Quiz — Lycée Pilote Sfax - Similitudes 2.pdf

Question 1 sur 10 20:00

[{"id":85140,"question":"Quelle transformation géométrique conserve les distances et les angles ?","option_a":"Homothétie","option_b":"Translation","option_c":"Projection","option_d":"Symétrie axiale","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une translation est une isométrie qui conserve les distances et les angles. Elle déplace chaque point d’un vecteur fixe sans modifier les longueurs ni les angles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Homothétie\", \"b\": \"Translation\", \"c\": \"Projection\", \"d\": \"Symét","_debug_options_count":4},{"id":85141,"question":"Vrai ou Faux ? Une homothétie de rapport -2 est une similitude directe.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une homothétie de rapport négatif est une similitude indirecte, car elle inverse l’orientation de la figure.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":85142,"question":"Quel est le rapport de similitude d’une homothétie qui transforme un segment de longueur 5 en un segment de longueur 15 ?","option_a":"1\/3","option_b":"3","option_c":"5","option_d":"15","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le rapport de similitude est le facteur par lequel les distances sont multipliées. Ici, 15\/5 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"1\/3\", \"b\": \"3\", \"c\": \"5\", \"d\": \"15\"}}","_debug_options_count":4},{"id":85143,"question":"Quelle propriété n’est PAS conservée par une similitude ?","option_a":"Les angles","option_b":"Les rapports de distances","option_c":"Les aires","option_d":"L’orientation","option_e":"","option_f":"","bonne_reponse":"d","explication":"Une similitude indirecte (comme une homothétie de rapport négatif) inverse l’orientation de la figure.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"Les angles\", \"b\": \"Les rapports de distances\", \"c\": \"Les aires\", ","_debug_options_count":4},{"id":85144,"question":"Vrai ou Faux ? Toute similitude peut être décomposée en une isométrie suivie d’une homothétie.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Toute similitude peut effectivement être décomposée en une isométrie suivie d’une homothétie (ou inversement), selon la définition des similitudes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":85145,"question":"Quel est l’effet d’une rotation de 90° dans le sens direct sur un point d’affixe z = 1 + i ?","option_a":"z' = 1 - i","option_b":"z' = -1 + i","option_c":"z' = -1 - i","option_d":"z' = 1 + i","option_e":"","option_f":"","bonne_reponse":"b","explication":"Multiplier z par i (rotation de 90° dans le sens direct) donne z' = i(1 + i) = -1 + i.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"z' = 1 - i\", \"b\": \"z' = -1 + i\", \"c\": \"z' = -1 - i\", \"d\": \"z' = 1","_debug_options_count":4},{"id":85146,"question":"Quelle transformation géométrique n’est PAS une isométrie ?","option_a":"Translation","option_b":"Rotation","option_c":"Homothétie de rapport 2","option_d":"Symétrie centrale","option_e":"","option_f":"","bonne_reponse":"c","explication":"Une homothétie de rapport différent de 1 ou -1 modifie les distances et n’est donc pas une isométrie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"Translation\", \"b\": \"Rotation\", \"c\": \"Homothétie de rapport 2\", \"","_debug_options_count":4},{"id":85147,"question":"Vrai ou Faux ? Deux figures semblables ont nécessairement le même périmètre.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Deux figures semblables ont des périmètres proportionnels à leur rapport de similitude, mais pas nécessairement égaux.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":85148,"question":"Quel est le rapport de similitude d’une similitude qui transforme un cercle de rayon 4 en un cercle de rayon 12 ?","option_a":"1\/3","option_b":"3","option_c":"4","option_d":"12","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le rapport de similitude est le facteur par lequel les rayons sont multipliés. Ici, 12\/4 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"1\/3\", \"b\": \"3\", \"c\": \"4\", \"d\": \"12\"}}","_debug_options_count":4},{"id":85149,"question":"Quelle est l’image d’un point M d’affixe z par une similitude de rapport 2 et d’angle 180° ?","option_a":"z' = 2z","option_b":"z' = -2z","option_c":"z' = 2\\overline{z}","option_d":"z' = -2\\overline{z}","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une similitude de rapport 2 et d’angle 180° est une homothétie de rapport -2, donc z' = -2z.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"z' = 2z\", \"b\": \"z' = -2z\", \"c\": \"z' = 2\\\\overline{z}\", \"d\": \"z' =","_debug_options_count":4}]