Séquence sur les angles pour les 6e

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Bertrand Benjamin 2018-03-08 11:13:09 +03:00
parent 9fd124074e
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15 changed files with 5595 additions and 10 deletions

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\documentclass[a4paper,12pt,landscape]{article}
\usepackage{myXsim}
\author{}
\date{Mars 2018}
\title{Mesures d'angles}
\tribe{Sixième}
\newcommand{\angleTable}{%
\hspace{-1.5cm}
\begin{tabular}{|c|*{10}{p{1.5cm}|}*{3}{p{2cm}|}}
\hline
Angle &
\begin{tikzpicture}[scale=0.5]
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(0,0) -- (0:1) arc (0:0:1) -- cycle;
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(0,0) -- (0:1) arc (0:60:1) -- cycle;
\end{tikzpicture} &
\begin{tikzpicture}[scale=0.5]
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\filldraw[fill=green!20!white, draw=green!50!black]
(0,0) -- (0:1) arc (0:75:1) -- cycle;
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(0,0) -- (0:1) arc (0:150:1) -- cycle;
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\end{tikzpicture} \\
\hline
Famille&&&&&&&&&&&&&\\
\hline
Mesure&&&&&&&&&&&&&\\
\hline
\end{tabular}
\begin{itemize}
\item La mesure des angles \textbf{aigus} est \dotfill
\item La mesure des angles \textbf{droits} est \dotfill
\item La mesure des angles \textbf{obtus} est \dotfill
\end{itemize}%
}
\pagestyle{empty}
\begin{document}
\angleTable
\vfill
\angleTable
\vfill
\angleTable
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "master"
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id="path1949-9"
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id="path1949-8-3"
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<text
id="text2420"
y="274.77972"
x="45.926552"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
xml:space="preserve"><tspan
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
y="274.77972"
x="45.926552"
id="tspan2418"
sodipodi:role="line">100°</tspan></text>
<text
id="text2424"
y="282.3212"
x="51.39138"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
xml:space="preserve"><tspan
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
y="282.3212"
x="51.39138"
id="tspan2422"
sodipodi:role="line">130°</tspan></text>
<text
id="text2428"
y="283.52344"
x="68.441658"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
xml:space="preserve"><tspan
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
y="283.52344"
x="68.441658"
id="tspan2426"
sodipodi:role="line">130°</tspan></text>
<text
id="text2432"
y="271.06363"
x="78.715546"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
xml:space="preserve"><tspan
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
y="271.06363"
x="78.715546"
id="tspan2430"
sodipodi:role="line">150°</tspan></text>
<text
id="text2436"
y="252.26462"
x="105.71183"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
xml:space="preserve"><tspan
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
y="252.26462"
x="105.71183"
id="tspan2434"
sodipodi:role="line">155°</tspan></text>
<text
id="text2440"
y="202.86253"
x="148.7747"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
xml:space="preserve"><tspan
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
y="202.86253"
x="148.7747"
id="tspan2438"
sodipodi:role="line">100°</tspan></text>
<text
id="text2444"
y="199.47433"
x="164.51341"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
xml:space="preserve"><tspan
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
y="199.47433"
x="164.51341"
id="tspan2442"
sodipodi:role="line">20°</tspan></text>
<text
id="text2448"
y="192.58864"
x="163.96693"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
xml:space="preserve"><tspan
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
y="192.58864"
x="163.96693"
id="tspan2446"
sodipodi:role="line">30°</tspan></text>
<text
id="text2452"
y="185.37506"
x="161.78099"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
xml:space="preserve"><tspan
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
y="185.37506"
x="161.78099"
id="tspan2450"
sodipodi:role="line">25°</tspan></text>
<text
id="text2456"
y="262.53851"
x="41.226791"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
xml:space="preserve"><tspan
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
y="262.53851"
x="41.226791"
id="tspan2454"
sodipodi:role="line">3,5cm</tspan></text>
<text
id="text2460"
y="283.08627"
x="36.527046"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
xml:space="preserve"><tspan
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
y="283.08627"
x="36.527046"
id="tspan2458"
sodipodi:role="line">2,5cm</tspan></text>
<text
id="text2464"
y="291.50214"
x="56.856213"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
xml:space="preserve"><tspan
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
y="291.50214"
x="56.856213"
id="tspan2462"
sodipodi:role="line">3cm</tspan></text>
<text
id="text2468"
y="287.78601"
x="79.480629"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
xml:space="preserve"><tspan
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
y="287.78601"
x="79.480629"
id="tspan2466"
sodipodi:role="line">3cm</tspan></text>
<text
id="text2472"
y="265.05231"
x="95.547218"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
xml:space="preserve"><tspan
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
y="265.05231"
x="95.547218"
id="tspan2470"
sodipodi:role="line">5cm</tspan></text>
<text
id="text2476"
y="223.19171"
x="128.44553"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
xml:space="preserve"><tspan
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
y="223.19171"
x="128.44553"
id="tspan2474"
sodipodi:role="line">10cm</tspan></text>
<text
id="text2480"
y="208.43666"
x="163.85762"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
xml:space="preserve"><tspan
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
y="208.43666"
x="163.85762"
id="tspan2478"
sodipodi:role="line">6cm</tspan></text>
<text
id="text2484"
y="194.77458"
x="173.14786"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
xml:space="preserve"><tspan
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
y="194.77458"
x="173.14786"
id="tspan2482"
sodipodi:role="line">5cm</tspan></text>
<text
id="text2488"
y="183.29843"
x="170.85262"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
xml:space="preserve"><tspan
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
y="183.29843"
x="170.85262"
id="tspan2486"
sodipodi:role="line">5cm</tspan></text>
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xml:space="preserve"><tspan
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.17499995px;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.37147501;stroke-miterlimit:4;stroke-dasharray:none"
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style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:4.23333311px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.26458332"
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x="24.623953"
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style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.26458332">Constellation de Cassiopée</tspan></text>
<text
xml:space="preserve"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:4.23333311px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.26458332;"
x="117.31223"
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sodipodi:role="line"
id="tspan2695"
x="117.31223"
y="261.92249"
style="stroke-width:0.26458332;-inkscape-font-specification:sans-serif;font-family:sans-serif;font-weight:normal;font-style:normal;font-stretch:normal;font-variant:normal;">Constellation du Scorpion</tspan></text>
<text
xml:space="preserve"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:4.23333311px;line-height:1.25;font-family:Consolas, 'Liberation Mono', Menlo, Courier, monospace;-inkscape-font-specification:'Consolas, Liberation Mono, Menlo, Courier, monospace';letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.26458332"
x="17.190306"
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sodipodi:role="line"
id="tspan2699"
x="17.190306"
y="168.36693"
style="stroke-width:0.26458332" /></text>
<flowRoot
xml:space="preserve"
id="flowRoot2703"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:16px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none"
transform="matrix(0.26458333,0,0,0.26458333,0,152.94912)"><flowRegion
id="flowRegion2705"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:sans-serif;-inkscape-font-specification:sans-serif"><rect
id="rect2707"
width="553.13354"
height="85.165001"
x="31.60763"
y="20.284359"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:sans-serif;-inkscape-font-specification:sans-serif" /></flowRegion><flowPara
id="flowPara2709"
style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold'">Constellations</flowPara><flowPara
style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold'"
id="flowPara2713" /><flowPara
id="flowPara2711">Reproduit ces 2 constellations en respectant les angles et les mesures.</flowPara></flowRoot> </g>
</svg>

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@ -2,7 +2,7 @@ Angles avec les 6e pour l'année 2017-2018
#########################################
:date: 2018-02-24
:modified: 2018-02-24
:modified: 2018-03-08
:authors: Bertrand Benjamin
:category: 6e
:tags: Geométrie, Angles
@ -12,29 +12,30 @@ Angles avec les 6e pour l'année 2017-2018
Étape 1
=======
À partir d'une "production d'élève" d'une course 24du mans. Les élèves doivent trouver les angles droits et les angles erronés. Ensuite on classe les erreurs en fonction de plus de 90° et moins de 90°.
À partir d'une `production d'élève <./24hMans_validite.pdf>`_ d'une course 24du mans. Les élèves doivent trouver les angles droits et les angles erronés.
Quand ces angles seront trouvés, il faudra réfléchir à comment les désigner sans ambigüités. Ensuite on classe les erreurs en fonction de plus de 90° et moins de 90°.
Bilan: Définition d'angle aigu et obtus. On introduit la notation d'un angle (la vraie avec les 3 lettres et le chapeau).
Bilan: `Définition d'angle aigu et obtus <./B1_voca_angle.pdf>`_ On introduit la notation d'un angle (la vraie avec les 3 lettres et le chapeau).
Étape 2
=======
Un dessin avec pleins d'angles. Les élèves cherchent les angles droits, les obtus et les aigus et les rangent par familles.
Les élèves cherchent les angles droits, les obtus et les aigus et les rangent par familles dans un superbe `space invader amoché <./E2_space_invader.pdf>`_. Les élèves peuvent commencer par marquer les angles avec des couleurs différentes puis en groupe établir la liste des angles trouvées. Il sera aussi surement nécessaire de nommer les points de la figure.
Bilan: Mesure au rapporteur d'un angle et la notion d'angle (avec les exemples)
Aux groupes les plus avancés, on pourra leur demander de classer les angles qu'ils ont trouvés en ordre croissant.
Bilan: `Mesurer au rapporteur un angle <./B2_rapporteur.pdf>`_
Étape 3
=======
Une série d'angles à classer par famille puis à mesurer et à classer en ordre croissant.
`Une série d'angles <./E3_mesure_angle.pdf>`_ à classer par famille puis à mesurer et à classer en ordre croissant.
Bilan: correspondance obtus/aigus/droit et mesure d'angle (tableau)
Bilan: `correspondance obtus/aigus/droit et mesure d'angle <./B3_mesures_angles.pdf>`_
Étape 4
=======
Double choix!
Travail de `reproduction de constellations <./E4_constellation.pdf>`_ .
- Ligne brisée à tracer avec des angles pour atteindre un objectif
- Polygones réguliers à tracer.