1$} \mathop{\smash{#1}\setbox1\copy0\ht1 0.8\ht0
\vphantom{\copy1}\mskip0.8\thinmuskip}
\limits^{\hbox to\wd0{$\mskip0.8\thinmuskip$\rightarrowfill}}\mskip-0.8\thinmuskip}}

\newcommand{\system}[2]{
\left\{
\begin{array}{l}
#1\\
#2
\end{array}
\right.
}

\newcolumntype{I}{!{\vrule width 1.5pt}}
\newlength\savedwidth
\newcommand\whline{\noalign{\global\savedwidth\arrayrulewidth\global\arrayrulewidth
1.5pt} \hline \noalign{\global\arrayrulewidth\savedwidth}}
% Marges
\geometry{ hmargin=1.5cm, vmargin=1.5cm }
% Exo
\newcounter{nexo}
\setcounter{nexo}{0}
\newcommand{\exo}{
    \stepcounter{nexo}
    {\textbf{$\triangleright$ Exercice \arabic{nexo} :}}
}
% Questions
\newenvironment{questions}{\begin{enumerate}[1 $\, \diamond$]}{\end{enumerate}}

    \lhead{\textsf{Collège Château Forbin} - \textit{Mathématiques}}
    \chead{}
    \rhead{\textit{Année} 2005/2006}
    \pagestyle{fancy}
  \renewcommand{\headrulewidth}{0.5pt}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Début du document %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{document}
{\noindent \textbf{NOM :} \hfill \textit{mercredi $30$ novembre
$2005$}}

\vskip 0.3cm

{\noindent \textbf{Prénom :} \hfill \textbf{Classe
:\dots\ldots\ldots}}
\begin{center}
    {\large \textbf{Contrôle de cours \textit{\no}2}}\\
    \textit{durée : $20$ minutes}
\end{center}

\vskip 0.3cm \hrule\vspace{\baselineskip}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% DEBUT DES EXERCICES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Présentation

\exo
\begin{multicols}{2}
Dans la figure suivante,
\begin{questions}
\item Nommer de deux façons possibles les angles marqués :
\begin{itemize}
 \item \dotfill
 \item \dotfill
 \item \dotfill
\end{itemize}
\item Marquer en bleu l'angle $\widehat{ACB}$, en rouge l'angle
$\widehat{EFM}$, en vert l'angle $\widehat{CDF}$.
\end{questions}
\columnbreak
% Generated by eukleides 1.0.0
\psset{linecolor=black, linewidth=.5pt, arrowsize=2pt 4}
\psset{unit=1.0000cm}
\pspicture(-1.0000,0.0000)(7.0000,5.50000)
\pspolygon(0.0000,0.0000)(6.0000,0.0000)(0.0000,4.5000)
\pspolygon(0.0000,0.0000)(6.0000,0.0000)(3.0000,5.1962)
\psline(0.0000,0.0000)(4.5000,2.5981)
\psline(3.0000,5.1962)(3.6260,0.0000)
\uput{0.3000}[180.0000](0.0000,0.0000){$A$}
\uput{0.3000}[0.0000](6.0000,0.0000){$B$}
\uput{0.3000}[90.0000](0.0000,4.5000){$C$}
\uput{0.3000}[90.0000](3.0000,5.1962){$D$}
\uput{0.3000}[180.0000](1.8130,3.1402){$E$}
\uput{0.3000}[0.0000](4.5000,2.5981){$M$}
\uput{0.3000}[180.0000](3.3902,1.9573){$F$}
\uput{0.3000}[-90.0000](3.6260,0.0000){$G$}
\psarc(0.0000,0.0000){0.45000}{0.0000}{30.0000}
\psarc(0.0000,0.0000){0.55000}{0.0000}{30.0000}
\psarc(0.0000,0.0000){0.65000}{0.0000}{30.0000}
\psarc(3.0000,5.1962){0.4500}{-120.0000}{-83.1301}
\psarc(3.0000,5.1962){0.5500}{-120.0000}{-83.1301}
\psarc(3.3902,1.9573){0.5000}{-83.1301}{30.0000}
\endpspicture
% End of figure
\end{multicols}

\vskip 0.3cm

\exo
\begin{multicols}{2}
Compléter le tableau suivant à l'aide de la figure ci-contre :

%\begin{center}
\begin{tabular}{|c|c|c|c|c|}
\hline
Nom                & Aigu    & Droit & Obtus & Plat \\ \hline
$\widehat{ADF}$    &         &       &       &      \\ \hline
$\widehat{FCE}$    &         &       &       &      \\ \hline
$\widehat{BMA}$    &         &       &       &      \\ \hline
$\widehat{DCF}$    &         &       &       &      \\ \hline
                   &         &       &  $\*$ &      \\ \hline
                   &         &       &       & $\*$ \\ \hline


\end{tabular}
%\end{center}

\columnbreak
% Generated by eukleides 1.0.0
\psset{linecolor=black, linewidth=.5pt, arrowsize=2pt 4}
\psset{unit=1.0000cm}
\pspicture*(-1.5000,-0.2000)(6.0000,3.8000)
\pspolygon(0.0000,0.0000)(4.0000,0.0000)(4.0000,3.0000)
\pspolygon(0.0000,0.0000)(4.0000,0.0000)(-1.0000,2.2913)
\psline(0.0000,0.0000)(4.0000,0.8249)
\uput{0.3000}[180.0000](0.0000,0.0000){$A$}
\uput{0.3000}[0.0000](4.0000,0.0000){$B$}
\uput{0.3000}[90.0000](4.0000,3.0000){$C$}
\uput{0.3000}[90.0000](-1.0000,2.2913){$D$}
\uput{0.3000}[0.0000](4.0000,0.8249){$E$}
\uput{0.3000}[90.0000](2.7585,0.5689){$M$}
\uput{0.3000}[90.0000](1.5171,1.1378){$F$}
\endpspicture
% End of figure
\end{multicols}

 \vskip 0.5cm
\exo
\begin{multicols}{2}
Sur la figure ci-contre, coder les égalites d'angles suivantes :
\begin{questions}
    \item $\widehat{IEG}=\widehat{JFH}$ ;
    \item $\widehat{FJD}=\widehat{tJB}$ ;
    \item $\widehat{EGC}=\widehat{tHy}=\widehat{tDB}$ ;
    \item $\widehat{GIE}=\widehat{FJt}=\widehat{DJB}$.
\end{questions}
\columnbreak
\pspicture*(-1,-.5)(6,3.5)
\rput{-10}{
\pstGeonode[PointName=none,PointSymbol=none](0,1){AA}
\pstGeonode[PointName=none,PointSymbol=none](5,1){BB}
\pstGeonode[PointSymbol=none](5,1){x}
\pstGeonode[PointName=none,PointSymbol=none](0,3){CC}
\pstGeonode[PointName=none,PointSymbol=none](5,3){DD}
\pstGeonode[PointSymbol=none](5,3){y}
\pstGeonode[PointName=none,PointSymbol=none](0,4){EE}
\pstGeonode[PointName=none,PointSymbol=none](3,4){FF}
\pstGeonode[PointName=none,PointSymbol=none](1,0){GG}
\pstGeonode[PointName=none,PointSymbol=none](4,0){HH}
\pstGeonode[PointName=none,PointSymbol=none](2.5,4){II}
\pstGeonode[PointName=none,PointSymbol=none](5,4){JJ}
\pstGeonode[PointSymbol=none](5,4){t}
\pstGeonode[PointName=none,PointSymbol=none](-0.5,0){KK}
\pstGeonode[PointName=none,PointSymbol=none](2,0){LL}
\psline(AA)(BB)
\psline(CC)(DD)
\psline(EE)(GG)
\psline(FF)(HH)
\psline(II)(KK)
\psline(JJ)(LL)

\pstInterLL[PosAngle=-45,PointSymbol=none]{AA}{BB}{EE}{GG}{A}
\pstInterLL[PosAngle=-45,PointSymbol=none]{AA}{BB}{FF}{HH}{B}
\pstInterLL[PosAngle=135,PointSymbol=none]{AA}{BB}{II}{KK}{C}
\pstInterLL[PosAngle=-45,PointSymbol=none]{AA}{BB}{JJ}{LL}{D}

\pstInterLL[PosAngle=45,PointSymbol=none]{CC}{DD}{EE}{GG}{E}
\pstInterLL[PosAngle=45,PointSymbol=none]{CC}{DD}{FF}{HH}{F}
\pstInterLL[PosAngle=135,PointSymbol=none]{CC}{DD}{II}{KK}{G}
\pstInterLL[PosAngle=135,PointSymbol=none]{CC}{DD}{JJ}{LL}{H}

\pstInterLL[PointSymbol=none]{II}{KK}{EE}{GG}{I}
\pstInterLL[PointSymbol=none]{FF}{HH}{JJ}{LL}{J}
}
\endpspicture
\end{multicols}

\exo Construire ci-dessous un triangle $ABC$ tel que $BC=8$~cm,
$\widehat{ABC}=45$\degres et $\widehat{BCA}=30$\degres.
\end{document}

