144 lines
5.0 KiB
TeX
144 lines
5.0 KiB
TeX
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
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\usepackage{tikz}
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\usetikzlibrary{calc}
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% Title Page
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\title{Thalès - Travail de groupe}
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\author{}
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\date{}
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\fancyhead[L]{Quatrième}
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\fancyhead[C]{\Thetitle}
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\fancyhead[R]{\thepage}
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\begin{document}
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\thispagestyle{fancy}
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Dans tous les dessins suivants, $ABC$ et $AMN$ sont deux triangles tels que $M$ est un point de $[AB]$, $N$ un point de $[AC]$ et $(MN)//(BC)$. Dans chacunes des figures, les longueurs de quatres côtés sont données. (Les mesures sur les dessins ne sont pas respectées)
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\textbf{Conjecturer les valeurs des longueurs des deux cotés manquants pour remplir les tableaux des longueurs.} Justifier quand c'est possible les valeurs trouvées.
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\begin{itemize}
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\item \textbf{Cas 1}
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\begin{tikzpicture}
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\coordinate (A) at (0,0);
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\coordinate (M) at (3,0);
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\coordinate (B) at (6,0);
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\coordinate (C) at (6,4);
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\coordinate (N) at (3,2);
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\draw (A) node [left] {$A$}
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-- (M) node [below] {$M$} node[midway, below] {$4$}
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-- (B) node [right] {$B$}
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-- (C) node [right] {$C$}
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-- (N) node [above] {$N$}
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-- (A) node [midway, sloped, above] {5};
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\draw (N) -- (M) node[midway, right] {3};
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\draw[<->] ($(A)+(0,-0.5)$) -- ($(B) + (0,-0.5)$) node [midway, below] {$8$};
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\end{tikzpicture}
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\begin{tabular}{|c|*{3}{p{2cm}|}}
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\hline
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Triangle $AMN$ & AM = & AN = & MN = \\
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\hline
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Triangle $ABC$ & AB = & AC = & BC = \\
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\hline
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\end{tabular}
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\item \textbf{Cas 2}
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\begin{tikzpicture}
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\coordinate (A) at (0,0);
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\coordinate (M) at (2.3,0);
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\coordinate (B) at (9.2,0);
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\coordinate (C) at (8,4);
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\coordinate (N) at (2,1);
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\draw (A) node [left] {$A$}
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-- (M) node [below] {$M$} node[midway, below] {$1$}
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-- (B) node [right] {$B$}
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-- (C) node [right] {$C$}
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-- (N) node [above] {$N$}
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-- (A) node [midway, sloped, above] {5};
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\draw (N) -- (M) node[midway, right] {3};
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\draw[<->] ($(A)+(0,-0.5)$) -- ($(B) + (0,-0.5)$) node [midway, below] {4};
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\draw (A) --++ (2.3,0) --++ (2.3,0) node {$|$} --++ (2.3,0) node {$|$};
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\end{tikzpicture}
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\begin{tabular}{|c|*{3}{p{2cm}|}}
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\hline
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Triangle $AMN$ & AM = & AN = & MN = \\
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\hline
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Triangle $ABC$ & AB = & AC = & BC = \\
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\hline
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\end{tabular}
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\item \textbf{Cas 3}
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\begin{tikzpicture}
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\coordinate (A) at (0,0);
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\coordinate (M) at (3,0);
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\coordinate (B) at (6,0);
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\coordinate (C) at (6.8,4);
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\coordinate (N) at (3.4,2);
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\draw (A) node [left] {$A$}
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-- (M) node [below] {$M$} node[midway, below] {$4$}
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-- (B) node [right] {$B$}
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-- (C) node [right] {$C$}
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-- (N) node [above] {$N$}
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-- (A) node [midway, sloped, above] {5};
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\draw (N) -- (M) node[midway, right] {4.4};
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\draw[<->] ($(A)+(-0.5,+0.5)$) -- ($(C) + (0,+0.75)$) node [midway, above, sloped] {$10$};
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\end{tikzpicture}
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\begin{tabular}{|c|*{3}{p{2cm}|}}
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\hline
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Triangle $AMN$ & AM = & AN = & MN = \\
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\hline
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Triangle $ABC$ & AB = & AC = & BC = \\
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\hline
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\end{tabular}
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\item \textbf{Cas 4}
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\begin{tikzpicture}
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\coordinate (A) at (0,0);
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\coordinate (M) at (3,0);
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\coordinate (B) at (6,0);
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\coordinate (C) at (6,4);
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\coordinate (N) at (3,2);
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\draw (A) node [left] {$A$}
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-- (M) node [below] {$M$} node[midway, below] {$4$}
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-- (B) node [right] {$B$}
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-- (C) node [right] {$C$} node [midway, right] {15}
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-- (N) node [above] {$N$}
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-- (A) node [midway, sloped, above] {5};
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\draw (N) -- (M) node[midway, right] {3};
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\end{tikzpicture}
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\begin{tabular}{|c|*{3}{p{2cm}|}}
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\hline
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Triangle $AMN$ & AM = & AN = & MN = \\
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\hline
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Triangle $ABC$ & AB = & AC = & BC = \\
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\hline
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\end{tabular}
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\end{itemize}
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\end{document}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: "master"
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%%% End:
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