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Sequence sur les agrandissements pour les 3e

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Bertrand Benjamin 2017-09-11 08:46:28 +03:00
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3e/Geometrie/Thales_agrandissement/TC_tipi.pdf Normal file
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3e/Geometrie/Thales_agrandissement/TC_tipi.tex Normal file
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\documentclass[a4paper,12pt]{article}
\usepackage{myXsim}
\title{Tache complexe: chapeau du tipi}
\tribe{Troisième}
\date{Septembre 2017}
\pagestyle{empty}
\geometry{left=10mm,right=10mm,top=10mm,bottom=10mm}
\begin{document}
\begin{exercise}[subtitle={Chapeau du tipi\Mod\Rep\Com}]
L’habitation traditionnelle des Indiens des plaines d’Amérique du Nord est le tipi.
Un tipi est constitué de longues tiges de bois appuyées les unes aux autres, d’une enveloppe extérieure faite de peaux d’animaux et d’une porte toujours orientée vers l’Est.
Chaque perche en bois mesure 21 pieds et dépasse de 3 pieds. Le rayon du cercle tracé au sol mesure 7,5 pieds.
Le grand chef indien veut coiffer le cercle formé par le haut des perches de son tipi d’un chapeau de plumes.
Quel doit être le diamètre de son chapeau?
\includegraphics[scale=0.3]{./fig/tipis.jpeg}
\hfill
\includegraphics[scale=0.25]{./fig/tipi2.jpg}
\end{exercise}
\vfill
\printexercise{exercise}{1}
\vfill
\printexercise{exercise}{1}
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "master"
%%% End:

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Découverte de Thalès avec les 3e pour l'année 2017-2018
#######################################################
:date: 2017-09-11
:modified: 2017-09-11
:tags: Geometrie, Thales, Agrandissement
:category: 3e
:authors: Bertrand Benjamin
:summary: Découverte du théorème de Thalès à travers l'agrandissement de figure avec les 3e pour l'année 2017-2018.
Étape 1
--------
Activité de découpage du `puzzle <./puzzle.pdf>`_.
Le but est que les élèves trouvent que lors de la réduction d'une figure, les longueurs sont toutes multipliées par un même nombre. On l'appellera la coefficient de réduction.
On ramasse les productions et on fait une photocopie des différents agrandissements. Trace écrite sur l'agrandissement et la proportion des longueurs.
Étape 2
--------
Situations des "Thalès" (sans le nommer) pour calculer une longueur du triangle et présentation de deux situations pathologiques (non alignement et non parallélisme) pour mettre en lumière les hypothèses du théorème de Thalès (`decouverte de thales <./decouverte_de_thales.pdf>`_)
Écriture du théorème de Thalès et présentation de `situation où l'on retrouve Thalès <./situations_Thales.pdf>`_.
Étape 3
--------
Exercices techniques sur Thalès (à écrire au tableau). Possibilité de faire avec l'égalité des rapports
Étape 4 (tache complexe)
------------------------
`Tache complexe du tipi <./TC_tipi.pdf>`_

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\documentclass[a4paper,12pt]{article}
\usepackage{myXsim}
\title{Thalès agrandissement - Exercices}
\tribe{Troisième}
\date{Septembre 2017}
\begin{document}
\begin{exercise}
La figure ci-dessous est un puzzle de 5 pièces inscrite dans dans un carré de côté 18cm. Reproduire le puzzle de sorte qu'il soit inscrit dans un carré dont le côté est une des valeurs suivantes:
\begin{center}
\hfill 9 cm \hfill 6cm \hfill 3cm \hfill (bonus) 12cm
\end{center}
\vfill
\begin{center}
\includegraphics[scale=1]{./fig/puzzle}
\end{center}
\end{exercise}
\vfill
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "master"
%%% End:

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