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Feat: ajoute des exercices de calcul de distance

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This commit is contained in:
Bertrand Benjamin 2022-05-03 15:58:48 +02:00
parent 5d26b077e9
commit f86411ebf8
2 changed files with 197 additions and 20 deletions
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211
4e/15_Pythagore_reciproque/exercises.tex
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@ -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]
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[sloped, midway, left]{3cm}
(-6,0) -- node[midway, below]{4cm}
(-6,4) --
(0,0) -- node[ midway, sloped, below]{3cm}
(-3,0) -- node[midway, sloped, above]{2cm}
(-3,2) --
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;
\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}

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4e/15_Pythagore_reciproque/plan_de_travail.pdf
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