Import work from year 2013-2014
This commit is contained in:
Benjamin Bertrand
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3e/Geometrie/Thales/Conn0202/Conn0202.pdf
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3e/Geometrie/Thales/Conn0202/Conn0202.pdf
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3e/Geometrie/Thales/Conn0202/Conn0202.tex
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3e/Geometrie/Thales/Conn0202/Conn0202.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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\usepackage{pstricks-add}
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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 la réciproque du théorème de Thales avec les lettres du dessin ci dessous
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\includegraphics[scale=0.5]{./fig/Thales_base1}
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~\\[4cm]
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\item Écrire les deux identités remarquables
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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 la réciproque du théorème de Thales avec les lettres du dessin ci dessous
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\includegraphics[scale=0.5]{./fig/Thales_base2}
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~\\[4cm]
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\item Écrire les deux identités remarquables
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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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3e/Geometrie/Thales/Conn0202/fig/Thales_base.pdf
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3e/Geometrie/Thales/Conn0202/fig/Thales_base1.png
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3e/Geometrie/Thales/Conn0202/fig/Thales_base1.png
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3e/Geometrie/Thales/Conn0202/fig/Thales_base2.png
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3e/Geometrie/Thales/Conn0202/fig/Thales_base2.png
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3e/Geometrie/Thales/demo_recip/demo_recip.pdf
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3e/Geometrie/Thales/demo_recip/demo_recip.pdf
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3e/Geometrie/Thales/demo_recip/demo_recip.tex
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3e/Geometrie/Thales/demo_recip/demo_recip.tex
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\documentclass[a4paper,12pt]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classCours}
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\usepackage{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/2013_2014}
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% Title Page
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\titre{Démonstration de la réciproque de Pythagore}
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% \quatreC \quatreD \troisB \troisPro
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\classe{\troisB}
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\date{03 février 2014}
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%\fancyhead[L]{<++classes++> : \Thetitle}
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\begin{document}
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\maketitle
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Le but de cette fiche d'exercices est de démontrer la réciproque du théorème de Thalès. Rappelons cette réciproque.
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\begin{center}
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\begin{minipage}[c]{0.4\textwidth}
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\begin{center}
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\includegraphics[scale=0.5]{./fig/Thales_base.pdf}
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\end{center}
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\end{minipage}
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\begin{minipage}[c]{0.5\textwidth}
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Si
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\begin{itemize}
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\item .\dotfill
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\item .\dotfill
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\item .\dotfill
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\end{itemize}
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Alors \\[0.2cm]
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.\dotfill
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\end{minipage}
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\end{center}
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Dans toutes les questions suivantes, nous pourrons utiliser les hypothèses. Et le but à atteindre sera la conclusion de ce théorème.
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\paragraph{Rappel:} Cette démonstration est basée sur des calculs d'aires.
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\begin{center}
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\begin{minipage}[c]{0.4\textwidth}
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\begin{center}
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\includegraphics[scale=0.08]{./fig/aireTriangle.pdf}
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\end{center}
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\end{minipage}
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\begin{minipage}[c]{0.5\textwidth}
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\begin{eqnarray*}
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\mathcal{A}\mbox{ire} = \frac{ .. .. .. \times .. .. .. }{ .. .. ..}
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\end{eqnarray*}
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\end{minipage}
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\end{center}
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\section*{Démonstration}
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\begin{center}
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\begin{minipage}[c]{0.3\textwidth}
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\begin{center}
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\includegraphics[scale=0.5]{./fig/Thales_ADC.pdf}
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\end{center}
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\end{minipage}
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\begin{minipage}[c]{0.65\textwidth}
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\begin{enumerate}
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\item
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\begin{enumerate}
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\item Exprimer l'aire du triangle $ACD$ (notée $\mathcal{A}_{ACD}$) en fonction de $CM$ et $DA$.
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\item Exprimer l'aire du triangle $ABC$ (notée $\mathcal{A}_{ABC}$) en fonction de $CM$ et $BA$.
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\item Exprimer $\displaystyle \frac{\mathcal{A}_{ACD}}{\mathcal{A}_{ABC}}$ (simplifier la fraction le plus possible).
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\end{enumerate}
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\end{enumerate}
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\end{minipage}
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\end{center}
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\begin{center}
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\begin{minipage}[c]{0.4\textwidth}
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\begin{center}
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\includegraphics[scale=0.5]{./fig/Thales_ABE.pdf}
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\end{center}
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\end{minipage}
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\begin{minipage}[c]{0.5\textwidth}
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\begin{enumerate}[start=2]
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\item En reproduisant ce qui a été faire à la première question, exprimer $\displaystyle \frac{\mathcal{A}_{ABE}}{\mathcal{A}_{ABC}}$.
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\end{enumerate}
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\end{minipage}
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\end{center}
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\begin{enumerate}[start=3]
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\item Démontrer que $\mathcal{A}_{ACD} = \mathcal{A}_{ABE}$.
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\begin{minipage}[h]{0.4\textwidth}
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\includegraphics[scale=0.5]{./fig/Thales_DEB.pdf}
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\end{minipage}
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\begin{minipage}[h]{0.4\textwidth}
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\includegraphics[scale=0.5]{./fig/Thales_DEC.pdf}
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\end{minipage}
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\item
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\begin{enumerate}
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\item En faisant un bon découpage, démontrer que $\mathcal{A}_{BED} = \mathcal{A}_{DEC}$.
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\item Exprimer $\mathcal{A}_{DEB}$ en fonction de $DE$ et $BI$.
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\item Exprimer $\mathcal{A}_{DEC}$ en fonction de $DE$ et $CJ$.
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\item Démontrer que $BI = CJ$.
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\end{enumerate}
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\end{enumerate}
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\begin{center}
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\begin{minipage}[c]{0.3\textwidth}
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\begin{center}
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\includegraphics[scale=0.5]{./fig/Thales_BCJI.pdf}
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\end{center}
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\end{minipage}
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\begin{minipage}[c]{0.65\textwidth}
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\begin{enumerate}[start=5]
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\item
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\begin{enumerate}
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\item Démontrer que $BCIJ$ est un rectangle.
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\item Conclure la démonstration, démontrer que $(BC)$ est parallèle à $(DE)$.
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\end{enumerate}
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\end{enumerate}
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\end{minipage}
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\end{center}
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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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3e/Geometrie/Thales/demo_recip/fig/Thales_ABE.pdf
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39
3e/Geometrie/Thales/demo_recip/index.rst
Normal file
39
3e/Geometrie/Thales/demo_recip/index.rst
Normal file
@@ -0,0 +1,39 @@
|
||||
Notes sur la démonstration de la réciproque de Thales
|
||||
#####################################################
|
||||
|
||||
:date: 2014-07-01
|
||||
:modified: 2014-07-01
|
||||
:tags: Geometrie
|
||||
:category: 3e
|
||||
:authors: Benjamin Bertrand
|
||||
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
|
||||
|
||||
|
||||
|
||||
`Lien vers demo_recip.pdf <demo_recip.pdf>`_
|
||||
|
||||
`Lien vers demo_recip.tex <demo_recip.tex>`_
|
||||
|
||||
`Lien vers fig/Thales_ADC.pdf <fig/Thales_ADC.pdf>`_
|
||||
|
||||
`Lien vers fig/Thales_base.pdf <fig/Thales_base.pdf>`_
|
||||
|
||||
`Lien vers fig/Thales_joined.pdf <fig/Thales_joined.pdf>`_
|
||||
|
||||
`Lien vers fig/Thales_calques.ggb <fig/Thales_calques.ggb>`_
|
||||
|
||||
`Lien vers fig/aireTriangle.pdf <fig/aireTriangle.pdf>`_
|
||||
|
||||
`Lien vers fig/Thales_BCJI.pdf <fig/Thales_BCJI.pdf>`_
|
||||
|
||||
`Lien vers fig/Thales_DEB.pdf <fig/Thales_DEB.pdf>`_
|
||||
|
||||
`Lien vers fig/Thales_ABE.pdf <fig/Thales_ABE.pdf>`_
|
||||
|
||||
`Lien vers fig/Thales_base.ggb <fig/Thales_base.ggb>`_
|
||||
|
||||
`Lien vers fig/Thales_DEC.pdf <fig/Thales_DEC.pdf>`_
|
||||
|
||||
`Lien vers fig/aireTriangle.ggb <fig/aireTriangle.ggb>`_
|
||||
|
||||
`Lien vers fig/Thales_triADC.ggb <fig/Thales_triADC.ggb>`_
|
||||
Reference in New Issue
Block a user