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b/2nd/04_Demontrastion_Geometrique/index.rst @@ -2,7 +2,7 @@ Démonstration Géométrique ######################### :date: 2021-08-25 -:modified: 2021-08-25 +:modified: 2021-10-12 :authors: Benjamin Bertrand :tags: Géométrie, Démonstration :category: 2nd @@ -11,21 +11,54 @@ Démonstration Géométrique Étape 1: Propriétés des quadrilatères ===================================== -Seul puis en groupe les élèves cherchent à énumérer toutes les propriétés possibles du quadrilatère et de ses "enfants". +.. image:: ./1P_recherche_proprietes.pdf + :height: 200px + :alt: Chercher les propriétés des quadrilatères + +Seul puis en groupe les élèves cherchent à énumérer toutes les propriétés possibles du quadrilatère et de ses "enfants". Ce travail débouche à la rédaction d'un poster A3 avec les quadrilatères et leurs propriétés. + +On ramasse le travail et on l'utilise pour illustrer en début du cours suivant comment justifier qu'une affirmation est fausse ou juste. Les élèves doivent ensuite étudier le travail de leurs camarades et justifier si les propriétés sont justes ou fausses. + +Bilan: les quadrilatères et quelques propriétés dont des fausses avec des contre-exemples. -Soit on fait la compétition de l'équipe qui trouve le plus de propriété soit on fait échanger les productions entre les groupes qui doivent ensuite confirmer que ces propriétés sont justes ou non (et donc de trouver un contre exemple). Étape 2: Exercices de géométrie =============================== +Avant cette étape, le cours sur les triangles devra avoir été complété par les élèves + +.. image:: ./0B_triangles.pdf + :height: 200px + :alt: Cours sur les triangles + 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. +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 + Étape 3: Projeté orthogonal =========================== +.. image:: ./3P_decouverte_proj_otho.pdf + :height: 200px + :alt: Activité de découverte du projeté othogonal + Découverte, définition et démonstration du projeté orthogonal sous forme d'un exercice le moins guidé possible. +Bilan: Définition du projeté orthogonal. + +.. image:: ./3B_projete_ortho.pdf + :height: 200px + :alt: Définition du projeté othogonal + + Étape 4: Exercices de géométrie =============================== Exercices divers de géométrie avec des exercices qui vont chercher des situations d'autres matières. L'accent sera mis sur la rigueur de la rédaction. + +31 p 123 : recherche d’une figure correspondant à des propriétés, projeté orthogonal et propriétés des quadrilatères, +41 p 128 : construction du projeté orthogonal, calcul d'aire utilisation du théorème de Pythagore pour calculer des longueurs, propriétés sur les quadrilatères +42 p 128 : construction du projeté orthogonal, exercice de recherche à partir d'une figure + connaissance de l'orthocentre. +BONUS : 101 p 129 : modélisation, recherche, calcul de volume