index.tex

\documentclass[a4paper,11pt]{article}
\usepackage{francois_meria}
\usepackage[dvips]{graphicx}
\usepackage[dvips]{epsfig}
\setlength{\parindent}{0mm}
    \lhead{\textsf{Collège Château Forbin} - \textit{Mathématiques} - \textsf{5\ieme}}
    \chead{}
    \rhead{\textit{Année} 2005/2006}
    %\rfoot{Fait avec \LaTeX}
    \pagestyle{fancy}
  \renewcommand{\headrulewidth}{0.5pt}
 
 
\begin{document}
\vskip 0.3cm
 
\begin{tabularx}{\textwidth}{|X|}
\hline \\
 
\centerline{\Huge Atelier 5\ieme~: Géométrie, constructions}\\
\hline
\end{tabularx}
\vskip 0.5cm
 
\textbf{NOM :}\\
 
\vskip 0.3cm
 
{\textbf{Prénom :} \hfill \textbf{Classe : 5\ieme \ldots}}\\
\begin{center}
\psset{unit=0.75cm}
  \pspicture(-2.5,-1)(12,16)
    \psframe(-3,-1.4)(12,16)
\pstGeonode[PointSymbol=none,PosAngle={225,-45,90,90,-45,225}](0,0){A}(9,0){B}(9,9){C}(0,9){D}(11,9){E}(-2,9){F}
    \pstGeonode[PointSymbol=none,PosAngle={45,135,45,135}](4,0){J}(6,0){K}(6,3){H}(4,3){I}
    \pstGeonode[PointSymbol=none,PointName=none](6,9){T}(2,9){T'}(7,0){K'}(7,9){C'}(0,1.5){H'}
\pstInterCC[PointNameB=none,PointSymbol=none,PosAngleA=90]{F}{T}{E}{T'}{G}{M_2}
    \pstInterLL[PosAngle=225,PointSymbol=none]{E}{G}{K}{T}{L}
    \pstInterLL[PosAngle=10,PointSymbol=none]{E}{G}{K'}{C'}{M}
\pstTranslation[PosAngle=135,PointSymbol=none]{A}{H'}{L}{P}
    \pstTranslation[PosAngle=45,PointSymbol=none]{T}{C'}{P}{N}
\pstSegmentMark[SegmentSymbol=pstslashh]{A}{D}
    \pstSegmentMark[SegmentSymbol=pstslashh]{B}{C}
    \pstLineAB{A}{J}
    \pstLineAB{J}{K}
    \pstSegmentMark[SegmentSymbol=pstslash]{K}{B}
    \pstLineAB{D}{C}
 
    \pstSegmentMark[SegmentSymbol=pstslashhh]{F}{D}
    \pstSegmentMark[SegmentSymbol=pstslashhh]{C}{E}
    \pstLineAB{I}{H}
    \pstSegmentMark[SegmentSymbol=pstslash]{H}{K}
    \pstSegmentMark[SegmentSymbol=pstslash]{I}{J}
    \pstLineAB{F}{G}
    \pstLineAB{E}{G}
    \pstLineAB{P}{N}
    \pstLineAB{N}{M}
    \pstLineAB{L}{P}
\psline[linestyle=dashed](0,0)(0,-1)
    \psline[linestyle=dashed](4,0)(4,-0.75)
    \psline[linestyle=dashed](6,0)(6,-0.75)
    \psline[linestyle=dashed](9,0)(9,-0.75)
    \psline[linestyle=dashed](11,13.5)(11,8.3)
\psline[linestyle=dashed](0,0)(-0.75,0)
    \pcline{<->}(0,-0.5)(4,-0.5) \lput*{:U}{4~cm}
    \pcline{<->}(4,-0.5)(6,-0.5) \lput*{:U}{2~cm}
    \pcline{<->}(6,-0.5)(9,-0.5) \lput*{:U}{3~cm}
    \pcline{<->}(0,-0.5)(4,-0.5) \lput*{:U}{4~cm}
    \pcline{<->}(7,13)(11,13) \lput*{:U}{4~cm}
    \pcline{<->}(-2.7,9.45)(3.1,14.85) \mput*{8~cm}
    \pcline{<->}(9,8.35)(11,8.35) \mput*{2~cm}
    \pcline{<->}(-0.95,0)(-0.95,9) \mput*{9~cm}
    \pstRightAngle[RightAngleSize=0.2]{D}{A}{B}
    \pstRightAngle[RightAngleSize=0.2]{A}{D}{C}
    \pstRightAngle[RightAngleSize=0.2]{A}{B}{C}
    \pstRightAngle[RightAngleSize=0.2]{I}{J}{A}
    \pstRightAngle[RightAngleSize=0.2]{H}{K}{B}
    \pstRightAngle[RightAngleSize=0.15]{L}{P}{N}
    \pstRightAngle[RightAngleSize=0.15]{P}{N}{M}
    \put(-2,14){$\begin{array}{l} GE=9~ \text{cm} \\PL=1,5~\text{cm} \\ PN=1~\text{cm}\end{array}$}
\psset{linestyle=none}
    \pstextpath[c]{\psarcn(6.7,7){1.25}{180}{0}}{La Maison des}
    \pstextpath[c]{\psarc(6.7,7){1.25}{180}{0}}{Mathématiques}
  \endpspicture
\end{center}
 
\vskip 0.5cm
 
\begin{enumerate}[1.]
    \item Reproduire la figure ci-dessus en vraies grandeurs en
    utilisant le codage.
    \item Compléter le tableau suivant à l'aide de la figure
    construite à la question 1.
\end{enumerate}
\begin{center}
\begin{tabularx}{\textwidth}{|c|X|X|X|}
\hline
Angles &                       &                  &                   \\
de la  & $\widehat{EFG}=$      & $\widehat{FGE}=$ & $\widehat{GEF}=$  \\
maison &                       &                  &                   \\
\hline
Angles &                       &   \multicolumn{2}{X|}{}               \\
de la  & $\widehat{PLM}=$      &  \multicolumn{2}{X|}{$\widehat{LMN}=$} \\
cheminée & & \multicolumn{2}{X|}{} \\
\hline
\end{tabularx}
\end{center}
\newpage
\textbf{NOM :}\\
 
\vskip 0.3cm
 
{\textbf{Prénom :} \hfill \textbf{Classe : 5\ieme \ldots}}\\
 
\begin{center}
\psset{unit=0.75cm}
  \pspicture(-3,-9.5)(12,8)
  \psframe(-3,-9.5)(12,8)
\rput{-5}{
\pstGeonode[PointSymbol=none,PosAngle={225,-45,90,45,-45,225}](0,0){A}(9,0){B}(9,9){C}(0,9){D}(11,9){E}(-2,9){F}
    \pstGeonode[PointSymbol=none,PosAngle={45,135,45,90}](4,0){J}(6,0){K}(6,3){H}(4,3){I}
    \pstGeonode[PointSymbol=none,PointName=none](6,9){T}(2,9){T'}(7,0){K'}(7,9){C'}(0,1.5){H'}
\pstInterCC[PointNameB=none,PointSymbol=none,PosAngleA=90]{F}{T}{E}{T'}{G}{M_2}
    \pstInterLL[PosAngle=225,PointSymbol=none]{E}{G}{K}{T}{L}
    \pstInterLL[PosAngle=10,PointSymbol=none]{E}{G}{K'}{C'}{M}
\pstTranslation[PosAngle=90,PointSymbol=none]{A}{H'}{L}{P}
    \pstTranslation[PosAngle=90,PointSymbol=none]{T}{C'}{P}{N}
\pstSegmentMark[SegmentSymbol=pstslashh]{A}{D}
    \pstSegmentMark[SegmentSymbol=pstslashh]{B}{C}
    \pstLineAB{A}{J}
    \pstLineAB{J}{K}
    \pstSegmentMark[SegmentSymbol=pstslash]{K}{B}
    \pstLineAB{D}{C}
    \pstSegmentMark[SegmentSymbol=pstslashhh]{F}{D}
    \pstSegmentMark[SegmentSymbol=pstslashhh]{C}{E}
    \pstLineAB{I}{H}
    \pstSegmentMark[SegmentSymbol=pstslash]{H}{K}
    \pstSegmentMark[SegmentSymbol=pstslash]{I}{J}
    \pstLineAB{F}{G}
    \pstLineAB{E}{G}
    \pstLineAB{P}{N}
    \pstLineAB{N}{M}
    \pstLineAB{L}{P}
    \pstLineAB[linestyle=dashed]{A}{C}
\psline[linestyle=dashed](4,0)(4,-0.75)
    \psline[linestyle=dashed](6,0)(6,-0.75)
    \psline[linestyle=dashed](9,0)(9,-0.75)
    \psline[linestyle=dashed](11,9)(11,8.1)
\pcline{<->}(0,-0.5)(4,-0.5) \lput*{:U}{4~cm}
    \pcline{<->}(4,-0.5)(6,-0.5) \lput*{:U}{2~cm}
    \pcline{<->}(6,-0.5)(9,-0.5) \lput*{:U}{3~cm}
    \pcline{<->}(0,-0.5)(4,-0.5) \lput*{:U}{4~cm}
\pcline{<->}(9,8.35)(11,8.35) \mput*{2~cm}
\pstRightAngle[RightAngleSize=0.2]{D}{A}{B}
    \pstRightAngle[RightAngleSize=0.2]{A}{D}{C}
    \pstRightAngle[RightAngleSize=0.2]{A}{B}{C}
    \pstRightAngle[RightAngleSize=0.2]{I}{J}{A}
    \pstRightAngle[RightAngleSize=0.2]{H}{K}{B}
    \pstRightAngle[RightAngleSize=0.15]{L}{P}{N}
    \pstRightAngle[RightAngleSize=0.15]{P}{N}{M}
\pstMarkAngle[arrows=->,MarkAngleRadius=1.5]{E}{F}{G}{}
    \pstMarkAngle[arrows=->,MarkAngleRadius=1.5]{F}{G}{E}{}
    \pstMarkAngle[arrows=<-,MarkAngleRadius=1]{P}{L}{G}{}
    \pstMarkAngle[arrows=->,MarkAngleRadius=1.5]{B}{A}{C}{}
    \put(-0.5,9.5){$60^{\circ}$}
    \put(3.75,12.25){$80^{\circ}$}
    \put(5,14){$50^{\circ}$}
    \put(1.8,0.5){$40^{\circ}$}
}
    \put(-2,6){$\begin{array}{l} GL=2,5~ \text{cm} \\PL=2~\text{cm} \\ PN=1,5~\text{cm}\end{array}$}
  \endpspicture
\end{center}
 
\vskip 0.5cm
 
Pour cette construction,
\begin{enumerate}[(a)]
    \item la figure n'est pas faite en vraies grandeurs ;
    \item on rappelle que la somme des mesures des angles d'un triangle est égale à $180^{\circ}$ ;
    \item le quadrilatère $ABCD$ n'est plus un carré !
\end{enumerate}
 
\vskip 0.5cm
 
\begin{enumerate}[1.]
    \item Reproduire la figure ci-dessus en vraies grandeurs en
    utilisant les codages.
    \item Compléter le tableau suivant à l'aide de la figure
    construite à la question 1. Les longueurs seront données au mm
    près.
\end{enumerate}
 
\begin{center}
\begin{tabularx}{\textwidth}{|c|X|X|X|}
\hline
Longueurs &         &       &        \\
de la     & $AB=$   & $AD=$ & $BC=$  \\
maison    &         &       &        \\
\hline
Longueurs &         &       &        \\
du        & $FE=$   & $FG=$ & $EG=$  \\
toit      &         &       &        \\
\hline
\end{tabularx}
\end{center}
\end{document}