\documentclass[a4paper,11pt]{article} \usepackage{francois_meria} \usepackage[dvips]{graphicx} \usepackage[dvips]{epsfig} \usepackage{calc} \setlength{\parindent}{0mm} \lhead{\textsf{Collège Château Forbin} - \textit{Mathématiques} - \textsf{4\ieme 1}} \chead{} \rhead{\textit{Année} 2005/2006} \pagestyle{fancy} \renewcommand{\headrulewidth}{0.5pt} \begin{document} {\noindent \textbf{NOM :} \hfill \textit{jeudi $6$ avril $2006$}} \vskip 0.3cm {\noindent \textbf{Prénom :} \hfill \textbf{Classe : 4\ieme 1}} \begin{center} {\large \textbf{Contrôle de cours}}\\ \vskip 0.3cm \textit{durée : $20$ minutes} \end{center} \vskip 0.3cm \hrule\vspace{\baselineskip} %DEBUT DES EXERCICES \begin{exercice} - \og \textit{parallèles et sécantes, reconnaître les données dans une configuration} \fg\\ Les droites en pointillés sont parallèles. Retrouver pour chaque figure la configuration du cours avec le petit et le grand triangle et les deux droites parallèles, remplir le tableau de proportionnalité puis écrire l'égalité de rapports correspondante. \begin{multicols}{2} \begin{center} \psset{unit=1cm} \pspicture(7,7) \pstGeonode[PointSymbol=none,PosAngle={0,180}](4,0.5){A}(3,1.5){B} \pstGeonode[PointSymbol=none,PointName=none](5.5,1.5){T} \pstCurvAbsNode[PointSymbol=none,PosAngle=0]{B}{T}{C}{50} \pstHomO[HomCoef=2.3,PointSymbol=+,PosAngle=180]{A}{B}{M} \pstHomO[HomCoef=2.3,PointSymbol=+,PosAngle=0]{A}{C}{N} \pstLineAB[nodesep=-1]{A}{M} \pstLineAB[nodesep=-1]{A}{N} \pstLineAB[nodesep=-1,linestyle=dashed]{C}{B} \pstLineAB[nodesep=-1,linestyle=dashed]{M}{N} \put(0,6.5){\pscirclebox{1}} \endpspicture \end{center} \columnbreak Petit triangle : \dotfill\\ Grand triangle : \dotfill\\ Droites parallèles : \dotfill \\ \begin{center} % Table generated by Excel2LaTeX from sheet 'Feuil1' \begin{tabular}{|l*{3}{|p{2cm}}|} \cline{2-4} \multicolumn{1}{c|}{} & \multicolumn{3}{c|}{Côtés correspondants} \\ \hline Petit & & & \\ triangle & & & \\ \hline Grand & & & \\ triangle & & & \\ \hline \end{tabular} \end{center} \vskip 0.4cm \'Egalité des rapports : \dotfill \end{multicols} \hrule\vspace{\baselineskip} \vskip 0.2cm \begin{multicols}{2} \begin{center} \psset{unit=1cm} \pspicture(7,7) \pstGeonode[PointSymbol=none,PosAngle={180,180}](0.5,0.5){D}(2.5,3.5){E} \pstGeonode[PointSymbol=none,PointName=none](4,3.5){T} \pstCurvAbsNode[PointSymbol=none,PosAngle=0]{E}{T}{F}{-40} \pstHomO[HomCoef=1.6,PointSymbol=+,PosAngle=180]{D}{E}{I} \pstHomO[HomCoef=1.6,PointSymbol=+,PosAngle=0]{D}{F}{J} \pstLineAB[nodesep=-1]{D}{I} \pstLineAB[nodesep=-1]{D}{J} \pstLineAB[nodesep=-1,linestyle=dashed]{F}{E} \pstLineAB[nodesep=-1,linestyle=dashed]{I}{J} \put(0,6.5){\pscirclebox{2}} \endpspicture \end{center} \columnbreak Petit triangle : \dotfill\\ Grand triangle : \dotfill\\ Droites parallèles : \dotfill \\ \begin{center} % Table generated by Excel2LaTeX from sheet 'Feuil1' \begin{tabular}{|l*{3}{|p{2cm}}|} \cline{2-4} \multicolumn{1}{c|}{} & \multicolumn{3}{c|}{Côtés correspondants} \\ \hline Petit & & & \\ triangle & & & \\ \hline Grand & & & \\ triangle & & & \\ \hline \end{tabular} \end{center} \vskip 0.4cm \'Egalité des rapports : \dotfill \end{multicols} \newpage \begin{multicols}{2} \begin{center} \psset{unit=1cm} \pspicture(7,7) \pstGeonode[PointSymbol=none,PosAngle={45,150}](0.5,3.5){L}(6,5){M} \pstGeonode[PointSymbol=none,PointName=none](6,2){T} \pstCurvAbsNode[PointSymbol=none,PosAngle=225]{M}{T}{N}{10} \pstHomO[HomCoef=0.35,PointSymbol=+,PosAngle=150]{L}{M}{A} \pstHomO[HomCoef=0.35,PointSymbol=+,PosAngle=225]{L}{N}{B} \pstLineAB[nodesep=-1]{L}{M} \pstLineAB[nodesep=-1]{L}{N} \pstLineAB[nodesep=-1,linestyle=dashed]{N}{M} \pstLineAB[nodesep=-1,linestyle=dashed]{A}{B} \put(0,6.5){\pscirclebox{3}} \endpspicture \end{center} \columnbreak Petit triangle : \dotfill\\ Grand triangle : \dotfill\\ Droites parallèles : \dotfill \\ \begin{center} % Table generated by Excel2LaTeX from sheet 'Feuil1' \begin{tabular}{|l*{3}{|p{2cm}}|} \cline{2-4} \multicolumn{1}{c|}{} & \multicolumn{3}{c|}{Côtés correspondants} \\ \hline Petit & & & \\ triangle & & & \\ \hline Grand & & & \\ triangle & & & \\ \hline \end{tabular} \end{center} \vskip 0.4cm \'Egalité des rapports : \dotfill \end{multicols} \hrule\vspace{\baselineskip} \vskip 0.2cm \begin{multicols}{2} \begin{center} \psset{unit=1cm} \pspicture(7,7) \pstGeonode[PointSymbol=none,PosAngle={145,140}](1,0.5){K}(0.25,5){L}(6,0.2){J} \pstGeonode[PointSymbol=none,PointName=none](4,5){T} \pstCurvAbsNode[PointSymbol=none,PosAngle=-15]{L}{T}{I}{30} \pstHomO[HomCoef=0.75,PointSymbol=+,PosAngle=140]{K}{L}{A} \pstHomO[HomCoef=0.75,PointSymbol=+,PosAngle=-15]{K}{I}{B} \pstLineAB[nodesep=-1]{K}{L} \pstLineAB[nodesep=-1]{K}{I} \pstLineAB[nodesep=-1,linestyle=dashed]{I}{L} \pstLineAB[nodesepA=-1,nodesepB=-2.5,linestyle=dashed]{A}{B} \pstLineAB[nodesep=-1]{K}{J} \pstLineAB[nodesep=-1]{I}{J} \put(0,6.5){\pscirclebox{4}} \pstInterLL[PointSymbol=none,PosAngle=45]{A}{B}{I}{J}{C} \endpspicture \end{center} \columnbreak Petit triangle : \dotfill\\ Grand triangle : \dotfill\\ Droites parallèles : \dotfill \\ \begin{center} % Table generated by Excel2LaTeX from sheet 'Feuil1' \begin{tabular}{|l*{3}{|p{2cm}}|} \cline{2-4} \multicolumn{1}{c|}{} & \multicolumn{3}{c|}{Côtés correspondants} \\ \hline Petit & & & \\ triangle & & & \\ \hline Grand & & & \\ triangle & & & \\ \hline \end{tabular} \end{center} \vskip 0.4cm \'Egalité des rapports : \dotfill \end{multicols} \hrule\vspace{\baselineskip} \vskip 0.2cm \begin{multicols}{2} \begin{center} \psset{unit=1cm} \pspicture(7,7) \pstGeonode[PointSymbol=none,PosAngle={180,-90}](4.5,2.5){D}(2,4.5){E} \pstGeonode[PointSymbol=none,PointName=none](3,3.5){T} \pstCurvAbsNode[PointSymbol=none,PosAngle=-35]{E}{T}{F}{50} \pstHomO[HomCoef=1.35,PointSymbol=+,PosAngle=-90]{D}{E}{I} \pstHomO[HomCoef=1.35,PointSymbol=+,PosAngle=-35]{D}{F}{J} \pstLineAB[nodesep=-1]{D}{I} \pstLineAB[nodesep=-1]{D}{J} \pstLineAB[nodesep=-1,linestyle=dashed]{F}{E} \pstLineAB[nodesep=-1,linestyle=dashed]{I}{J} \pstHomO[HomCoef=-1,PointSymbol=+,PosAngle=0]{D}{E}{A} \pstHomO[HomCoef=-1,PointSymbol=+,PosAngle=180]{D}{F}{B} \pstLineAB[linestyle=dashed]{A}{B} \pstLineAB[nodesepB=-1]{D}{A} \pstLineAB[nodesepB=-1]{D}{B} \put(0,6.5){\pscirclebox{5}} \endpspicture \end{center} \columnbreak Petit triangle : \dotfill\\ Grand triangle : \dotfill\\ Droites parallèles : \dotfill \\ \begin{center} % Table generated by Excel2LaTeX from sheet 'Feuil1' \begin{tabular}{|l*{3}{|p{2cm}}|} \cline{2-4} \multicolumn{1}{c|}{} & \multicolumn{3}{c|}{Côtés correspondants} \\ \hline Petit & & & \\ triangle & & & \\ \hline Grand & & & \\ triangle & & & \\ \hline \end{tabular} \end{center} \vskip 0.4cm \'Egalité des rapports : \dotfill \end{multicols} \end{exercice} \end{document}