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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After Width: | Height: | Size: 9.2 KiB |
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)
|
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node[near start, sloped, above] {Mer}
|
||||
node[near start, sloped, below] {Plage};
|
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\draw (6, 0) node {$\times$};
|
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\draw (6, 0) node[above right] {André};
|
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\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] {$(d)$};
|
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\draw (4, 0) node {$\times$};
|
||||
\draw (4, 0) node[right] {$B$};
|
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\end{tikzpicture}
|
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|
||||
\end{center}
|
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\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] {$d_1$};
|
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\draw (8, 5) -- (0,1)
|
||||
node[left] {$d_2$};
|
||||
\draw (8, 2) -- (1,5)
|
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node[left] {$d_3$};
|
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\draw (4, 1) node {$\times$} node[above right] {$A$};
|
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\end{tikzpicture}
|
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\end{center}
|
||||
|
||||
\end{Exo}
|
||||
|
||||
|
||||
% Changer de coté de la page
|
||||
\vfill
|
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\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:
|
||||
|
||||
Reference in New Issue
Block a user