From 6fe341b064770d2ccf236e06113277fe35e17052 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Tue, 17 May 2022 09:39:18 +0200 Subject: [PATCH] Feat: Ajoute les derniers exercices sur pythagore --- 4e/15_Pythagore_reciproque/exercises.tex | 109 +++++++++++++++++- .../fig/etagere_fleurs.png | Bin 0 -> 61624 bytes 4e/15_Pythagore_reciproque/fig/mur.png | Bin 0 -> 41793 bytes .../plan_de_travail.pdf | Bin 421953 -> 529349 bytes .../plan_de_travail.tex | 4 + 5 files changed, 107 insertions(+), 6 deletions(-) create mode 100644 4e/15_Pythagore_reciproque/fig/etagere_fleurs.png create mode 100644 4e/15_Pythagore_reciproque/fig/mur.png diff --git a/4e/15_Pythagore_reciproque/exercises.tex b/4e/15_Pythagore_reciproque/exercises.tex index b85db80..995d5bc 100644 --- a/4e/15_Pythagore_reciproque/exercises.tex +++ b/4e/15_Pythagore_reciproque/exercises.tex @@ -372,10 +372,107 @@ Pouvez-vous l'aider? \end{enumerate} \end{exercise} -\begin{exercise}[subtitle={Ça passe pas}, step={4}, origin={Sesamath}, topics={ Pythagore reciproque }, tags={ Pythagore, géométrie }] - Bob est en train de construire un bibliothèque. Pour cela, il a placer les planches verticales espacée de 60cm. Pour faire les étagères, il utilise des planches de 2cm d'épaisseur et de 60cm de long. - \begin{enumerate} - \item Il la rentre en diagonal pour la mettre à plat mais elle reste bloquée avant de pouvoir être posée. Expliquez pourquoi. - \item - \end{enumerate} + +\begin{exercise}[subtitle={Le losange}, step={4}, origin={MEpC}, topics={ Pythagore reciproque }, tags={ Pythagore, géométrie }] + Le côté d'un losange mesure 27,4cm et l'une de ses diagonales 42cm. + + Quelle est la longueur de sa seconde diagonale? +\end{exercise} + +% \begin{exercise}[subtitle={Ça passe pas}, step={4}, origin={Sesamath}, topics={ Pythagore reciproque }, tags={ Pythagore, géométrie }] +% Bob est en train de construire un bibliothèque. Pour cela, il a placer les planches verticales espacée de 60cm. Pour faire les étagères, il utilise des planches de 2cm d'épaisseur et de 60cm de long. +% \begin{enumerate} +% \item Il la rentre en diagonal pour la mettre à plat mais elle reste bloquée avant de pouvoir être posée. Expliquez pourquoi. +% \item Pour la faire passer, il decide de la découper. +% \begin{enumerate} +% \item +% \end{enumerate} +% \end{enumerate} +% \end{exercise} + +% ---- +\begin{exercise}[subtitle={A-t-on un triangle rectangle?}, step={5}, origin={MEpC}, topics={ Pythagore reciproque }, tags={ Pythagore, géométrie }] + Démontrer si les triangles suivants sont rectangles ou pas. + \begin{multicols}{4} + \begin{enumerate} + \item + \begin{tikzpicture}[baseline=(a.north west), rotate=50, scale=0.9, transform shape] + \draw[fill=blue!20] + (0,0) -- node[ midway, sloped, below]{\large 11cm} + (-3,0) -- node[midway, sloped, above]{\large 60cm} + (-3,2.4) -- node[midway, sloped, above]{\large 61cm} + cycle; + \end{tikzpicture} + + \item + \begin{tikzpicture}[baseline=(a.north west), rotate=80, scale=0.9, transform shape] + \draw[fill=blue!20] + (0,0) -- node[ midway, below, sloped]{\large 1,6cm} + (-3,0) -- node[midway, above, sloped]{\large 6,3cm} + (-3,2.6) -- node[midway, above, sloped]{\large 6,7cm} + cycle; + \end{tikzpicture} + + \item + \begin{tikzpicture}[baseline=(a.north west), rotate=100, scale=0.9, transform shape] + \draw[fill=blue!20] + (0,0) -- node[ midway, above, sloped, rotate=180]{\large 6.5m} + (-3,0) -- node[midway, above, sloped]{\large 7.2m} + (-3,1.9) -- node[midway, above, sloped]{\large 7.5m} + cycle; + \end{tikzpicture} + + \item + \begin{tikzpicture}[baseline=(a.north west), rotate=-100, scale=0.9, transform shape] + \draw[fill=blue!20] + (0,0) -- node[ midway, above, sloped, rotate=180]{\large 60m} + (-3,0) -- node[midway, above, sloped]{\large 109m} + (-3,2) -- node[midway, above, sloped]{\large 91m} + cycle; + \end{tikzpicture} + \end{enumerate} + \end{multicols} + + \vspace{1cm} + \begin{enumerate} + \setcounter{enumi}{4} + \item Triangle $ABC$ tel que $AB = 60mm$, $BC=30mm$ et $AC=91mm$ + \item Triangle $IJK$ tel que $KJ = 13m$, $IJ=85m$ et $KI=84m$ + \item Triangle $LMN$ tel que $LN = 3cm$, $MN=5cm$ et $LM=7m$ + \item Triangle $EFG$ tel que $EG = 37m$, $FG=35cm$ et $EF=12m$ + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Fleurs sur une étagère}, step={5}, origin={sesamaths}, topics={ Pythagore reciproque }, tags={ Pythagore, géométrie }] + \begin{minipage}{0.4\linewidth} + Sur un mur vertical, Arnaud a installé une étagère pour y poser un pot de fleurs. + + Les mesures qu'il a utilisées sont les suivantes + \[ + AT = 42cm \qquad AE = 58cm \qquad TE = 40cm + \] + L'étagère d'Arnaud est-elle horizontale? Justifier. + \end{minipage} + \hfill + \begin{minipage}{0.4\linewidth} + \includegraphics[scale=0.3]{./fig/etagere_fleurs.png} + \end{minipage} +\end{exercise} + +\begin{exercise}[subtitle={Construction d'un mur}, step={5}, origin={sesamaths}, topics={ Pythagore reciproque }, tags={ Pythagore, géométrie }] + \begin{minipage}{0.5\linewidth} + Pour apprendre sont métier, un apprenti maçon a monté un mur en briques de 0.90m de hauteur. Son patron arriver pour vérifier son travail: il marque un point B sur le mur à 80cm et un point A à 60cm du pied du mur. Il mesure alors la distance entre les points A et B et obtient 1m. + + L'apprenti a-t-il bien construit son mur perpendiculaire au sol? + \end{minipage} + \hfill + \begin{minipage}{0.4\linewidth} + \includegraphics[scale=0.3]{./fig/mur.png} + \end{minipage} +\end{exercise} + +\begin{exercise}[subtitle={A-t-on un rectangle?}, step={5}, origin={MEpC}, topics={ Pythagore reciproque }, tags={ Pythagore, géométrie }] + $EFGH$ est un parallélogramme tel que $EF=36$, $EH=77$ et $HF=85$. + + $EFGH$ est-il un rectangle? \end{exercise} diff --git a/4e/15_Pythagore_reciproque/fig/etagere_fleurs.png b/4e/15_Pythagore_reciproque/fig/etagere_fleurs.png new file mode 100644 index 0000000000000000000000000000000000000000..98ddbbcfeabd3580bd18d192acaed298f651eb4e GIT binary patch literal 61624 zcmXt9Wl$U35)DpEfKV*ByGwC*r%3VQuEiD$ z8GhWmcjfG!vymTEWYOOez6AgP=<;$>>Hq+oI{*OBj|va_W#&W}7XTm!$V-W9dgUB< zYp0uQd+fK~^6#&nCnna+YNd^Fo+A~k09IXA(P=QOV)L5PO5*$D$q(h(xV&e_nQiK` 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