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zXt%3$uy~(i;preX_NlK`=Ak3-;l6m}kS*B=Pv_ST-gy)ip0a-cR+sC+(6B>q(X)f$PEc zpV*sw3971We*`qQf1qO3Z>>*x-MvYjZ5Ye=wLf>gQm9PoassI zvqAV&a5w4E_uCAtj=2I%EpIHr4b4JRwXDW_PH@+%jWs6SwwmATD; z`eC&=#oEGspoenS%2Q_VkqCQGb5d+szMCxg4qm>kNbWuw33i`Te9VALmSp)K)B{VDl(!SsD;fQP}k6FhLIkQ79u0iquuY?^!Mim8tF#W-@1;O2`v2^x&r zT8!Q8XSuC@IK`%2evrqTQwnwkLSwR97@M&c$Dx}P%_=^tD{&lB^IaP3#)(gU_y~`s z6Xd}+MUtK0T&m)&U=XY5K$>U{8{&RF-zc;?pY!JzztNs+D{vwF%JKZg$A~*l$**rI zB^wQt#t1`4dg)jU^Lo!%$hxuMtX`x@d)sOApGVatDLgHYQ&fDB$lmlKmEV!f@t1Nh z!c;bDFFK_5_saTIQ14Ce4Z^%U+l^H4>=*XmVedqWeguhvSN4FP(*+j(_s0t&Vgrd` UH2ww1D}, step={1}, origin={<++>}, topics={ Demontrastion Geometrique }, tags={ Géométrie, Démonstration }] - <++> +\begin{exercise}[subtitle={Triangle rectange}, step={2}, origin={Magnard 2nd 26p123}, topics={ Demontrastion Geometrique }, tags={ Géométrie, Démonstration }] + Dans un triangle $ABC$, on a : $AB = 9$, $BC = 12$ et $AC = 15$. + \begin{enumerate} + \item Démontrer que $ABC$ est un triangle rectangle. + \item Calculer le périmètre puis l'aire du triangle. + \end{enumerate} \end{exercise} -\begin{solution} - <++> -\end{solution} -\collectexercisesstop{banque} + +\begin{exercise}[subtitle={Carré inscrit}, step={2}, origin={Magnard 2nd 47p 124}, topics={ Demontrastion Geometrique }, tags={ Géométrie, Démonstration }] + On considère un carré $ABCD$ de centre $0$ et de côté $4cm$ et un disque de centre $0$ passant par les quatre sommets du carré. + \begin{enumerate} + \item Calculer l'aire du carré. + \item Calculer le rayon du disque. + \item Calculer l'aire du disque. + \item En déduire la proportion de l'aire du disque qui n'est pas dans le carré. + \end{enumerate} +\end{exercise} + + +\begin{exercise}[subtitle={Carré inscrit}, step={2}, origin={Magnard 2nd 82p127}, topics={ Demontrastion Geometrique }, tags={ Géométrie, Démonstration }] + \begin{minipage}{0.6\linewidth} + On considère la figure ci-contre. + + On sait que les points $A$, $B$, $C$ et $D$ sont sur le cercle de centre $O$, que $(CD)$ coupe $(AB)$ en angle droit et $[OB]$ en sont milieu. + + + \begin{enumerate} + \item Compléter la figure avec éléments du texte. + \item Quelle est la médiatrice du segment $[OB]$? + \item Expliquer pourquoi $OD = DB = OB$. + \item Quelle est la nature du quadrilatère $ODBC$ + \end{enumerate} + \end{minipage} + \hfill + \begin{minipage}{0.4\linewidth} + \definecolor{uuuuuu}{rgb}{0.26666666666666666,0.26666666666666666,0.26666666666666666} + \definecolor{ududff}{rgb}{0.30196078431372547,0.30196078431372547,1} + \begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,scale=0.4] + \clip(-14.06647017330993,-4.5399522546746125) rectangle (-1.0197835656300533,9.036755996442249); + \draw [line width=2pt] (-7.26,1.79) circle (4.932220595228888cm); + \draw [line width=2pt,domain=-14.06647017330993:-1.0197835656300533] plot(\x,{(--25.0116--2.38*\x)/4.32}); + \draw [line width=2pt,domain=-14.06647017330993:-1.0197835656300533] plot(\x,{(--14.9396--4.32*\x)/-2.38}); + \draw [fill=ududff] (-7.26,1.79) circle (2.5pt); + \draw[color=ududff] (-7.271320898476661,2.472641796953316) node {$O$}; + \draw [fill=ududff] (-2.94,4.17) circle (2.5pt); + \draw[color=ududff] (-2.80011267563637,4.946076132992624) node {$B$}; + \draw [fill=uuuuuu] (-11.58,-0.59) circle (2pt); + \draw[color=uuuuuu] (-11.416361956124955,0.14870074496033941) node {$A$}; + \draw [fill=uuuuuu] (-7.161140461006964,6.721229744348776) circle (2pt); + \draw[color=uuuuuu] (-6.9451537332846645,7.297197782084933) node {$C$}; + \draw [fill=uuuuuu] (-3,-0.7612297443487751) circle (2pt); + \draw[color=uuuuuu] (-2.4,-0.40850149557598825) node {$D$}; + \end{tikzpicture} + \end{minipage} +\end{exercise} diff --git a/2nd/04_Demontrastion_Geometrique/index.rst b/2nd/04_Demontrastion_Geometrique/index.rst index 0044c94..9a95c62 100644 --- a/2nd/04_Demontrastion_Geometrique/index.rst +++ b/2nd/04_Demontrastion_Geometrique/index.rst @@ -2,7 +2,7 @@ Démonstration Géométrique ######################### :date: 2021-08-25 -:modified: 2021-10-12 +:modified: 2021-10-18 :authors: Benjamin Bertrand :tags: Géométrie, Démonstration :category: 2nd @@ -33,6 +33,11 @@ Avant cette étape, le cours sur les triangles devra avoir été complété par Exercices divers de géométrie. Le but est que les élèves résolvent ces exercices et que petit à petit, on arrive à définir et pratique les attentes en terme de rédaction. +.. image:: ./2E_demonstration.pdf + :height: 200px + :alt: Exercices simples de géométrie pour mettre l'accent sur la démonstration + + 26 p 123 : utilisation de la réciproque de Pythagore et calcul d’aire de triangle 47 p 124 : calculs d’aires et de longueurs dans des quadrilatères et propriétés des carrés 82 p 127 : propriétés des quadrilatères + cercles + médiatrice