Import work from year 2013-2014
This commit is contained in:
Benjamin Bertrand
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4e/Geometrie/Pythagore/Conn/Conn0114.pdf
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4e/Geometrie/Pythagore/Conn/Conn0114.pdf
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4e/Geometrie/Pythagore/Conn/Conn0114.tex
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4e/Geometrie/Pythagore/Conn/Conn0114.tex
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\documentclass{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classConn}
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% Title Page
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\title{}
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\author{}
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\date{}
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\begin{document}
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\begin{multicols}{2}
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Nom - Prénom:
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\section{Connaissance}
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\begin{enumerate}
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\item Enoncer le théorème de Pythagore.
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\\[0.5cm]
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. \dotfill
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\\[0.5cm]
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. \dotfill
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\\[0.5cm]
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. \dotfill
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\\[0.5cm]
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\item Soient $a$, $b$, $c$ et $d$ trois entiers relatifs tels que .. .. .. .. \\ Alors
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\begin{eqnarray*}
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\frac{a}{b} \times \frac{c}{d} & = &
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\end{eqnarray*}
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\item Calculer l'expression suivante
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\begin{eqnarray*}
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A &=& 4(2 \times (-3) + 1) - 3
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\end{eqnarray*}
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\\[2cm]
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\begin{eqnarray*}
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B &=& 10 \times \frac{2}{7}
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\end{eqnarray*}
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\end{enumerate}
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\columnbreak
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Nom - Prénom
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\section{Connaissance}
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\begin{enumerate}
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\item Soient $a$, $b$, $c$ et $d$ trois entiers relatifs tels que .. .. .. .. \\ Alors
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\begin{eqnarray*}
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\frac{a}{b} \times \frac{c}{d} & = &
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\end{eqnarray*}
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\item Enoncer le théorème qui permet de montrer que deux droites sont parallèles.
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\\[0.5cm]
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. \dotfill
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\\[0.5cm]
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. \dotfill
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\\[0.5cm]
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. \dotfill
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\\[0.5cm]
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\item Calculer l'expression suivante
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\begin{eqnarray*}
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A &=& -4 + 4(-2 \times 3 + 1)
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\end{eqnarray*}
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\\[2cm]
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\begin{eqnarray*}
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B &=& 10 \times \frac{3}{17}
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\end{eqnarray*}
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\end{enumerate}
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\end{multicols}
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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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4e/Geometrie/Pythagore/Conn0217/Conn0217.pdf
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4e/Geometrie/Pythagore/Conn0217/Conn0217.pdf
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4e/Geometrie/Pythagore/Conn0217/Conn0217.tex
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4e/Geometrie/Pythagore/Conn0217/Conn0217.tex
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\documentclass{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classConn}
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% Title Page
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\title{}
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\author{}
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\date{}
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\begin{document}
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\begin{multicols}{2}
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Nom - Prénom:
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\section{Connaissance}
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\begin{enumerate}
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\item Énoncer le théorème de Pythagore pour le triangle suivant
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\begin{minipage}[h]{0.2\textwidth}
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\includegraphics[scale=0.15]{./fig/triangleRectABC}
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\end{minipage}
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\begin{minipage}[h]{0.25\textwidth}
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~\\[0.5cm]
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Si \dotfill
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\\[0.5cm]
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.\dotfill
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\\[0.5cm]
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Alors \dotfill
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\\[0.5cm]
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\end{minipage}
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\item Sur la figure suivante, indiquer \textbf{l'axe des abscisses},et \textbf{l'origine du repère}.
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\begin{center}
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\includegraphics[scale=0.6]{./fig/graph}
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\end{center}
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\item Compléter les pointillés
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\begin{tabular}{|c|c|c}
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\hline
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Première ligne & $a$ & \hspace{1cm} \\
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\hline
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Deuxième ligne & $b$ & \\
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\hline
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\end{tabular}
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\hspace{1cm}
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$\times$ \dotfill
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\end{enumerate}
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\columnbreak
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Nom - Prénom
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\section{Connaissance}
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\begin{enumerate}
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\item Énoncer le théorème de Pythagore pour le triangle suivant
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\begin{minipage}[h]{0.2\textwidth}
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\includegraphics[scale=0.15]{./fig/triangleRectABC_2}
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\end{minipage}
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\begin{minipage}[h]{0.25\textwidth}
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~\\[0.5cm]
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Si \dotfill
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\\[0.5cm]
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.\dotfill
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\\[0.5cm]
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Alors \dotfill
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\\[0.5cm]
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\end{minipage}
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\item Sur la figure suivante, indiquer \textbf{l'axe des ordonnées} et \textbf{l'origine du repère}.
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\begin{center}
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\includegraphics[scale=0.5]{./fig/graph}
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\end{center}
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\item Le tableau suivant est un tableau de proportionnalité. Quel est le chiffre manquant?
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\begin{center}
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\begin{tabular}{|c|c|}
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\hline
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2 & 10 \\
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\hline
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4 & \\
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\hline
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\end{tabular}
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\end{center}
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\end{enumerate}
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\end{multicols}
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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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4e/Geometrie/Pythagore/Conn0217/fig/graph.pdf
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4e/Geometrie/Pythagore/Conn0217/fig/graph.pdf
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4e/Geometrie/Pythagore/Conn0217/fig/graph.tex
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\end{pspicture}
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4e/Geometrie/Pythagore/Conn0217/fig/pstricks.sh
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4e/Geometrie/Pythagore/Conn0217/fig/pstricks.sh
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#!/bin/sh
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# on enlève l’extension du 1er argument
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FILE=${1%.*}
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TMPFILE=pstemp
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# création d’un fichier temporaire psttemp.tex
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cat > $TMPFILE.tex <<EOF
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\documentclass{article}
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\usepackage{pstricks}
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\usepackage{pstricks-add}
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\usepackage{pst-eps}
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\usepackage{pst-eucl}
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\usepackage{pst-plot}
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\usepackage{pst-math}
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\thispagestyle{empty}
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\begin{TeXtoEPS}
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\input{$FILE}
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\end{document}
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EOF
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# Création du fichier dvi
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latex $TMPFILE
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# Création du fichier eps
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dvips -E $TMPFILE.dvi -o $TMPFILE.eps
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# Création du fichier pdf
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epstopdf $TMPFILE.eps --debug --outfile=$FILE.pdf
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# effacement des fichiers temporaires
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rm -f $TMPFILE.*
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4e/Geometrie/Pythagore/Conn0217/fig/triangleRectABC.pdf
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4e/Geometrie/Pythagore/Conn0217/fig/triangleRectABC.pdf
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BIN
4e/Geometrie/Pythagore/Conn0311/Conn0311.pdf
Normal file
BIN
4e/Geometrie/Pythagore/Conn0311/Conn0311.pdf
Normal file
Binary file not shown.
69
4e/Geometrie/Pythagore/Conn0311/Conn0311.tex
Normal file
69
4e/Geometrie/Pythagore/Conn0311/Conn0311.tex
Normal file
@@ -0,0 +1,69 @@
|
||||
\documentclass{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classConn}
|
||||
|
||||
|
||||
% Title Page
|
||||
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|
||||
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|
||||
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|
||||
|
||||
|
||||
\begin{document}
|
||||
|
||||
\begin{multicols}{2}
|
||||
|
||||
Nom - Prénom:
|
||||
\section{Connaissance}
|
||||
|
||||
\begin{enumerate}
|
||||
\item Énoncer le théorème de Pythagore pour le triangle suivant
|
||||
|
||||
\begin{center}
|
||||
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|
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|
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Si \dotfill
|
||||
\\[0.5cm]
|
||||
.\dotfill
|
||||
\\[0.5cm]
|
||||
Alors \dotfill
|
||||
\\[0.5cm]
|
||||
\item Calculer les expressions suivantes
|
||||
\begin{eqnarray*}
|
||||
A & = & 5 - 12 \\
|
||||
B & = & (4 - 2) \times 5 \\
|
||||
C & = & -4 \times (-2) \times (-2)
|
||||
\end{eqnarray*}
|
||||
|
||||
\end{enumerate}
|
||||
|
||||
|
||||
\columnbreak
|
||||
Nom - Prénom
|
||||
\section{Connaissance}
|
||||
|
||||
\begin{enumerate}
|
||||
\item Énoncer le théorème de Pythagore pour le triangle suivant
|
||||
\begin{center}
|
||||
\includegraphics[scale=0.25]{./fig/triangleRectABC_2}
|
||||
\end{center}
|
||||
Si \dotfill
|
||||
\\[0.5cm]
|
||||
.\dotfill
|
||||
\\[0.5cm]
|
||||
Alors \dotfill
|
||||
\\[0.5cm]
|
||||
\item Calculer les expressions suivantes
|
||||
\begin{eqnarray*}
|
||||
A & = & 9 - 12 \\[0.5cm]
|
||||
B & = & 2 \times 4 - 2 \\[0.5cm]
|
||||
C & = & -3 \times 2 \times (-2)
|
||||
\end{eqnarray*}
|
||||
\end{enumerate}
|
||||
|
||||
|
||||
\end{multicols}
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
28
4e/Geometrie/Pythagore/Conn0311/fig/pstricks.sh
Executable file
28
4e/Geometrie/Pythagore/Conn0311/fig/pstricks.sh
Executable file
@@ -0,0 +1,28 @@
|
||||
#!/bin/sh
|
||||
# on enlève l’extension du 1er argument
|
||||
FILE=${1%.*}
|
||||
TMPFILE=pstemp
|
||||
# création d’un fichier temporaire psttemp.tex
|
||||
cat > $TMPFILE.tex <<EOF
|
||||
\documentclass{article}
|
||||
\usepackage{pstricks}
|
||||
\usepackage{pstricks-add}
|
||||
\usepackage{pst-eps}
|
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\usepackage{pst-eucl}
|
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\usepackage{pst-plot}
|
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\usepackage{pst-math}
|
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\thispagestyle{empty}
|
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\begin{document}
|
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\begin{TeXtoEPS}
|
||||
\input{$FILE}
|
||||
\end{TeXtoEPS}
|
||||
\end{document}
|
||||
EOF
|
||||
# Création du fichier dvi
|
||||
latex $TMPFILE
|
||||
# Création du fichier eps
|
||||
dvips -E $TMPFILE.dvi -o $TMPFILE.eps
|
||||
# Création du fichier pdf
|
||||
epstopdf $TMPFILE.eps --debug --outfile=$FILE.pdf
|
||||
# effacement des fichiers temporaires
|
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rm -f $TMPFILE.*
|
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4e/Geometrie/Pythagore/Conn0311/fig/triangleRectABC.pdf
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15
4e/Geometrie/Pythagore/Exo/index.rst
Normal file
15
4e/Geometrie/Pythagore/Exo/index.rst
Normal file
@@ -0,0 +1,15 @@
|
||||
Notes sur des exercices d'applications du théorème de Pythagore
|
||||
###############################################################
|
||||
|
||||
:date: 2014-07-01
|
||||
:modified: 2014-07-01
|
||||
:tags: Geometrie, Exo
|
||||
:category: 4e
|
||||
:authors: Benjamin Bertrand
|
||||
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
|
||||
|
||||
|
||||
|
||||
`Lien vers pythagore.pdf <pythagore.pdf>`_
|
||||
|
||||
`Lien vers pythagore2.pdf <pythagore2.pdf>`_
|
||||
BIN
4e/Geometrie/Pythagore/Exo/pythagore.pdf
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4e/Geometrie/Pythagore/Exo/pythagore.pdf
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358
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358
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|
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\usepackage{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/2013_2014}
|
||||
|
||||
% Title Page
|
||||
\titre{Téléphérique du Mont Blanc}
|
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% \quatreC \quatreD \troisB \troisPro
|
||||
\classe{\quatreD}
|
||||
\date{13 mars 2014}
|
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|
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%\fancyhead[L]{<++classes++> : \Thetitle}
|
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|
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%% Tache complexe inspiré de http://wwwacad.ac-clermont.fr/disciplines/fileadmin/user_upload/Mathematiques/pages/outils/Irem_Clermont-Ferrand_le_Mont_Blanc.pdf
|
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\begin{document}
|
||||
\maketitle
|
||||
|
||||
Rémi Manfredi a un rêve, construire un téléphérique qui partirait de la ville Chamonix et qui arriverait au sommet du Mont Blanc.
|
||||
|
||||
Quelle serait alors la longueur du trajet?
|
||||
|
||||
Répondre par un texte présentant la démarche, les calculs et les arguments même non abouties.
|
||||
|
||||
Vous êtes autorisé à utiliser l'outil informatique.
|
||||
|
||||
\vfill
|
||||
|
||||
\textbf{Document 1:} Carte des environs de Chamonix et du Mont Blanc.
|
||||
\begin{center}
|
||||
\includegraphics[scale=0.5]{./fig/carte}
|
||||
\end{center}
|
||||
|
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|
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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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|
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BIN
4e/Geometrie/Pythagore/TelepheriqueMtBlanc/fig/carte.png
Normal file
BIN
4e/Geometrie/Pythagore/TelepheriqueMtBlanc/fig/carte.png
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|
After Width: | Height: | Size: 479 KiB |
17
4e/Geometrie/Pythagore/TelepheriqueMtBlanc/index.rst
Normal file
17
4e/Geometrie/Pythagore/TelepheriqueMtBlanc/index.rst
Normal file
@@ -0,0 +1,17 @@
|
||||
Notes sur la tache complexe Telepherique Mt Blanc
|
||||
#################################################
|
||||
|
||||
:date: 2014-07-01
|
||||
:modified: 2014-07-01
|
||||
:tags: Geometrie, Tache Complexe,
|
||||
:category: 4e
|
||||
:authors: Benjamin Bertrand
|
||||
:summary: Quelle serait la longueur du cable si l'on construisait un téléphérique pour relier Chamonix et le Mont Blanc?
|
||||
|
||||
|
||||
|
||||
`Lien vers TelepheriqueMtBlanc.tex <TelepheriqueMtBlanc.tex>`_
|
||||
|
||||
`Lien vers TelepheriqueMtBlanc.pdf <TelepheriqueMtBlanc.pdf>`_
|
||||
|
||||
`Lien vers fig/carte.png <fig/carte.png>`_
|
||||
BIN
4e/Geometrie/Pythagore/dist_point_droite/exo_dist_dte.pdf
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4e/Geometrie/Pythagore/dist_point_droite/exo_dist_dte.pdf
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39
4e/Geometrie/Pythagore/dist_point_droite/exo_dist_dte.tex
Normal file
39
4e/Geometrie/Pythagore/dist_point_droite/exo_dist_dte.tex
Normal file
@@ -0,0 +1,39 @@
|
||||
\documentclass[a4paper,10pt]{beamer}
|
||||
\usepackage[utf8]{inputenc}
|
||||
\usepackage[french]{babel}
|
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|
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|
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|
||||
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|
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|
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|
||||
\usepackage{subfig}
|
||||
\usepackage{amssymb}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\begin{frame}{Exercices}
|
||||
\textbf{Exercice 54 p 183}:
|
||||
\begin{enumerate}
|
||||
\item Tracer la droite $(d)$ et placer un point $A$ sur $(d)$.
|
||||
\item Construire tous les points situés à 4cm de la droite $(d)$ et à 6cm du point $A$.
|
||||
\end{enumerate}
|
||||
|
||||
\textbf{Exercice 56 p 183}\\
|
||||
On assimile le poste-avions Charles de Gulle à un rectangle de dimension 260m sur 65m.
|
||||
\begin{enumerate}
|
||||
\item Construire ce rectangle à l'échelle 1/4000.
|
||||
\item Sur ce plan, construire toutes les positions d'un bateau situé à 25m du porte-avions.
|
||||
\end{enumerate}
|
||||
|
||||
\textbf{Exercice 55 p 183}
|
||||
\begin{enumerate}
|
||||
\item Tracer une droite $(d)$ et un point $A$ à 3,6cm de $(d)$.
|
||||
\item Construire le symétrique $B$ de $A$ par rapport à $(d)$. Determiner la distance de $B$ à la droite $(d)$.
|
||||
\item Construire les points $C$ et $D$ sur la droite $(d)$ situés à 6cm de $A$.
|
||||
\item Quelle est la nature du quadrilatère $ABCD$? Justifier.
|
||||
\end{enumerate}
|
||||
\end{frame}
|
||||
|
||||
|
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\end{document}
|
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4e/Geometrie/Pythagore/dist_point_droite/exo_dist_dte_2.pdf
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4e/Geometrie/Pythagore/dist_point_droite/exo_dist_dte_2.pdf
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63
4e/Geometrie/Pythagore/dist_point_droite/exo_dist_dte_2.tex
Normal file
63
4e/Geometrie/Pythagore/dist_point_droite/exo_dist_dte_2.tex
Normal file
@@ -0,0 +1,63 @@
|
||||
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|
||||
|
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\usepackage{tikz}
|
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|
||||
% Title Page
|
||||
\title{Distance d'un point à une droite - Exercices}
|
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\author{}
|
||||
\date{}
|
||||
|
||||
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|
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|
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|
||||
|
||||
\begin{document}
|
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\thispagestyle{fancy}
|
||||
|
||||
\begin{Exo}
|
||||
\begin{center}
|
||||
\includegraphics[scale=0.5]{./fig/plage}
|
||||
\end{center}
|
||||
Jean, debout sur la digue, veut aller se baigner mais il doit dabord passer par le parasol (point $P$). Représente le trajet que doit emprunter Jean afin de marcher le moins longtemps sur le sable rendu brûlant par les rayons du soleil.
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
Soient une droite $(d)$ et un point $T$ sur cette droite.
|
||||
\begin{enumerate}
|
||||
\item Faire le dessin.
|
||||
\item Colorier en vert la région qui est à plus de 3cm de la droite $(d)$ et à moins de 4cm du point $T$.
|
||||
\item Placer $U$ un point à 4cm de $(d)$ et à plus de 5cm de $T$.
|
||||
\item Colorier en bleu la région qui est à moins de 1cm de $U$ et à moins de 3cm de $(d)$.
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
|
||||
% Changer de coté de la page
|
||||
\vfill
|
||||
\eject
|
||||
|
||||
\begin{Exo}
|
||||
Avant une course, on donne le plan du parcours aux coureurs. Ils vont ainsi pouvoir determiner le chemin le plus court entre le départ et l'arrivée en passant par les balises avant la course.
|
||||
\begin{center}
|
||||
\includegraphics[scale=0.4]{./fig/course}
|
||||
\end{center}
|
||||
Tracer le plus court chemin entre le départ et l'arrivée en passant par les balises $B1$ et $B2$. Mesurer la longueur du chemin.
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
Jack veut faire tondre son jardin par sa chèvre. Son jardin est un carré de 5m de coté. Malheureusement, il ne peut pas mettre de barrière autour de son jardin et si sa chèvre sort du jardin, son voisin sera furieux et tuera la chèvre. Il cherche donc un moyen d'attacher la chèvre pour qu'elle tonde tout son jardin sans en sortir.
|
||||
\begin{enumerate}
|
||||
\item S'il met un piquet au milieu de son jardin et qu'il y attache la chèvre, est-ce qu'elle tondra tout le jardin sans en sortir?
|
||||
\item Trouver une façon d'attacher la chèvre.
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
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|
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4e/Geometrie/Pythagore/dist_point_droite/fig/course.pdf
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228
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Normal file
228
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BIN
4e/Geometrie/Pythagore/dist_point_droite/fig/plage.png
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BIN
4e/Geometrie/Pythagore/dist_point_droite/fig/plage.png
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|
After Width: | Height: | Size: 192 KiB |
27
4e/Geometrie/Pythagore/dist_point_droite/index.rst
Normal file
27
4e/Geometrie/Pythagore/dist_point_droite/index.rst
Normal file
@@ -0,0 +1,27 @@
|
||||
Notes sur une fiche d'exercice sur comment calculer la distance d'un point à une droite
|
||||
#######################################################################################
|
||||
|
||||
:date: 2014-07-01
|
||||
:modified: 2014-07-01
|
||||
:tags: Geometrie, Exo
|
||||
:category: 4e
|
||||
:authors: Benjamin Bertrand
|
||||
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
|
||||
|
||||
|
||||
|
||||
`Lien vers exo_dist_dte.pdf <exo_dist_dte.pdf>`_
|
||||
|
||||
`Lien vers intro_dist_pt_dte.tex <intro_dist_pt_dte.tex>`_
|
||||
|
||||
`Lien vers exo_dist_dte.tex <exo_dist_dte.tex>`_
|
||||
|
||||
`Lien vers exo_dist_dte_2.tex <exo_dist_dte_2.tex>`_
|
||||
|
||||
`Lien vers exo_dist_dte_2.pdf <exo_dist_dte_2.pdf>`_
|
||||
|
||||
`Lien vers intro_dist_pt_dte.pdf <intro_dist_pt_dte.pdf>`_
|
||||
|
||||
`Lien vers fig/plage.png <fig/plage.png>`_
|
||||
|
||||
`Lien vers fig/course.pdf <fig/course.pdf>`_
|
||||
BIN
4e/Geometrie/Pythagore/dist_point_droite/intro_dist_pt_dte.pdf
Normal file
BIN
4e/Geometrie/Pythagore/dist_point_droite/intro_dist_pt_dte.pdf
Normal file
Binary file not shown.
119
4e/Geometrie/Pythagore/dist_point_droite/intro_dist_pt_dte.tex
Normal file
119
4e/Geometrie/Pythagore/dist_point_droite/intro_dist_pt_dte.tex
Normal file
@@ -0,0 +1,119 @@
|
||||
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
|
||||
|
||||
\usepackage{tikz}
|
||||
|
||||
% Title Page
|
||||
\title{Distance d'un point à une droite - Exercices}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
\fancyhead[L]{Quatrième}
|
||||
\fancyhead[C]{\Thetitle}
|
||||
\fancyhead[R]{\thepage}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\thispagestyle{fancy}
|
||||
|
||||
\begin{Exo}
|
||||
\begin{enumerate}
|
||||
\item
|
||||
André veut rejoindre la mer par le plus court chemin. Tracer le chemin qu'il va devoir parcourir et mesurer la distance parcourue (sur le dessin
|
||||
|
||||
\begin{center}
|
||||
\begin{tikzpicture}
|
||||
\draw (0,0) -- (8, 2)
|
||||
node[near start, sloped, above] {Mer}
|
||||
node[near start, sloped, below] {Plage};
|
||||
\draw (6, 0) node {$\times$};
|
||||
\draw (6, 0) node[above right] {André};
|
||||
\end{tikzpicture}
|
||||
\end{center}
|
||||
Distance parcourue: \dotfill
|
||||
|
||||
|
||||
\item Tracer le plus court chemin entre le point $B$ et la droite $(d)$ puis mesurer la distance entre $B$ et $(d)$.
|
||||
\begin{center}
|
||||
\begin{tikzpicture}
|
||||
\draw (7,2) -- (0, 0)
|
||||
node[sloped, above] {$(d)$};
|
||||
\draw (4, 0) node {$\times$};
|
||||
\draw (4, 0) node[right] {$B$};
|
||||
\end{tikzpicture}
|
||||
|
||||
\end{center}
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
Tracer le chemin le plus court entre $A$ et chacune des trois droites, puis mesurer la distance entre $A$ et chacune des droites.
|
||||
\begin{center}
|
||||
\begin{tikzpicture}
|
||||
\draw (5, 5) -- (0,0)
|
||||
node[left] {$d_1$};
|
||||
\draw (8, 5) -- (0,1)
|
||||
node[left] {$d_2$};
|
||||
\draw (8, 2) -- (1,5)
|
||||
node[left] {$d_3$};
|
||||
\draw (4, 1) node {$\times$} node[above right] {$A$};
|
||||
\end{tikzpicture}
|
||||
\end{center}
|
||||
|
||||
\end{Exo}
|
||||
|
||||
|
||||
% Changer de coté de la page
|
||||
\vfill
|
||||
\eject
|
||||
|
||||
\begin{Exo}
|
||||
$ABC$ est un triangle rectangle en $C$ tel que $AB = 5$, $BC = 4$ et $D$ un point de $(AB)$ tel que $AD = 1$ comme sur le dessin ci dessous.
|
||||
\begin{center}
|
||||
\begin{tikzpicture}
|
||||
\coordinate (A) at (0,0);
|
||||
\coordinate (B) at (5,0);
|
||||
\coordinate (C) at (2,2.23);
|
||||
\coordinate (D) at (2,0);
|
||||
\draw (A) -- (B) -- (C) -- (A);
|
||||
\draw (C) -- (D);
|
||||
\draw (2.2, 0) -- (2.2, 0.2) -- (2, 0.2);
|
||||
\draw (A) node[left] {$A$};
|
||||
\draw (B) node[right] {$B$};
|
||||
\draw (C) node[above] {$C$};
|
||||
\draw (D) node[below] {$D$};
|
||||
\end{tikzpicture}
|
||||
\end{center}
|
||||
\begin{enumerate}
|
||||
\item Calculer la distance de $A$ à la droite $(BC)$.
|
||||
|
||||
\hspace{-1cm}
|
||||
\framebox{\parbox{0.49\textwidth}{
|
||||
Calculer la distance de $A$ à la droite $(BC)$ revient à calculer la distance $AC$ car le triangle $ABC$ est rectangle en $C$.
|
||||
|
||||
\parbox{1.5cm}{\dotfill} est un triangle rectangle en \parbox{1cm}{\dotfill} donc d'après le théorème de \parbox{3cm}{\dotfill} on a
|
||||
\begin{eqnarray*}
|
||||
\parbox{1cm}{\dotfill} & = & \parbox{1cm}{\dotfill} + \parbox{1cm}{\dotfill} \\[0.5cm]
|
||||
\parbox{1cm}{\dotfill} & = & \parbox{1cm}{\dotfill} + \parbox{1cm}{\dotfill} \\[0.5cm]
|
||||
\parbox{1cm}{\dotfill} & = & \parbox{1cm}{\dotfill} - \parbox{1cm}{\dotfill} \\[0.5cm]
|
||||
\parbox{1cm}{\dotfill} & = & \parbox{1cm}{\dotfill} \\[0.5cm]
|
||||
\parbox{1cm}{\dotfill} & = & \sqrt{\parbox{1cm}{\dotfill}} = \parbox{1cm}{\dotfill}
|
||||
\end{eqnarray*}
|
||||
Donc la distance entre $A$ et $(BC)$ est de \parbox{1cm}{\dotfill}.
|
||||
}}
|
||||
\item Calculer la distance de $C$ à la droite $(AB)$.
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
\exo{51 p 183}
|
||||
\exo{55 p 183}
|
||||
\end{Exo}
|
||||
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
BIN
4e/Geometrie/Thales/activite_decouverte/act_dec.pdf
Normal file
BIN
4e/Geometrie/Thales/activite_decouverte/act_dec.pdf
Normal file
Binary file not shown.
143
4e/Geometrie/Thales/activite_decouverte/act_dec.tex
Normal file
143
4e/Geometrie/Thales/activite_decouverte/act_dec.tex
Normal file
@@ -0,0 +1,143 @@
|
||||
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
|
||||
\usepackage{tikz}
|
||||
\usetikzlibrary{calc}
|
||||
|
||||
% Title Page
|
||||
\title{Thalès - Travail de groupe}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
\fancyhead[L]{Quatrième}
|
||||
\fancyhead[C]{\Thetitle}
|
||||
\fancyhead[R]{\thepage}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\thispagestyle{fancy}
|
||||
|
||||
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)
|
||||
|
||||
\textbf{Conjecturer les valeurs des longueurs des deux cotés manquants pour remplir les tableaux des longueurs.} Justifier quand c'est possible les valeurs trouvées.
|
||||
|
||||
\begin{itemize}
|
||||
\item \textbf{Cas 1}
|
||||
|
||||
\begin{tikzpicture}
|
||||
\coordinate (A) at (0,0);
|
||||
\coordinate (M) at (3,0);
|
||||
\coordinate (B) at (6,0);
|
||||
\coordinate (C) at (6,4);
|
||||
\coordinate (N) at (3,2);
|
||||
|
||||
\draw (A) node [left] {$A$}
|
||||
-- (M) node [below] {$M$} node[midway, below] {$4$}
|
||||
-- (B) node [right] {$B$}
|
||||
-- (C) node [right] {$C$}
|
||||
-- (N) node [above] {$N$}
|
||||
-- (A) node [midway, sloped, above] {5};
|
||||
|
||||
\draw (N) -- (M) node[midway, right] {3};
|
||||
\draw[<->] ($(A)+(0,-0.5)$) -- ($(B) + (0,-0.5)$) node [midway, below] {$8$};
|
||||
|
||||
\end{tikzpicture}
|
||||
|
||||
\begin{tabular}{|c|*{3}{p{2cm}|}}
|
||||
\hline
|
||||
Triangle $AMN$ & AM = & AN = & MN = \\
|
||||
\hline
|
||||
Triangle $ABC$ & AB = & AC = & BC = \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\item \textbf{Cas 2}
|
||||
|
||||
\begin{tikzpicture}
|
||||
\coordinate (A) at (0,0);
|
||||
\coordinate (M) at (2.3,0);
|
||||
\coordinate (B) at (9.2,0);
|
||||
\coordinate (C) at (8,4);
|
||||
\coordinate (N) at (2,1);
|
||||
|
||||
\draw (A) node [left] {$A$}
|
||||
-- (M) node [below] {$M$} node[midway, below] {$1$}
|
||||
-- (B) node [right] {$B$}
|
||||
-- (C) node [right] {$C$}
|
||||
-- (N) node [above] {$N$}
|
||||
-- (A) node [midway, sloped, above] {5};
|
||||
|
||||
\draw (N) -- (M) node[midway, right] {3};
|
||||
\draw[<->] ($(A)+(0,-0.5)$) -- ($(B) + (0,-0.5)$) node [midway, below] {4};
|
||||
\draw (A) --++ (2.3,0) --++ (2.3,0) node {$|$} --++ (2.3,0) node {$|$};
|
||||
|
||||
\end{tikzpicture}
|
||||
|
||||
\begin{tabular}{|c|*{3}{p{2cm}|}}
|
||||
\hline
|
||||
Triangle $AMN$ & AM = & AN = & MN = \\
|
||||
\hline
|
||||
Triangle $ABC$ & AB = & AC = & BC = \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\item \textbf{Cas 3}
|
||||
|
||||
\begin{tikzpicture}
|
||||
\coordinate (A) at (0,0);
|
||||
\coordinate (M) at (3,0);
|
||||
\coordinate (B) at (6,0);
|
||||
\coordinate (C) at (6.8,4);
|
||||
\coordinate (N) at (3.4,2);
|
||||
|
||||
\draw (A) node [left] {$A$}
|
||||
-- (M) node [below] {$M$} node[midway, below] {$4$}
|
||||
-- (B) node [right] {$B$}
|
||||
-- (C) node [right] {$C$}
|
||||
-- (N) node [above] {$N$}
|
||||
-- (A) node [midway, sloped, above] {5};
|
||||
|
||||
\draw (N) -- (M) node[midway, right] {4.4};
|
||||
\draw[<->] ($(A)+(-0.5,+0.5)$) -- ($(C) + (0,+0.75)$) node [midway, above, sloped] {$10$};
|
||||
|
||||
\end{tikzpicture}
|
||||
|
||||
\begin{tabular}{|c|*{3}{p{2cm}|}}
|
||||
\hline
|
||||
Triangle $AMN$ & AM = & AN = & MN = \\
|
||||
\hline
|
||||
Triangle $ABC$ & AB = & AC = & BC = \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\item \textbf{Cas 4}
|
||||
|
||||
\begin{tikzpicture}
|
||||
\coordinate (A) at (0,0);
|
||||
\coordinate (M) at (3,0);
|
||||
\coordinate (B) at (6,0);
|
||||
\coordinate (C) at (6,4);
|
||||
\coordinate (N) at (3,2);
|
||||
|
||||
\draw (A) node [left] {$A$}
|
||||
-- (M) node [below] {$M$} node[midway, below] {$4$}
|
||||
-- (B) node [right] {$B$}
|
||||
-- (C) node [right] {$C$} node [midway, right] {15}
|
||||
-- (N) node [above] {$N$}
|
||||
-- (A) node [midway, sloped, above] {5};
|
||||
|
||||
\draw (N) -- (M) node[midway, right] {3};
|
||||
|
||||
\end{tikzpicture}
|
||||
|
||||
\begin{tabular}{|c|*{3}{p{2cm}|}}
|
||||
\hline
|
||||
Triangle $AMN$ & AM = & AN = & MN = \\
|
||||
\hline
|
||||
Triangle $ABC$ & AB = & AC = & BC = \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{itemize}
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
BIN
4e/Geometrie/Thales/activite_decouverte/act_dec_corr.pdf
Normal file
BIN
4e/Geometrie/Thales/activite_decouverte/act_dec_corr.pdf
Normal file
Binary file not shown.
146
4e/Geometrie/Thales/activite_decouverte/act_dec_corr.tex
Normal file
146
4e/Geometrie/Thales/activite_decouverte/act_dec_corr.tex
Normal file
@@ -0,0 +1,146 @@
|
||||
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
|
||||
\usepackage{tikz}
|
||||
\usetikzlibrary{calc}
|
||||
|
||||
% Title Page
|
||||
\title{Thalès - Travail de groupe}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
\fancyhead[L]{Quatrième}
|
||||
\fancyhead[C]{\Thetitle}
|
||||
\fancyhead[R]{\thepage}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\thispagestyle{fancy}
|
||||
|
||||
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)
|
||||
|
||||
\textbf{Conjecturer les valeurs des longueurs des deux cotés manquants pour remplir les tableaux des longueurs.} Justifier quand c'est possible les valeurs trouvées.
|
||||
|
||||
\begin{itemize}
|
||||
\item \textbf{Cas 1}
|
||||
|
||||
\begin{tikzpicture}
|
||||
\coordinate (A) at (0,0);
|
||||
\coordinate (M) at (3,0);
|
||||
\coordinate (B) at (6,0);
|
||||
\coordinate (C) at (6,4);
|
||||
\coordinate (N) at (3,2);
|
||||
|
||||
\draw (A) node [left] {$A$}
|
||||
-- (M) node [below] {$M$} node[midway, below] {$4$}
|
||||
-- (B) node [right] {$B$}
|
||||
-- (C) node [right] {$C$}
|
||||
-- (N) node [above] {$N$}
|
||||
-- (A) node [midway, sloped, above] {5};
|
||||
|
||||
\draw (N) -- (M) node[midway, right] {3};
|
||||
\draw[<->] ($(A)+(0,-0.5)$) -- ($(B) + (0,-0.5)$) node [midway, below] {$8$};
|
||||
|
||||
\end{tikzpicture}
|
||||
|
||||
\begin{tabular}{|c|*{3}{p{2cm}|}}
|
||||
\hline
|
||||
Triangle $AMN$ & AM = \color{blue}{4} & AN = \color{blue}{5} & MN = \color{blue}{3} \\
|
||||
\hline
|
||||
Triangle $ABC$ & AB = \color{blue}{8} & AC = \color{red}{10} & BC = \color{red}{6} \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\item \textbf{Cas 2}
|
||||
|
||||
\begin{tikzpicture}
|
||||
\coordinate (A) at (0,0);
|
||||
\coordinate (M) at (2.3,0);
|
||||
\coordinate (B) at (9.2,0);
|
||||
\coordinate (C) at (8,4);
|
||||
\coordinate (N) at (2,1);
|
||||
|
||||
\draw (A) node [left] {$A$}
|
||||
-- (M) node [below] {$M$} node[midway, below] {$1$}
|
||||
-- (B) node [right] {$B$}
|
||||
-- (C) node [right] {$C$}
|
||||
-- (N) node [above] {$N$}
|
||||
-- (A) node [midway, sloped, above] {5};
|
||||
|
||||
\draw (N) -- (M) node[midway, right] {3};
|
||||
\draw[<->] ($(A)+(0,-0.5)$) -- ($(B) + (0,-0.5)$) node [midway, below] {4};
|
||||
\draw (A) --++ (2.3,0) --++ (2.3,0) node {$|$} --++ (2.3,0) node {$|$};
|
||||
|
||||
\end{tikzpicture}
|
||||
|
||||
\begin{tabular}{|c|*{3}{p{2cm}|}}
|
||||
\hline
|
||||
Triangle $AMN$ & AM = \color{blue}{1} & AN = \color{blue}{5} & MN = \color{blue}{3} \\
|
||||
\hline
|
||||
Triangle $ABC$ & AB = \color{blue}{4} & AC = \color{red}{20} & BC = \color{red}{12} \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
|
||||
\item \textbf{Cas 3}
|
||||
|
||||
\begin{tikzpicture}
|
||||
\coordinate (A) at (0,0);
|
||||
\coordinate (M) at (3,0);
|
||||
\coordinate (B) at (6,0);
|
||||
\coordinate (C) at (6.8,4);
|
||||
\coordinate (N) at (3.4,2);
|
||||
|
||||
\draw (A) node [left] {$A$}
|
||||
-- (M) node [below] {$M$} node[midway, below] {$4$}
|
||||
-- (B) node [right] {$B$}
|
||||
-- (C) node [right] {$C$}
|
||||
-- (N) node [above] {$N$}
|
||||
-- (A) node [midway, sloped, above] {5};
|
||||
|
||||
\draw (N) -- (M) node[midway, right] {4.4};
|
||||
\draw[<->] ($(A)+(-0.5,+0.5)$) -- ($(C) + (0,+0.75)$) node [midway, above, sloped] {$15$};
|
||||
|
||||
\end{tikzpicture}
|
||||
|
||||
|
||||
\begin{tabular}{|c|*{3}{p{2cm}|}}
|
||||
\hline
|
||||
Triangle $AMN$ & AM = \color{blue}{4} & AN = \color{blue}{5} & MN = \color{blue}{4.4} \\
|
||||
\hline
|
||||
Triangle $ABC$ & AB = \color{red}{12} & AC = \color{blue}{15} & BC = \color{red}{13.2} \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\item \textbf{Cas 4}
|
||||
|
||||
\begin{tikzpicture}
|
||||
\coordinate (A) at (0,0);
|
||||
\coordinate (M) at (3,0);
|
||||
\coordinate (B) at (6,0);
|
||||
\coordinate (C) at (6,4);
|
||||
\coordinate (N) at (3,2);
|
||||
|
||||
\draw (A) node [left] {$A$}
|
||||
-- (M) node [below] {$M$} node[midway, below] {$4$}
|
||||
-- (B) node [right] {$B$}
|
||||
-- (C) node [right] {$C$} node [midway, right] {15}
|
||||
-- (N) node [above] {$N$}
|
||||
-- (A) node [midway, sloped, above] {5};
|
||||
|
||||
\draw (N) -- (M) node[midway, right] {3};
|
||||
|
||||
\end{tikzpicture}
|
||||
|
||||
\begin{tabular}{|c|*{3}{p{2cm}|}}
|
||||
\hline
|
||||
Triangle $AMN$ & AM = \color{blue}{4} & AN = \color{blue}{5} & MN = \color{blue}{3} \\
|
||||
\hline
|
||||
Triangle $ABC$ & AB = \color{red}{12} & AC = \color{red}{15} & BC = \color{blue}{15} \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
|
||||
\end{itemize}
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
19
4e/Geometrie/Thales/activite_decouverte/index.rst
Normal file
19
4e/Geometrie/Thales/activite_decouverte/index.rst
Normal file
@@ -0,0 +1,19 @@
|
||||
Notes sur une activité decouverte du théorème de Thales
|
||||
#######################################################
|
||||
|
||||
:date: 2014-07-01
|
||||
:modified: 2014-07-01
|
||||
:tags: Geometrie, Exo
|
||||
:category: 4e
|
||||
:authors: Benjamin Bertrand
|
||||
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
|
||||
|
||||
|
||||
|
||||
`Lien vers act_dec_corr.tex <act_dec_corr.tex>`_
|
||||
|
||||
`Lien vers act_dec.tex <act_dec.tex>`_
|
||||
|
||||
`Lien vers act_dec_corr.pdf <act_dec_corr.pdf>`_
|
||||
|
||||
`Lien vers act_dec.pdf <act_dec.pdf>`_
|
||||
BIN
4e/Geometrie/Thales/ecran/ecran.pdf
Normal file
BIN
4e/Geometrie/Thales/ecran/ecran.pdf
Normal file
Binary file not shown.
129
4e/Geometrie/Thales/ecran/ecran.tex
Normal file
129
4e/Geometrie/Thales/ecran/ecran.tex
Normal file
@@ -0,0 +1,129 @@
|
||||
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
|
||||
\usepackage{tikz}
|
||||
\usetikzlibrary{calc}
|
||||
|
||||
% Title Page
|
||||
\title{Thalès- Exercices}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
\fancyhead[L]{Quatrième}
|
||||
\fancyhead[C]{\Thetitle}
|
||||
\fancyhead[R]{\thepage}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\thispagestyle{fancy}
|
||||
|
||||
\begin{Exo}
|
||||
Lors d'un spectacle d'ombre chinoise, l'acteur place ses mains à 1m de la lampe et l'ombre de ses mains se projette sur l'écran. On considère que ses mains, ensembles, mesurent 40cm.
|
||||
\begin{enumerate}
|
||||
\item On place l'écran à 2m comme sur le dessin ci-dessous. Quel sera la taille de l'ombre sur l'écran?
|
||||
|
||||
\begin{center}
|
||||
\begin{tikzpicture}
|
||||
\coordinate (A) at (0,0);
|
||||
\coordinate (B) at (2,0);
|
||||
\coordinate (C) at (4,0);
|
||||
\coordinate (D) at (4,1.5);
|
||||
\coordinate (E) at (2,0.75);
|
||||
|
||||
\draw (A) -- (B)
|
||||
-- (C)
|
||||
-- (D) node [midway, right] {Ombre}
|
||||
-- (E)
|
||||
-- (A);
|
||||
\draw (B) -- (E) node [above] {Mains};
|
||||
|
||||
\draw[<->] ($(A)+(0,-0.5)$) -- ($(B) + (0,-0.5)$) node [midway, above] {$1m$};
|
||||
\draw[<->] ($(A)+(0,-0.75)$) -- ($(C) + (0,-0.75)$) node [midway, above, near end] {$2m$};
|
||||
|
||||
\end{tikzpicture}
|
||||
|
||||
\end{center}
|
||||
\item On effectue plusieurs tests où l'on place l'écran à différentes distances. Les dessins suivants sont à l'échelle 1/50 ($1cm \Leftrightarrow 50cm$) . Dans chacun des cas, mesurer la taille de l'ombre.
|
||||
|
||||
\begin{itemize}
|
||||
\item Écran placé à 3m
|
||||
|
||||
\begin{tikzpicture}
|
||||
\coordinate (A) at (0,0);
|
||||
\coordinate (B) at (2,0);
|
||||
\coordinate (C) at (6,0);
|
||||
\coordinate (D) at (6,2.25);
|
||||
\coordinate (E) at (2,0.75);
|
||||
|
||||
\draw (A) -- (B)
|
||||
-- (C)
|
||||
-- (D)
|
||||
-- (E)
|
||||
-- (A);
|
||||
\draw (B) -- (E);
|
||||
|
||||
\end{tikzpicture}
|
||||
\item Écran placé à 4m
|
||||
|
||||
\begin{tikzpicture}
|
||||
\coordinate (A) at (0,0);
|
||||
\coordinate (B) at (2,0);
|
||||
\coordinate (C) at (8,0);
|
||||
\coordinate (D) at (8,3);
|
||||
\coordinate (E) at (2,0.75);
|
||||
|
||||
\draw (A) -- (B)
|
||||
-- (C)
|
||||
-- (D)
|
||||
-- (E)
|
||||
-- (A);
|
||||
\draw (B) -- (E);
|
||||
|
||||
\end{tikzpicture}
|
||||
\item Écran placé à 5m
|
||||
|
||||
\begin{tikzpicture}
|
||||
\coordinate (A) at (0,0);
|
||||
\coordinate (B) at (2,0);
|
||||
\coordinate (C) at (10,0);
|
||||
\coordinate (D) at (10,3.75);
|
||||
\coordinate (E) at (2,0.75);
|
||||
|
||||
\draw (A) -- (B)
|
||||
-- (C)
|
||||
-- (D)
|
||||
-- (E)
|
||||
-- (A);
|
||||
\draw (B) -- (E);
|
||||
|
||||
\end{tikzpicture}
|
||||
|
||||
\end{itemize}
|
||||
|
||||
|
||||
\item Quel sera la taille de l'ombre si l'on place l'écran aux distances suivantes:
|
||||
\begin{itemize}
|
||||
\item 7m:
|
||||
\item 10m:
|
||||
\item 20m:
|
||||
\end{itemize}
|
||||
\item Avec les distances trouvées aux questions précédentes, compléter le tableau suivant.
|
||||
|
||||
\begin{tabular}{|c|*{7}{p{0.7cm}|}}
|
||||
\hline
|
||||
Distance de l'écran & 2 & 3 & 4 & 5 & 7 & 10 & 20 \\
|
||||
\hline
|
||||
Taille de l'ombre & & & & & & & \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\item Est-ce que le tableau est un tableau de proportionnalité?
|
||||
\end{enumerate}
|
||||
|
||||
|
||||
\end{Exo}
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
15
4e/Geometrie/Thales/ecran/index.rst
Normal file
15
4e/Geometrie/Thales/ecran/index.rst
Normal file
@@ -0,0 +1,15 @@
|
||||
Notes sur un exercice autour du théorème de Thales
|
||||
##################################################
|
||||
|
||||
:date: 2014-07-01
|
||||
:modified: 2014-07-01
|
||||
:tags: Geometrie, Exo
|
||||
:category: 4e
|
||||
:authors: Benjamin Bertrand
|
||||
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
|
||||
|
||||
|
||||
|
||||
`Lien vers ecran.pdf <ecran.pdf>`_
|
||||
|
||||
`Lien vers ecran.tex <ecran.tex>`_
|
||||
BIN
4e/Geometrie/Thales/exo/exo1.pdf
Normal file
BIN
4e/Geometrie/Thales/exo/exo1.pdf
Normal file
Binary file not shown.
94
4e/Geometrie/Thales/exo/exo1.tex
Normal file
94
4e/Geometrie/Thales/exo/exo1.tex
Normal file
@@ -0,0 +1,94 @@
|
||||
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
|
||||
\usepackage{tikz}
|
||||
\usetikzlibrary{calc}
|
||||
|
||||
% Title Page
|
||||
\title{Thalès- Exercices}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
\fancyhead[L]{Quatrième}
|
||||
\fancyhead[C]{\Thetitle}
|
||||
\fancyhead[R]{\thepage}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\thispagestyle{fancy}
|
||||
|
||||
\textbf{Calcul de la hauteur d'une pyramide, une légende}
|
||||
\includegraphics[scale=0.45]{./fig/pyramide}
|
||||
|
||||
\vfill
|
||||
|
||||
Dimensions observées par Thalès (en coudées, 1 coudées $\approx$ 52.5cm)
|
||||
\begin{itemize}
|
||||
\item Côté de la pyramide: 442 coudées
|
||||
\item Taille de l'ombre de la pyramide: 404 coudées.
|
||||
\item Taille du baton: 5 coudées.
|
||||
\item Taille de l'ombre du baton: 11 coudées.
|
||||
\end{itemize}
|
||||
|
||||
\textbf{La légende dit que, grâce à ces informations, Thalès, lors d'un voyage en Égypte, a réussi à mesurer la hauteur de la pyramide.}
|
||||
|
||||
\vfill
|
||||
\eject
|
||||
|
||||
\begin{Exo}
|
||||
Calculer les longueurs manquantes sur les dessins suivants.
|
||||
\begin{enumerate}
|
||||
\item
|
||||
\begin{minipage}{0.2\textwidth}
|
||||
\includegraphics[scale=0.2]{./fig/ABCMN.pdf}
|
||||
\end{minipage}
|
||||
\begin{minipage}{0.15\textwidth}
|
||||
\begin{itemize}
|
||||
\item $(BC) // (MN)$
|
||||
\item $AN = 3$
|
||||
\item $AC = 6$
|
||||
\item $MN = 4$
|
||||
\item $AM = 5$
|
||||
\end{itemize}
|
||||
\end{minipage}
|
||||
|
||||
\item
|
||||
\begin{minipage}{0.2\textwidth}
|
||||
\includegraphics[scale=0.2]{./fig/IJKLM.pdf}
|
||||
\end{minipage}
|
||||
\begin{minipage}{0.2\textwidth}
|
||||
\begin{itemize}
|
||||
\item $(JK) // (LM)$
|
||||
\item $IM = 6$
|
||||
\item $IL = 6$
|
||||
\item $LM = 5$
|
||||
\item $JK = 9$
|
||||
\end{itemize}
|
||||
\end{minipage}
|
||||
|
||||
\item
|
||||
\begin{minipage}{0.2\textwidth}
|
||||
\includegraphics[scale=0.2]{./fig/USTXY.pdf}
|
||||
\end{minipage}
|
||||
\begin{minipage}{0.2\textwidth}
|
||||
\begin{itemize}
|
||||
\item $(YX) // (ST)$
|
||||
\item $US = 10$
|
||||
\item $ST = 11$
|
||||
\item $UT = 5$
|
||||
\item $YX = 10$
|
||||
\end{itemize}
|
||||
\end{minipage}
|
||||
\end{enumerate}
|
||||
|
||||
Le coefficent de proportionnalité des longueurs des triangles est appelé rapport de réduction (ou d'agrandissement). Calculer ce rapport pour tous les triangles.
|
||||
|
||||
\end{Exo}
|
||||
|
||||
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
BIN
4e/Geometrie/Thales/exo/exo2.pdf
Normal file
BIN
4e/Geometrie/Thales/exo/exo2.pdf
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Binary file not shown.
92
4e/Geometrie/Thales/exo/exo2.tex
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92
4e/Geometrie/Thales/exo/exo2.tex
Normal file
@@ -0,0 +1,92 @@
|
||||
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
|
||||
\usepackage{tikz}
|
||||
\usetikzlibrary{calc}
|
||||
|
||||
% Title Page
|
||||
\title{Thalès- Exercices}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
\fancyhead[L]{Quatrième}
|
||||
\fancyhead[C]{\Thetitle}
|
||||
\fancyhead[R]{\thepage}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\thispagestyle{fancy}
|
||||
|
||||
\textbf{Évacuation d'un téléphérique}
|
||||
Le téléphérique qui lie Chamonix au sommet du Mont Blanc va être construit. Le constructeur pense avant tout à la sécurité. Il veut installer une corde dans le téléphérique pour évacuer les personnes en cas de panne. \textbf{De quelle longueur devra être cette corde?}
|
||||
\includegraphics[scale=0.45]{./fig/Telepherique}
|
||||
|
||||
\vfill
|
||||
|
||||
Dimensions enregistrées pour les travaux:
|
||||
\begin{itemize}
|
||||
\item Différence d'altitude entre Chamonix et le Mont Blanc: 3815m.
|
||||
\item Longueur du téléphérique: 10km.
|
||||
\item Distance parcourue par le téléphérique avant d'atteindre le pied de la montagne: 3km
|
||||
\end{itemize}
|
||||
|
||||
\vfill
|
||||
\eject
|
||||
|
||||
\begin{Exo}
|
||||
Calculer les longueurs manquantes sur les dessins suivants.
|
||||
\begin{enumerate}
|
||||
\item
|
||||
\begin{minipage}{0.2\textwidth}
|
||||
\includegraphics[scale=0.2]{./fig/ABCMN.pdf}
|
||||
\end{minipage}
|
||||
\begin{minipage}{0.15\textwidth}
|
||||
\begin{itemize}
|
||||
\item $(BC) // (MN)$
|
||||
\item $AN = 3$
|
||||
\item $AC = 6$
|
||||
\item $MN = 4$
|
||||
\item $AM = 5$
|
||||
\end{itemize}
|
||||
\end{minipage}
|
||||
|
||||
\item
|
||||
\begin{minipage}{0.2\textwidth}
|
||||
\includegraphics[scale=0.2]{./fig/IJKLM.pdf}
|
||||
\end{minipage}
|
||||
\begin{minipage}{0.2\textwidth}
|
||||
\begin{itemize}
|
||||
\item $(JK) // (LM)$
|
||||
\item $IM = 6$
|
||||
\item $IL = 6$
|
||||
\item $LM = 5$
|
||||
\item $JK = 9$
|
||||
\end{itemize}
|
||||
\end{minipage}
|
||||
|
||||
\item
|
||||
\begin{minipage}{0.2\textwidth}
|
||||
\includegraphics[scale=0.2]{./fig/USTXY.pdf}
|
||||
\end{minipage}
|
||||
\begin{minipage}{0.2\textwidth}
|
||||
\begin{itemize}
|
||||
\item $(YX) // (ST)$
|
||||
\item $US = 10$
|
||||
\item $ST = 11$
|
||||
\item $UT = 5$
|
||||
\item $YX = 10$
|
||||
\end{itemize}
|
||||
\end{minipage}
|
||||
\end{enumerate}
|
||||
|
||||
Le coefficent de proportionnalité des longueurs des triangles est appelé rapport de réduction (ou d'agrandissement). Calculer ce rapport pour tous les triangles.
|
||||
|
||||
\end{Exo}
|
||||
|
||||
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
BIN
4e/Geometrie/Thales/exo/exo3.pdf
Normal file
BIN
4e/Geometrie/Thales/exo/exo3.pdf
Normal file
Binary file not shown.
67
4e/Geometrie/Thales/exo/exo3.tex
Normal file
67
4e/Geometrie/Thales/exo/exo3.tex
Normal file
@@ -0,0 +1,67 @@
|
||||
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
|
||||
\usepackage{tikz}
|
||||
\usetikzlibrary{calc}
|
||||
|
||||
% Title Page
|
||||
\title{Thalès- Exercices}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
\fancyhead[L]{Quatrième}
|
||||
\fancyhead[C]{\Thetitle}
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\fancyhead[R]{\thepage}
|
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|
||||
|
||||
\begin{document}
|
||||
\thispagestyle{fancy}
|
||||
|
||||
\begin{Exo}
|
||||
|
||||
\textbf{Évacuation d'un téléphérique}
|
||||
|
||||
Le téléphérique qui lie Chamonix au sommet du Mont Blanc va être construit. Le constructeur pense avant tout à la sécurité. Il veut installer une corde dans le téléphérique pour évacuer les personnes en cas de panne. \textbf{De quelle longueur devra être cette corde?}
|
||||
\includegraphics[scale=0.45]{./fig/Telepherique}
|
||||
|
||||
\vfill
|
||||
|
||||
Dimensions enregistrées pour les travaux:
|
||||
\begin{itemize}
|
||||
\item Différence d'altitude entre Chamonix et le Mont Blanc: 3815m.
|
||||
\item Longueur du téléphérique: 10km.
|
||||
\item Distance parcourue par le téléphérique avant d'atteindre le pied de la montagne: 3km
|
||||
\end{itemize}
|
||||
\end{Exo}
|
||||
|
||||
\vfill
|
||||
\eject
|
||||
|
||||
\begin{Exo}
|
||||
Inspiré par l'expérience de Thalès, Tom en voyage à Pise veut mesurer la tour penchée grâce à son ombre. Il se renseigne et apprend qu'elle est penchée de $4,19^o$ comme sur le dessin suivant:
|
||||
\begin{center}
|
||||
\includegraphics[scale=0.4]{./fig/ombre_pise}
|
||||
\end{center}
|
||||
\begin{enumerate}
|
||||
\item Comment doit-il placer son bâton pour pouvoir appliquer le théorème de Thalès? Dessiner le baton sur le dessin.
|
||||
|
||||
Une fois le bâton installé, il mesure les distances suivantes:
|
||||
\begin{itemize}
|
||||
\item Diamètre de la tour: 15.5m.
|
||||
\item Taille du baton 1,5m.
|
||||
\item Taille de l'ombre du baton: 2m
|
||||
\item Taille de l'ombre de la tour: 66,95m
|
||||
\end{itemize}
|
||||
\item Reporter les mesures sur le dessin.
|
||||
\item Calculer la hauteur de la tour de Pise.
|
||||
\end{enumerate}
|
||||
|
||||
\end{Exo}
|
||||
|
||||
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
BIN
4e/Geometrie/Thales/exo/exo3_b.pdf
Normal file
BIN
4e/Geometrie/Thales/exo/exo3_b.pdf
Normal file
Binary file not shown.
72
4e/Geometrie/Thales/exo/exo3_b.tex
Normal file
72
4e/Geometrie/Thales/exo/exo3_b.tex
Normal file
@@ -0,0 +1,72 @@
|
||||
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
|
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\usepackage{tikz}
|
||||
\usetikzlibrary{calc}
|
||||
|
||||
% Title Page
|
||||
\title{Thalès- Exercices}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
\fancyhead[L]{Quatrième}
|
||||
\fancyhead[C]{\Thetitle}
|
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\fancyhead[R]{\thepage}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\thispagestyle{fancy}
|
||||
\begin{Exo}
|
||||
Inspiré par l'expérience de Thalès, Tom en voyage à Pise veut mesurer la tour penchée grâce à son ombre. Il se renseigne et apprend qu'elle est penchée de $4,19^o$ comme sur le dessin suivant:
|
||||
\begin{center}
|
||||
\includegraphics[scale=0.4]{./fig/ombre_pise}
|
||||
\end{center}
|
||||
\begin{enumerate}
|
||||
\item Comment doit-il placer son bâton pour pouvoir appliquer le théorème de Thalès? Dessiner le baton sur le dessin.
|
||||
|
||||
Une fois le bâton installé, il mesure les distances suivantes:
|
||||
\begin{itemize}
|
||||
\item Diamètre de la tour: 15.5m.
|
||||
\item Taille du baton 1,5m.
|
||||
\item Taille de l'ombre du baton: 2m
|
||||
\item Taille de l'ombre de la tour: 66,95m
|
||||
\end{itemize}
|
||||
\item Reporter les mesures sur le dessin.
|
||||
\item Calculer la hauteur de la tour de Pise.
|
||||
\end{enumerate}
|
||||
|
||||
\end{Exo}
|
||||
|
||||
\setcounter{exo}{0}
|
||||
|
||||
\eject
|
||||
|
||||
\begin{Exo}
|
||||
Inspiré par l'expérience de Thalès, Tom en voyage à Pise veut mesurer la tour penchée grâce à son ombre. Il se renseigne et apprend qu'elle est penchée de $4,19^o$ comme sur le dessin suivant:
|
||||
\begin{center}
|
||||
\includegraphics[scale=0.4]{./fig/ombre_pise}
|
||||
\end{center}
|
||||
\begin{enumerate}
|
||||
\item Comment doit-il placer son bâton pour pouvoir appliquer le théorème de Thalès? Dessiner le baton sur le dessin.
|
||||
|
||||
Une fois le bâton installé, il mesure les distances suivantes:
|
||||
\begin{itemize}
|
||||
\item Diamètre de la tour: 15.5m.
|
||||
\item Taille du baton 1,5m.
|
||||
\item Taille de l'ombre du baton: 2m
|
||||
\item Taille de l'ombre de la tour: 66,95m
|
||||
\end{itemize}
|
||||
\item Reporter les mesures sur le dessin.
|
||||
\item Calculer la hauteur de la tour de Pise.
|
||||
\end{enumerate}
|
||||
|
||||
\end{Exo}
|
||||
|
||||
\eject
|
||||
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
BIN
4e/Geometrie/Thales/exo/fig/ABCMN.pdf
Normal file
BIN
4e/Geometrie/Thales/exo/fig/ABCMN.pdf
Normal file
Binary file not shown.
BIN
4e/Geometrie/Thales/exo/fig/IJKLM.pdf
Normal file
BIN
4e/Geometrie/Thales/exo/fig/IJKLM.pdf
Normal file
Binary file not shown.
BIN
4e/Geometrie/Thales/exo/fig/Telepherique.pdf
Normal file
BIN
4e/Geometrie/Thales/exo/fig/Telepherique.pdf
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105
4e/Geometrie/Thales/exo/fig/Telepherique.svg
Normal file
105
4e/Geometrie/Thales/exo/fig/Telepherique.svg
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@@ -0,0 +1,105 @@
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4e/Geometrie/Thales/exo/fig/USTXY.svg
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429
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39
4e/Geometrie/Thales/exo/index.rst
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4e/Geometrie/Thales/exo/index.rst
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|
||||
Notes sur divers exercices autour du théorème de Thales
|
||||
#######################################################
|
||||
|
||||
:date: 2014-07-01
|
||||
:modified: 2014-07-01
|
||||
:tags: Geometrie,Exo
|
||||
:category: 4e
|
||||
:authors: Benjamin Bertrand
|
||||
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
|
||||
|
||||
|
||||
|
||||
`Lien vers exo3_b.pdf <exo3_b.pdf>`_
|
||||
|
||||
`Lien vers exo2.pdf <exo2.pdf>`_
|
||||
|
||||
`Lien vers exo1.pdf <exo1.pdf>`_
|
||||
|
||||
`Lien vers exo2.tex <exo2.tex>`_
|
||||
|
||||
`Lien vers exo3_b.tex <exo3_b.tex>`_
|
||||
|
||||
`Lien vers exo1.tex <exo1.tex>`_
|
||||
|
||||
`Lien vers exo3.tex <exo3.tex>`_
|
||||
|
||||
`Lien vers exo3.pdf <exo3.pdf>`_
|
||||
|
||||
`Lien vers fig/ombre_pise.pdf <fig/ombre_pise.pdf>`_
|
||||
|
||||
`Lien vers fig/pyramide.pdf <fig/pyramide.pdf>`_
|
||||
|
||||
`Lien vers fig/USTXY.pdf <fig/USTXY.pdf>`_
|
||||
|
||||
`Lien vers fig/ABCMN.pdf <fig/ABCMN.pdf>`_
|
||||
|
||||
`Lien vers fig/IJKLM.pdf <fig/IJKLM.pdf>`_
|
||||
|
||||
`Lien vers fig/Telepherique.pdf <fig/Telepherique.pdf>`_
|
||||
BIN
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|
||||
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
|
||||
\usepackage{tikz}
|
||||
\usetikzlibrary{calc}
|
||||
|
||||
% Title Page
|
||||
\title{Thalès - Géogebra }
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
\fancyhead[L]{Quatrième}
|
||||
\fancyhead[C]{\Thetitle}
|
||||
\fancyhead[R]{\thepage}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\thispagestyle{fancy}
|
||||
|
||||
\section{Construction de la figure}
|
||||
|
||||
\begin{enumerate}
|
||||
\item \includegraphics[scale=0.008]{fig/curseur} Placer 3 points $A$, $B$, $C$ (les renommer si necessaire avec clic droit).
|
||||
\item \includegraphics[scale=0.008]{fig/polygon} En utilisant l'outil "polygone", tracer le triangle $ABC$.
|
||||
\item \includegraphics[scale=0.008]{fig/point} Placer le point $M$ sur le segment $[AB]$.
|
||||
\item \includegraphics[scale=0.008]{fig/parallele} Tracer la parallèleà $(BC)$ passant par $M$.
|
||||
\item \includegraphics[scale=0.008]{fig/intersection} Placer le point $N$ point d'intersection de cette droite et de $[AC]$.
|
||||
\item Effacer la droite (clic droit puis décocher "Afficher l'objet").
|
||||
\item \includegraphics[scale=0.008]{fig/polygon} Tracer le triangle $AMN$ (toujours avec l'outil polygone).
|
||||
\item \includegraphics[scale=0.008]{fig/curseur} Déplacer les points pour vérifier que la figure est bien faite.
|
||||
\end{enumerate}
|
||||
|
||||
\section{Mesure et distance}
|
||||
Maintenant que la figure est faite nous allons utiliser les outils de Géogebra pour mesurer notre figure et faire les calculs à notre place.
|
||||
|
||||
\subsection{Un tableur}
|
||||
\begin{enumerate}
|
||||
\item Ouvrir le tableur de Géogebra (\textit{affichage > Tableur}).
|
||||
\item Completer le tableau pour qu'il soit le même que dans le figure ci dessous.
|
||||
|
||||
\includegraphics[scale=0.008]{./fig/tableau}
|
||||
|
||||
\end{enumerate}
|
||||
|
||||
\subsection{Mesure et calculs}
|
||||
\begin{enumerate}
|
||||
\item Nous allons commencer par mesurer la distance $AM$ pour cela taper dans la case \texttt{C3}: \textbf{=Distance[A,M]}.
|
||||
\item Puis dans la case \texttt{C4}, nous allons y mettre la distance $AB$ en tapant: \textbf{=Distance[A,B]}.
|
||||
\item Finir de completer les cases \texttt{E3}, \texttt{E4}, \texttt{G3} et \texttt{G4}.
|
||||
\item Le tableau ainsi créé est-il un tableau de proportionnalité? Proposer un calcul à faire faire par Géogebra pour vérifier que le tableau est un tableau de proportionnalité.
|
||||
|
||||
\end{enumerate}
|
||||
|
||||
\subsection{Vérfications}
|
||||
Déplacer les points pour vérifier que les distances sont bien proportionnelles quelque soit la forme du triangle et la position de $M$ sur le segment $[AB]$.
|
||||
|
||||
|
||||
\begin{center}
|
||||
\includegraphics[scale=0.3]{./fig/figure}
|
||||
\end{center}
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
39
4e/Geometrie/Thales/geogebra/index.rst
Normal file
39
4e/Geometrie/Thales/geogebra/index.rst
Normal file
@@ -0,0 +1,39 @@
|
||||
Notes sur une activité autour du théorème de Thales et de Geogébra
|
||||
##################################################################
|
||||
|
||||
:date: 2014-07-01
|
||||
:modified: 2014-07-01
|
||||
:tags: Geometrie, TICE, Géogébra
|
||||
:category: 4e
|
||||
:authors: Benjamin Bertrand
|
||||
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
|
||||
|
||||
|
||||
|
||||
`Lien vers geogebra.tex <geogebra.tex>`_
|
||||
|
||||
`Lien vers geogebra.pdf <geogebra.pdf>`_
|
||||
|
||||
`Lien vers fig/point.png <fig/point.png>`_
|
||||
|
||||
`Lien vers fig/2014-05-22_09-04-1400742280.jpg <fig/2014-05-22_09-04-1400742280.jpg>`_
|
||||
|
||||
`Lien vers fig/tableau.png <fig/tableau.png>`_
|
||||
|
||||
`Lien vers fig/figure.png <fig/figure.png>`_
|
||||
|
||||
`Lien vers fig/figure.jpg <fig/figure.jpg>`_
|
||||
|
||||
`Lien vers fig/parallele.png <fig/parallele.png>`_
|
||||
|
||||
`Lien vers fig/2014-05-22_08-58-1400741912.jpg <fig/2014-05-22_08-58-1400741912.jpg>`_
|
||||
|
||||
`Lien vers fig/curseur.png <fig/curseur.png>`_
|
||||
|
||||
`Lien vers fig/2014-05-22_08-58-1400741930.jpg <fig/2014-05-22_08-58-1400741930.jpg>`_
|
||||
|
||||
`Lien vers fig/polygon.png <fig/polygon.png>`_
|
||||
|
||||
`Lien vers fig/2014-05-22_08-58-1400741902.jpg <fig/2014-05-22_08-58-1400741902.jpg>`_
|
||||
|
||||
`Lien vers fig/intersection.png <fig/intersection.png>`_
|
||||
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21
4e/Geometrie/Triangle_cercle/Bissectrice/index.rst
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21
4e/Geometrie/Triangle_cercle/Bissectrice/index.rst
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@@ -0,0 +1,21 @@
|
||||
Notes sur des exercices autour de la bissectrice
|
||||
################################################
|
||||
|
||||
:date: 2014-07-01
|
||||
:modified: 2014-07-01
|
||||
:tags: Geometrie, Exo
|
||||
:category: 4e
|
||||
:authors: Benjamin Bertrand
|
||||
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
|
||||
|
||||
|
||||
|
||||
`Lien vers intro_bissec.pdf <intro_bissec.pdf>`_
|
||||
|
||||
`Lien vers intro_bissec.tex <intro_bissec.tex>`_
|
||||
|
||||
`Lien vers fig/contructionTriangle2.pdf <fig/contructionTriangle2.pdf>`_
|
||||
|
||||
`Lien vers fig/contructionTriangle.pdf <fig/contructionTriangle.pdf>`_
|
||||
|
||||
`Lien vers fig/triangles.pdf <fig/triangles.pdf>`_
|
||||
BIN
4e/Geometrie/Triangle_cercle/Bissectrice/intro_bissec.pdf
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BIN
4e/Geometrie/Triangle_cercle/Bissectrice/intro_bissec.pdf
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Binary file not shown.
77
4e/Geometrie/Triangle_cercle/Bissectrice/intro_bissec.tex
Normal file
77
4e/Geometrie/Triangle_cercle/Bissectrice/intro_bissec.tex
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@@ -0,0 +1,77 @@
|
||||
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
|
||||
|
||||
% Title Page
|
||||
\title{Bissectrice d'un angle - Exercices}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
\fancyhead[L]{Quatrième}
|
||||
\fancyhead[C]{\Thetitle}
|
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\fancyhead[R]{\thepage}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\thispagestyle{fancy}
|
||||
|
||||
\begin{Exo}
|
||||
|
||||
\begin{enumerate}
|
||||
\item Tracer les triangles suivants en respectant les distances et les mesures.
|
||||
\begin{itemize}
|
||||
\item Triangle $ABC$ tel que $AB = 4cm$, $BC = 6cm$ et $CA = 3cm$.
|
||||
\item Triangle $DEF$ tel que $EF = 5cm$, $FG = 3cm$ et $GE = 7cm$
|
||||
\item Triangle $GHI$ tel que $GH = 2cm$, $HI = 10cm$ et $IG = 9cm$.
|
||||
\item Triangle $JKL$ tel que $JK = 6cm$, $KL = 7cm$ et $\widehat{JKL} = 40^{\circ}$.
|
||||
\item Triangle $NMO$ tel que $NM = 5cm$, $MO = 9cm$ et $\widehat{OMN} = 45^{\circ}$.
|
||||
\item Triangle $PQR$ tel que $PQ = 6cm$, $RP = 6cm$ et $\widehat{PQR} = 60^{\circ}$.
|
||||
\end{itemize}
|
||||
\item Sur chaque figure, marquer les angles suivants et mesurez les.
|
||||
\begin{eqnarray*}
|
||||
\widehat{ABC} = \parbox{1cm}{\dotfill} &\hspace{1cm}& \widehat{EFD} = \parbox{1cm}{\dotfill} \\
|
||||
\widehat{IGH} = \parbox{1cm}{\dotfill} &\hspace{1cm}& \widehat{LJK} = \parbox{1cm}{\dotfill} \\
|
||||
\widehat{NMO} = \parbox{1cm}{\dotfill} &\hspace{1cm}&a\widehat{RPQ} = \parbox{1cm}{\dotfill}
|
||||
\end{eqnarray*}
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
\begin{enumerate}
|
||||
\item Sur les triangles ci-contre, tracer la bissectrice des angles suivants.
|
||||
\begin{eqnarray*}
|
||||
\widehat{ABC} \qquad
|
||||
\widehat{DFE} \qquad
|
||||
\widehat{IGH} \qquad
|
||||
\widehat{LJK} \qquad
|
||||
\widehat{MNO} \qquad
|
||||
\end{eqnarray*}
|
||||
\item Tracer la bissectrice de tous les angles du triangle $GHI$. Que remarque-t-on?
|
||||
\\[0.5cm]
|
||||
.\dotfill
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
\begin{enumerate}
|
||||
\item Tracer le triangle $XYZ$ tel que $XY = 10cm$, $YZ = 11cm$ et $ZX = 12cm$.
|
||||
\item Tracer les bissectrices de tous les angles de ce triangle.
|
||||
\item Tracer le cercle de centre le point d'intersection des bissectrices et qui ne touche que 3 fois les bords du triangle $XYZ$.
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
\eject
|
||||
|
||||
\begin{center}
|
||||
\includegraphics[scale=0.6]{./fig/triangles}
|
||||
\end{center}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
BIN
4e/Geometrie/Triangle_cercle/Conn/Conn1202.pdf
Normal file
BIN
4e/Geometrie/Triangle_cercle/Conn/Conn1202.pdf
Normal file
Binary file not shown.
55
4e/Geometrie/Triangle_cercle/Conn/Conn1202.tex
Normal file
55
4e/Geometrie/Triangle_cercle/Conn/Conn1202.tex
Normal file
@@ -0,0 +1,55 @@
|
||||
\documentclass{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classConn}
|
||||
|
||||
|
||||
% Title Page
|
||||
\title{}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
|
||||
\begin{document}
|
||||
|
||||
\begin{multicols}{2}
|
||||
|
||||
Nom - Prénom:
|
||||
\section{Connaissance}
|
||||
|
||||
\begin{enumerate}
|
||||
\item Pour \textbf{comparer} des fractions, il faut
|
||||
|
||||
\vspace{0.5cm}
|
||||
. \dotfill .
|
||||
\vspace{0.5cm}
|
||||
|
||||
\item Écrire le théorème qui permet de démontrer que le triangle suivant est rectangle (on précisera l'angle droit).
|
||||
\begin{center}
|
||||
\includegraphics[scale=1]{./fig/cercle2rect.png}
|
||||
\end{center}
|
||||
\end{enumerate}
|
||||
|
||||
|
||||
\columnbreak
|
||||
Nom - Prénom
|
||||
\section{Connaissance}
|
||||
|
||||
\begin{enumerate}
|
||||
\item Pour \textbf{additionner} des fractions, il faut
|
||||
|
||||
\vspace{0.5cm}
|
||||
. \dotfill .
|
||||
\vspace{0.5cm}
|
||||
|
||||
\item Sur le dessin suivant quels longeurs sont égales? Écrire le théorème qui permet d'obtenir ces égalités.
|
||||
\begin{center}
|
||||
\includegraphics[scale=1]{./fig/rect_mediane.png}
|
||||
\end{center}
|
||||
\end{enumerate}
|
||||
|
||||
|
||||
\end{multicols}
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
BIN
4e/Geometrie/Triangle_cercle/Conn/fig/cercle2rect.ggb
Normal file
BIN
4e/Geometrie/Triangle_cercle/Conn/fig/cercle2rect.ggb
Normal file
Binary file not shown.
BIN
4e/Geometrie/Triangle_cercle/Conn/fig/cercle2rect.png
Normal file
BIN
4e/Geometrie/Triangle_cercle/Conn/fig/cercle2rect.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 43 KiB |
BIN
4e/Geometrie/Triangle_cercle/Conn/fig/rect_mediane.png
Normal file
BIN
4e/Geometrie/Triangle_cercle/Conn/fig/rect_mediane.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 19 KiB |
BIN
4e/Geometrie/thm_milieux/Conn/Conn1004.pdf
Normal file
BIN
4e/Geometrie/thm_milieux/Conn/Conn1004.pdf
Normal file
Binary file not shown.
64
4e/Geometrie/thm_milieux/Conn/Conn1004.tex
Normal file
64
4e/Geometrie/thm_milieux/Conn/Conn1004.tex
Normal file
@@ -0,0 +1,64 @@
|
||||
\documentclass{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classConn}
|
||||
|
||||
|
||||
% Title Page
|
||||
\title{}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
|
||||
\begin{document}
|
||||
|
||||
\begin{multicols}{2}
|
||||
|
||||
Nom - Prénom:
|
||||
\section{Connaissance}
|
||||
|
||||
Completer les phrases suivantes
|
||||
|
||||
\begin{itemize}
|
||||
\renewcommand{\labelitemi}{$\star$}
|
||||
\item $[AB]$ se prononce \dotfill \\
|
||||
\item $[AC)$ se prononce \dotfill \\
|
||||
|
||||
\vspace{2cm}
|
||||
|
||||
\item Énoncer le théorème des milieux pour la figure suivante
|
||||
\begin{center}
|
||||
\includegraphics[scale=1.4]{fig/thmMilieux}
|
||||
\end{center}
|
||||
|
||||
Si \dotfill \\ \vfill . \dotfill \\ \vfill . \dotfill \\ \vfill Alors \dotfill
|
||||
\end{itemize}
|
||||
|
||||
|
||||
|
||||
|
||||
\columnbreak
|
||||
|
||||
Nom - Prénom:
|
||||
\section{Connaissance}
|
||||
|
||||
Completer les phrases suivantes
|
||||
|
||||
\begin{itemize}
|
||||
\renewcommand{\labelitemi}{$\star$}
|
||||
\item $AB$ se prononce \dotfill \\
|
||||
\item $(AC)$ se prononce \dotfill \\
|
||||
|
||||
\vspace{2cm}
|
||||
|
||||
\item Énoncer le théorème du \textbf{segment} du milieu pour la figure suivante
|
||||
\begin{center}
|
||||
\includegraphics[scale=1.4]{fig/thmMilieux2}
|
||||
\end{center}
|
||||
Si \dotfill \\ \vfill . \dotfill \\ \vfill . \dotfill \\ \vfill Alors \dotfill
|
||||
\end{itemize}
|
||||
|
||||
\end{multicols}
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
26
4e/Geometrie/thm_milieux/Conn/fig/pstricks.sh
Executable file
26
4e/Geometrie/thm_milieux/Conn/fig/pstricks.sh
Executable file
@@ -0,0 +1,26 @@
|
||||
#!/bin/sh
|
||||
# on enlève l’extension du 1er argument
|
||||
FILE=${1%.*}
|
||||
TMPFILE=pstemp
|
||||
# création d’un fichier temporaire psttemp.tex
|
||||
cat > $TMPFILE.tex <<EOF
|
||||
\documentclass{article}
|
||||
\usepackage{pstricks}
|
||||
\usepackage{pstricks-add}
|
||||
\usepackage{pst-eps}
|
||||
\usepackage{pst-eucl}
|
||||
\thispagestyle{empty}
|
||||
\begin{document}
|
||||
\begin{TeXtoEPS}
|
||||
\input{$FILE}
|
||||
\end{TeXtoEPS}
|
||||
\end{document}
|
||||
EOF
|
||||
# Création du fichier dvi
|
||||
latex $TMPFILE
|
||||
# Création du fichier eps
|
||||
dvips -E $TMPFILE.dvi -o $TMPFILE.eps
|
||||
# Création du fichier pdf
|
||||
epstopdf $TMPFILE.eps --debug --outfile=$FILE.pdf
|
||||
# effacement des fichiers temporaires
|
||||
rm -f $TMPFILE.*
|
||||
BIN
4e/Geometrie/thm_milieux/Conn/fig/thmMilieux.pdf
Normal file
BIN
4e/Geometrie/thm_milieux/Conn/fig/thmMilieux.pdf
Normal file
Binary file not shown.
21
4e/Geometrie/thm_milieux/Conn/fig/thmMilieux.tex
Normal file
21
4e/Geometrie/thm_milieux/Conn/fig/thmMilieux.tex
Normal file
@@ -0,0 +1,21 @@
|
||||
\begin{pspicture}*(-2.5,-1.5)(3.5,2.5)
|
||||
|
||||
\pstGeonode[PosAngle=180](-2,-1){A}
|
||||
\pstGeonode(2,2){B}
|
||||
\pstGeonode(3,-1){E}
|
||||
|
||||
\pspolygon(A)(B)(E)
|
||||
|
||||
\pstMiddleAB{A}{B}{M}
|
||||
\pstSegmentMark{A}{M}
|
||||
\pstSegmentMark{M}{B}
|
||||
\pstMiddleAB[PosAngle=0]{E}{B}{J}
|
||||
\pstSegmentMark[SegmentSymbol=pstslash]{E}{J}
|
||||
\pstSegmentMark[SegmentSymbol=pstslash]{J}{B}
|
||||
|
||||
\pstLineAB{M}{J}
|
||||
|
||||
\end{pspicture}
|
||||
|
||||
|
||||
|
||||
Some files were not shown because too many files have changed in this diff Show More
Reference in New Issue
Block a user