From 1ffaa517958eb49c5013ca4abc01e495bbe68ee7 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Tue, 10 May 2022 09:38:24 +0200 Subject: [PATCH] =?UTF-8?q?Feat:=20Ajoute=20une=20tache=20complexe=20et=20?= =?UTF-8?q?la=20d=C3=A9couverte=20de=20la=20racine=20carr=C3=A9?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 4e/15_Pythagore_reciproque/exercises.tex | 79 ++++++++++++++++-- 4e/15_Pythagore_reciproque/fig/carre_aire.pdf | Bin 0 -> 6425 bytes .../fig/carre_aire_sqrt.pdf | Bin 0 -> 6275 bytes .../fig/plate-bande.pdf | Bin 0 -> 349276 bytes .../plan_de_travail.pdf | Bin 57870 -> 420307 bytes .../plan_de_travail.tex | 22 +++-- 6 files changed, 88 insertions(+), 13 deletions(-) create mode 100644 4e/15_Pythagore_reciproque/fig/carre_aire.pdf create mode 100644 4e/15_Pythagore_reciproque/fig/carre_aire_sqrt.pdf create mode 100644 4e/15_Pythagore_reciproque/fig/plate-bande.pdf diff --git a/4e/15_Pythagore_reciproque/exercises.tex b/4e/15_Pythagore_reciproque/exercises.tex index 296b20c..3c51aa0 100644 --- a/4e/15_Pythagore_reciproque/exercises.tex +++ b/4e/15_Pythagore_reciproque/exercises.tex @@ -37,9 +37,67 @@ \end{enumerate} \end{exercise} +\begin{exercise}[subtitle={Plate bande}, step={1}, origin={MEpC}, topics={ Pythagore reciproque }, tags={ Pythagore, géométrie }] +Au début du printemps, un jardinier doit entretenir quatre plates-bandes : il doit les clôturer par un grillage et y semer du gazon. Dans sa remise, il lui reste 32 mètres de grillage et un sac de graines de gazon permettant d’ensemencer une surface de 50 m2. + +Il se demande si cela suffit pour entretenir au moins l’une des plates-bande. + +Pouvez-vous l'aider? + +\begin{center} + \includegraphics[scale=0.8]{./fig/plate-bande.pdf} +\end{center} + +\end{exercise} + + % ---- -\begin{exercise}[subtitle={Construction de triangles}, step={2}, origin={MEpC}, topics={ Pythagore reciproque }, tags={ Pythagore, géométrie }] +\begin{exercise}[subtitle={Retrouver la longueur d'un côté}, step={2}, origin={MEpC}, topics={ Pythagore reciproque }, tags={ Pythagore, géométrie }] + \begin{enumerate} + \item + \begin{enumerate} + \item Le périmètre d'un carré vaut 16cm. Son côté vaut donc ? + \item L'aire d'un carré vaut $16 cm^2$. Son côté vaut donc ? + \end{enumerate} + \item On a plusieurs carrés d'aires différentes + + \begin{center} + \includegraphics[scale=0.7]{./fig/carre_aire} + \end{center} + + Retrouver la longueur des côtés de chaque carrés. + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Racine carré}, step={2}, origin={MEpC}, topics={ Pythagore reciproque }, tags={ Pythagore, géométrie }] + \begin{enumerate} + \item Calculer les quantités suivantes \textbf{sans} calculatrices + \[ + \sqrt{4} \qquad + \sqrt{25} \qquad + \sqrt{64} \qquad + \sqrt{100} \qquad + \sqrt{9} + \] + \item Calculer les quantités suivantes \textbf{avec} calculatrices + \[ + \sqrt{5} \qquad + \sqrt{15} \qquad + \sqrt{30} \qquad + \sqrt{10} \qquad + \sqrt{256} + \] + \item Quelle est la longueur des côtés des carrés suivants + \begin{center} + \includegraphics[scale=0.7]{./fig/carre_aire_sqrt} + \end{center} + \end{enumerate} +\end{exercise} + +% ---- + +\begin{exercise}[subtitle={Construction de triangles}, step={3}, 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*:}] @@ -63,7 +121,7 @@ \end{enumerate} \end{exercise} -\begin{exercise}[subtitle={Mesure du 3e côté}, step={2}, origin={MEpC}, topics={ Pythagore reciproque }, tags={ Pythagore, géométrie }] +\begin{exercise}[subtitle={Mesure du 3e côté}, step={3}, 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} @@ -106,7 +164,7 @@ % ---- -\begin{exercise}[subtitle={Calcul du 3e côté}, step={3}, origin={MEpC}, topics={ Pythagore reciproque }, tags={ Pythagore, géométrie }] +\begin{exercise}[subtitle={Calcul du 3e côté}, step={4}, origin={MEpC}, topics={ Pythagore reciproque }, tags={ Pythagore, géométrie }] Pour chacun des triangles déterminer la longueur du côté manquant \begin{multicols}{3} @@ -200,13 +258,13 @@ \begin{enumerate} \setcounter{enumi}{7} \item Triangle $ABC$ rectangle en $A$ tel que $AB = 60mm$ et $AC=91mm$ - \item Triangle $IJK$ rectangle en $K$ tel que $AB = 13m$ et $AC=84m$ - \item Triangle $LMN$ rectangle en $L$ tel que $AB = 3cm$ et $AC=7m$ - \item Triangle $EFG$ rectangle en $E$ tel que $AB = 6m$ et $AC=12m$ + \item Triangle $IJK$ rectangle en $K$ tel que $KJ = 13m$ et $KI=84m$ + \item Triangle $LMN$ rectangle en $L$ tel que $LN = 3cm$ et $LM=7m$ + \item Triangle $EFG$ rectangle en $E$ tel que $EG = 6m$ et $EF=12m$ \end{enumerate} \end{exercise} -\begin{exercise}[subtitle={Calcul d'un petit côté}, step={3}, origin={MEpC}, topics={ Pythagore reciproque }, tags={ Pythagore, géométrie }] +\begin{exercise}[subtitle={Calcul d'un petit côté}, step={4}, origin={MEpC}, topics={ Pythagore reciproque }, tags={ Pythagore, géométrie }] Pour chacun des triangles déterminer la longueur du côté manquant \begin{multicols}{3} @@ -294,5 +352,12 @@ \end{tikzpicture} \end{enumerate} \end{multicols} + \begin{enumerate} + \setcounter{enumi}{7} + \item Triangle $ABC$ rectangle en $A$ tel que $AB = 15mm$ et $BC=17mm$ + \item Triangle $IJK$ rectangle en $K$ tel que $IJ = 29cm$ et $IK=21$ + \item Triangle $LMN$ rectangle en $L$ tel que $LM = 28cm$ et $MN=53cm$ + \item Triangle $EFG$ rectangle en $E$ tel que $EF = 26m$ et $FG=85m$ + \end{enumerate} \end{exercise} diff --git a/4e/15_Pythagore_reciproque/fig/carre_aire.pdf b/4e/15_Pythagore_reciproque/fig/carre_aire.pdf new file mode 100644 index 0000000000000000000000000000000000000000..38a21211ba36f66cdc360ea75cb34b3edfb2e362 GIT binary patch literal 6425 zcma)>2UJr_x5pJk5D-uSL0aftQXm0o(tEE;4GhX;NPR_1^E@yWaPboHBd%%$(W(J!h@?g;iZzmKStefRMFnrTBo59{>b6nAs4D zhyeJM5%yLXYk&aOq)7+>0Qh8)C=9|Gdqu%92x)}5g9U<6OpFkXaYn%H2;Gz8V?@<( zLBv73hlG)c+@%u1jphs2B_+)+*h>);a9r06ZfTzG&>LfF%gYrqD&*K$+EwVi`?F7o zUAHx#zIVNnYe_PxXk1BO4L2u+uL-ddROyg) 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