From 4868cdfdf6465da961181ed8de5cabc99315a329 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Sat, 15 Jan 2022 14:29:53 +0100 Subject: [PATCH] Feat: exercices pour 3E --- 2nd/10_Geometrie_reperee/exercises.tex | 41 +++++++++++++++--- .../fig/deux_triangles.png | Bin 0 -> 33361 bytes 2 files changed, 34 insertions(+), 7 deletions(-) create mode 100644 2nd/10_Geometrie_reperee/fig/deux_triangles.png diff --git a/2nd/10_Geometrie_reperee/exercises.tex b/2nd/10_Geometrie_reperee/exercises.tex index 4312b4c..1cb6ef3 100644 --- a/2nd/10_Geometrie_reperee/exercises.tex +++ b/2nd/10_Geometrie_reperee/exercises.tex @@ -81,6 +81,8 @@ \end{enumerate} \end{exercise} + +% ---- étape 2 \begin{exercise}[subtitle={Distance sur une droite}, step={2}, origin={dMeedC}, topics={Géométrie repérée}, tags={Coordonnées, distance}] On considère une droite munie d'un repère et deux points $A$ et $B$ de cette droite. @@ -165,18 +167,14 @@ \end{tikzpicture} \end{solution} - \begin{exercise}[subtitle={Distance entre deux poins - bilan}, mode={En groupe} step={2}, origin={dMeedC}, topics={Géométrie repérée}, tags={Coordonnées, distance}] Proposer une formule pour calculer le distance entre deux points du plan. Vous illustrerez la formule avec un dessin et vous l'appliquerez à un exemple de votre choix. \end{exercise} \begin{exercise}[subtitle={Exercice technique}, step={2}, origin={dMeedC}, topics={Géométrie repérée}, tags={Coordonnées, distance}] - Soit les points $M(3; -2)$, $N(-2; -3)$ et $P(-4; 3)$. - \begin{enumerate} - \item Placer ces points dans un repère. - \item Calculer les distance $MN$, $MP$ et $NP$. - \item Le triangle $MNP$ est-il rectangle? - \end{enumerate} + Soit les points $M(3; -2)$, $N(-2; -3)$ et $P(-4; 3)$. \begin{enumerate} + \item Placer ces points dans un repère. \item Calculer les distance $MN$, +$MP$ et $NP$. \item Le triangle $MNP$ est-il rectangle? \end{enumerate} \end{exercise} \begin{exercise}[subtitle={Quadriltère}, step={2}, origin={Sesamath 60p125}, topics={Géométrie Repérée}, tags={Coordonnées, distance}] @@ -184,3 +182,32 @@ Déterminer la nature du quadrilatère $BACD$. \end{exercise} + +% ---- étape 3 + +\begin{exercise}[subtitle={BEAU triangle}, step={3}, origin={dMeedC}, topics={Géométrie repérée}, tags={Coordonnées, milieu, distance}] + Soit $B(3; 2)$, $E(-1; -2)$, $A(-3; 0)$ et $U(1; 4)$ quatre points du plan. + \begin{enumerate} + \item Calculer les coordonnées du milieu de $[BA]$ + \item Calculer les coordonnées du milieu de $[EU]$ + \item Déterminer la nature du triangle $BEA$. + \item En déduire que $BEAU$ est un rectangle. + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Presque}, step={3}, origin={dMeedC}, topics={Géométrie repérée}, tags={Coordonnées, milieu, distance}] + On a tracer la figure ci-dessous avec géogébra. + + \begin{center} + \includegraphics[scale=0.5]{./fig/deux_triangles} + \end{center} + \begin{multicols}{2} + \begin{enumerate} + \item Démontrer que $AC = \sqrt{\np{50 000}}$ + \item Le triangle $ABC$ est-il rectangle? + \item Le triangle $ACD$ est-il rectangle? + \item Peut-on affirmer que $ABCD$ est un carré? + \end{enumerate} + \end{multicols} + +\end{exercise} diff --git 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