diff --git a/4e/15_Pythagore_reciproque/exercises.tex b/4e/15_Pythagore_reciproque/exercises.tex index aba7ebb..e6eab3c 100644 --- a/4e/15_Pythagore_reciproque/exercises.tex +++ b/4e/15_Pythagore_reciproque/exercises.tex @@ -69,7 +69,7 @@ \begin{enumerate} \item \begin{tikzpicture}[rotate=0, scale=0.6] - \draw[fill=blue!50] + \draw[fill=blue!20] (-2,0) -- node[midway, left]{3cm} (-2,-3) -- node[midway, below]{4cm} (3,-3) -- @@ -77,20 +77,20 @@ \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} + \begin{tikzpicture}[rotate=30, scale=0.6, transform shape] + \draw[fill=blue!20] + (-2,0) -- node[sloped, midway, below]{\LARGE 8cm} + (-2,-3) -- node[sloped, midway, below]{\LARGE 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} + \begin{tikzpicture}[rotate=170, scale=0.6, transform shape] + \draw[fill=blue!20] + (-2,0) -- node[sloped, midway, below]{\LARGE 28cm} (-2,-3) -- - (3,-3) -- node[midway, left]{53cm} + (3,-3) -- node[sloped, midway, above]{\LARGE 53cm} cycle; \draw (-2, -3) rectangle (-1.8, -2.8); \end{tikzpicture} @@ -107,16 +107,193 @@ % ---- \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} + Pour chacun des triangles déterminer la longueur du côté manquant + + \begin{multicols}{3} + \begin{enumerate} + \item + \begin{tikzpicture}[baseline=(a.north west), rotate=0, scale=0.7] + \draw[fill=blue!20] + (0,0) -- node[ midway, sloped, below]{3cm} + (-3,0) -- node[midway, sloped, above]{2cm} + (-3,2) -- + cycle; + \draw (-3, 0) rectangle ++(0.2, 0.2); + \draw (0, 0) rectangle ++(-3, -3); + \draw (-3, 0) rectangle ++(-2, 2); + \draw (0, 0) -- (2, 3) -- (-1, 5) -- (-3, 2) -- cycle; + \end{tikzpicture} + \item + \begin{tikzpicture}[baseline=(a.north west), rotate=30, scale=0.7, transform shape] + \draw[fill=blue!20] + (0,0) -- node[ midway, below, sloped]{\large 36cm} + (-3,0) -- node[midway, above, sloped]{\large 77cm} + (-3,2) -- + cycle; + \draw (-3, 0) rectangle ++(0.2, 0.2); + \draw (0, 0) rectangle ++(-3, -3); + \draw (-3, 0) rectangle ++(-2, 2); + \draw (0, 0) -- (2, 3) -- (-1, 5) -- (-3, 2) -- cycle; + \end{tikzpicture} + \item + \begin{tikzpicture}[baseline=(a.north west), rotate=180, scale=0.7, transform shape] + \draw[fill=blue!20] + (0,0) -- node[ midway, above, sloped, rotate=180]{\large 48m} + (-3,0) -- node[midway, above, sloped]{\large 55m} + (-3,2) -- + cycle; + \draw (-3, 0) rectangle ++(0.2, 0.2); + \draw (0, 0) rectangle ++(-3, -3); + \draw (-3, 0) rectangle ++(-2, 2); + \draw (0, 0) -- (2, 3) -- (-1, 5) -- (-3, 2) -- cycle; + \end{tikzpicture} + \end{enumerate} + \end{multicols} + + \begin{multicols}{4} + \begin{enumerate} + \setcounter{enumi}{3} + \item + \begin{tikzpicture}[baseline=(a.north west), rotate=50, scale=0.7, transform shape] + \draw[fill=blue!20] + (0,0) -- node[ midway, sloped, below]{\large 7cm} + (-3,0) -- node[midway, sloped, above]{\large 24cm} + (-3,2) -- + cycle; + \draw (-3, 0) rectangle ++(0.2, 0.2); + \end{tikzpicture} + + \item + \begin{tikzpicture}[baseline=(a.north west), rotate=40, scale=0.7, transform shape] + \draw[fill=blue!20] + (0,0) -- node[ midway, below, sloped]{\large 1,6cm} + (-3,0) -- node[midway, above, sloped]{\large 63cm} + (-3,2) -- + cycle; + \draw (-3, 0) rectangle ++(0.2, 0.2); + \end{tikzpicture} + + \item + \begin{tikzpicture}[baseline=(a.north west), rotate=100, scale=0.7, transform shape] + \draw[fill=blue!20] + (0,0) -- node[ midway, above, sloped, rotate=180]{\large 6.5m} + (-3,0) -- node[midway, above, sloped]{\large 72m} + (-3,2) -- + cycle; + \draw (-3, 0) rectangle ++(0.2, 0.2); + \end{tikzpicture} + + \item + \begin{tikzpicture}[baseline=(a.north west), rotate=0, scale=0.7, transform shape] + \draw[fill=blue!20] + (0,0) -- node[ midway, above, sloped, rotate=180]{\large 2m} + (-3,0) -- node[midway, above, sloped]{\large 1m} + (-3,2) -- + cycle; + \draw (-3, 0) rectangle ++(0.2, 0.2); + \end{tikzpicture} + \end{enumerate} + \end{multicols} + + \begin{multicols}{2} + \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 $AC=12m$ + \end{enumerate} + \end{multicols} + +\end{exercise} + +\begin{exercise}[subtitle={Calcul d'un petit côté}, step={3}, origin={MEpC}, topics={ Pythagore reciproque }, tags={ Pythagore, géométrie }] + Pour chacun des triangles déterminer la longueur du côté manquant + + \begin{multicols}{3} + \begin{enumerate} + \item + \begin{tikzpicture}[baseline=(a.north west), rotate=0, scale=0.7] + \draw[fill=blue!20] + (0,0) -- node[ midway, sloped, below]{3cm} + (-3,0) -- node[midway, sloped, above]{2cm} + (-3,2) -- + cycle; + \draw (-3, 0) rectangle ++(0.2, 0.2); + \draw (0, 0) rectangle ++(-3, -3); + \draw (-3, 0) rectangle ++(-2, 2); + \draw (0, 0) -- (2, 3) -- (-1, 5) -- (-3, 2) -- cycle; + \end{tikzpicture} + \item + \begin{tikzpicture}[baseline=(a.north west), rotate=30, scale=0.7, transform shape] + \draw[fill=blue!20] + (0,0) -- node[ midway, below, sloped]{\large 36cm} + (-3,0) -- node[midway, above, sloped]{\large 77cm} + (-3,2) -- + cycle; + \draw (-3, 0) rectangle ++(0.2, 0.2); + \draw (0, 0) rectangle ++(-3, -3); + \draw (-3, 0) rectangle ++(-2, 2); + \draw (0, 0) -- (2, 3) -- (-1, 5) -- (-3, 2) -- cycle; + \end{tikzpicture} + \item + \begin{tikzpicture}[baseline=(a.north west), rotate=180, scale=0.7, transform shape] + \draw[fill=blue!20] + (0,0) -- node[ midway, above, sloped, rotate=180]{\large 48m} + (-3,0) -- node[midway, above, sloped]{\large 55m} + (-3,2) -- + cycle; + \draw (-3, 0) rectangle ++(0.2, 0.2); + \draw (0, 0) rectangle ++(-3, -3); + \draw (-3, 0) rectangle ++(-2, 2); + \draw (0, 0) -- (2, 3) -- (-1, 5) -- (-3, 2) -- cycle; + \end{tikzpicture} + \end{enumerate} + \end{multicols} + + \begin{multicols}{4} + \begin{enumerate} + \setcounter{enumi}{3} + \item + \begin{tikzpicture}[baseline=(a.north west), rotate=50, scale=0.7, transform shape] + \draw[fill=blue!20] + (0,0) -- node[ midway, sloped, below]{\large 7cm} + (-3,0) -- node[midway, sloped, above]{\large 24cm} + (-3,2) -- + cycle; + \draw (-3, 0) rectangle ++(0.2, 0.2); + \end{tikzpicture} + + \item + \begin{tikzpicture}[baseline=(a.north west), rotate=40, scale=0.7, transform shape] + \draw[fill=blue!20] + (0,0) -- node[ midway, below, sloped]{\large 1,6cm} + (-3,0) -- node[midway, above, sloped]{\large 63cm} + (-3,2) -- + cycle; + \draw (-3, 0) rectangle ++(0.2, 0.2); + \end{tikzpicture} + + \item + \begin{tikzpicture}[baseline=(a.north west), rotate=100, scale=0.7, transform shape] + \draw[fill=blue!20] + (0,0) -- node[ midway, above, sloped, rotate=180]{\large 6.5m} + (-3,0) -- node[midway, above, sloped]{\large 72m} + (-3,2) -- + cycle; + \draw (-3, 0) rectangle ++(0.2, 0.2); + \end{tikzpicture} + + \item + \begin{tikzpicture}[baseline=(a.north west), rotate=0, scale=0.7, transform shape] + \draw[fill=blue!20] + (0,0) -- node[ midway, above, sloped, rotate=180]{\large 2m} + (-3,0) -- node[midway, above, sloped]{\large 1m} + (-3,2) -- + cycle; + \draw (-3, 0) rectangle ++(0.2, 0.2); + \end{tikzpicture} + \end{enumerate} + \end{multicols} \end{exercise} diff --git a/4e/15_Pythagore_reciproque/plan_de_travail.pdf b/4e/15_Pythagore_reciproque/plan_de_travail.pdf index 609d862..402d7df 100644 Binary files a/4e/15_Pythagore_reciproque/plan_de_travail.pdf and b/4e/15_Pythagore_reciproque/plan_de_travail.pdf differ