From 5d26b077e9304ddc8d9eb8c78881596a78d27dbf Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Tue, 3 May 2022 09:48:00 +0200 Subject: [PATCH] =?UTF-8?q?Feat=20Cr=C3=A9er=20le=20d=C3=A9part=20du=20cha?= =?UTF-8?q?pitre=20sur=20la=20r=C3=A9ciproque=20de=20Pythagore?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 4e/15_Pythagore_reciproque/exercises.tex | 122 ++++++++++++++++++ .../fig/aire_polyognes.pdf | Bin 0 -> 13697 bytes .../fig/classer_perim_aire.pdf | Bin 0 -> 10479 bytes 4e/15_Pythagore_reciproque/index.rst | 12 ++ .../plan_de_travail.pdf | Bin 0 -> 52026 bytes .../plan_de_travail.tex | 47 +++++++ 4e/15_Pythagore_reciproque/solutions.tex | 28 ++++ 7 files changed, 209 insertions(+) create mode 100644 4e/15_Pythagore_reciproque/exercises.tex create mode 100644 4e/15_Pythagore_reciproque/fig/aire_polyognes.pdf create mode 100644 4e/15_Pythagore_reciproque/fig/classer_perim_aire.pdf create mode 100644 4e/15_Pythagore_reciproque/index.rst create mode 100644 4e/15_Pythagore_reciproque/plan_de_travail.pdf create mode 100644 4e/15_Pythagore_reciproque/plan_de_travail.tex create mode 100644 4e/15_Pythagore_reciproque/solutions.tex diff --git a/4e/15_Pythagore_reciproque/exercises.tex b/4e/15_Pythagore_reciproque/exercises.tex new file mode 100644 index 0000000..aba7ebb --- /dev/null +++ b/4e/15_Pythagore_reciproque/exercises.tex @@ -0,0 +1,122 @@ +\begin{exercise}[subtitle={Classement}, step={1}, origin={???}, topics={ Pythagore reciproque }, tags={ Pythagore, géométrie }] + On a représenté 5 figure géométriques à 2 échelles différentes sur les grilles ci-dessous + + \begin{center} + \includegraphics[scale=0.8]{./fig/classer_perim_aire.pdf} + \end{center} + + \begin{enumerate} + \item Classer les figures par ordre croissant de leur périmètre. + \item Classer les figures par ordre croissant de leur aire. + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Classement - avancé}, step={1}, origin={???}, topics={ Pythagore reciproque }, tags={ Pythagore, géométrie }] + On a représenté les polygones ci-dessous + + \begin{center} + \includegraphics[scale=0.7]{./fig/aire_polyognes.pdf} + \end{center} + + \begin{enumerate} + \item Avec quelle unité va-t-on mesurer le périmètre de ces polygones? Avec quelle unité va-t-on mesurer l'aire? + \item Calculer l'aire de chacune de ces figures. + \item Calculer quand c'est possible le périmètre de ces figures. + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Création}, step={1}, origin={MEpC}, topics={ Pythagore reciproque }, tags={ Pythagore, géométrie }] + \begin{enumerate} + \item Représenter sur quadrillage deux figures qui ont la même aire et des périmètres différents. + \item Représenter sur quadrillage deux figures qui ont le même périmètres et des aires différentes. + \item + \begin{enumerate} + \item Le périmètre d'un carré vaut 36cm. Son côté vaut donc ? + \item L'aire d'un carré vaut $36cm^2$. Son côté vaut donc ? + \end{enumerate} + \end{enumerate} +\end{exercise} + +% ---- + +\begin{exercise}[subtitle={Construction de triangles}, step={2}, origin={MEpC}, topics={ Pythagore reciproque }, tags={ Pythagore, géométrie }] + Voici des séries de 3 nombres représentant les longueurs des côtés de triangles. + \begin{multicols}{3} + \begin{enumerate}[label={$\triangle$ \Alph*:}] + \item 2; 5; 4 + \item 2; 5; 9 + + \item 3; 3; 3 + \item 3; 3; 4,2 + + \item 4; 5.9; 4,3 + \item 5,1; 2,2 ; 2,9 + \end{enumerate} + \end{multicols} + \begin{enumerate} + \item Pour chaque série, dire si on peu construire le triangle. + \begin{itemize} + \item Si non, expliquer pourquoi + \item Si oui, faire des remarques sur le type de triangle que l'on pourra obtenir. + \end{itemize} + \item Construire le triangle quand c'est possible et vérifier le type. + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Mesure du 3e côté}, step={2}, origin={MEpC}, topics={ Pythagore reciproque }, tags={ Pythagore, géométrie }] + Pour chacun des triangles suivant, le tracer et mesurer la longueur du côté manquant. + \begin{multicols}{3} + \begin{enumerate} + \item + \begin{tikzpicture}[rotate=0, scale=0.6] + \draw[fill=blue!50] + (-2,0) -- node[midway, left]{3cm} + (-2,-3) -- node[midway, below]{4cm} + (3,-3) -- + cycle; + \draw (-2, -3) rectangle (-1.8, -2.8); + \end{tikzpicture} + \item + \begin{tikzpicture}[rotate=30, scale=0.6] + \draw[fill=blue!50] + (-2,0) -- node[midway, left]{8cm} + (-2,-3) -- node[midway, right below]{15cm} + (3,-3) -- + cycle; + \draw (-2, -3) rectangle (-1.8, -2.8); + \end{tikzpicture} + \item + \begin{tikzpicture}[rotate=170, scale=0.6] + \draw[fill=blue!50] + (-2,0) -- node[midway, right]{28cm} + (-2,-3) -- + (3,-3) -- node[midway, left]{53cm} + cycle; + \draw (-2, -3) rectangle (-1.8, -2.8); + \end{tikzpicture} + + + \end{enumerate} + \end{multicols} + \begin{enumerate} + \setcounter{enumi}{3} + \item Triangle $ABC$ rectangle en A tel que $AB = 5cm$ et $AC = 12cm$ + \end{enumerate} +\end{exercise} + +% ---- + +\begin{exercise}[subtitle={Calcul du 3e côté}, step={3}, origin={MEpC}, topics={ Pythagore reciproque }, tags={ Pythagore, géométrie }] + \begin{tikzpicture}[rotate=0, scale=0.4] + \draw[fill=blue!20] + (0,0) -- node[sloped, midway, left]{3cm} + (-6,0) -- node[midway, below]{4cm} + (-6,4) -- + cycle; + \draw (-6, 0) rectangle ++(0.2, 0.2); + \draw (0, 0) rectangle ++(-6, -6); + \draw (-6, 0) rectangle ++(-4, 4); + \draw (0, 0) -- (4, 6) -- (-2, 10) -- (-6, 4) -- cycle; + \end{tikzpicture} +\end{exercise} + diff --git a/4e/15_Pythagore_reciproque/fig/aire_polyognes.pdf b/4e/15_Pythagore_reciproque/fig/aire_polyognes.pdf new file mode 100644 index 0000000000000000000000000000000000000000..475ca2b5f6bf3ba55b8de7577aea0b2be8052f63 GIT binary patch literal 13697 zcmcJ01#ld_)}<-7W2Ts4%*@Qp%*@Qp97BvTGjn2QW@e5#cFfGoYbW3LVBf2Mx3+5C zGd-iLE2;ZjsdeNzB9;>pp{A!{h9a&zE`Nk#0?+|$4J@FzxB#?L#x|x-W&q|llL8a~ 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+\pagestyle{empty} + +\DeclareExerciseCollection{banque} +\xsimsetup{ +} + + +\begin{document} +\maketitle + +% Résumé + +\bigskip + +Savoir-faire de la séquence +\begin{itemize} + \item +\end{itemize} + +\bigskip + +Ordre des étapes à respecter + + +\section{Aire et périmètre} + +\listsectionexercises + +\section{Lien entre les longueurs des côtés des triangles} + +\listsectionexercises + +\pagebreak + +\input{exercises.tex} +\printcollection{banque} + + +\end{document} diff --git a/4e/15_Pythagore_reciproque/solutions.tex b/4e/15_Pythagore_reciproque/solutions.tex new file mode 100644 index 0000000..08d1126 --- /dev/null +++ b/4e/15_Pythagore_reciproque/solutions.tex @@ -0,0 +1,28 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} + +\usetikzlibrary{shapes.geometric} + +\author{Benjamin Bertrand} +\title{Pythagore reciproque - Solutions} +\tribe{4e} +\date{mai 2022} + +\DeclareExerciseCollection{banque} +\xsimsetup{ + exercise/print=false, + solution/print=true, +} + +\pagestyle{empty} + + +\begin{document} + +\maketitle + +\input{exercises.tex} +%\printcollection{banque} +%\printsolutions{exercises} + +\end{document}