Quiz — magazine25-similitudes.pdf

Question 1 sur 10 20:00

[{"id":17329,"question":"Quelle transformation conserve les distances mais pas nécessairement les angles ?","option_a":"Une rotation","option_b":"Une translation","option_c":"Une homothétie","option_d":"Une symétrie axiale","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une translation conserve les distances et les angles, mais ne modifie pas l'orientation des figures. Les homothéties et symétries axiales modifient les angles ou l'orientation.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Une rotation\", \"b\": \"Une translation\", \"c\": \"Une homothétie\", \"d","_debug_options_count":4},{"id":17330,"question":"Une similitude de rapport 2 multiplie les distances par 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une similitude de rapport k multiplie les distances par |k|, mais conserve les angles. Ici, le rapport est 2, donc les distances sont multipliées par 2.","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":17331,"question":"Quelle est la nature d'une transformation qui associe à tout point M du plan le point M' tel que MM' = 2*AB et MM' est parallèle à AB ?","option_a":"Une translation de vecteur AB","option_b":"Une homothétie de centre A et de rapport 2","option_c":"Une rotation d'angle 90° autour de A","option_d":"Une symétrie centrale de centre B","option_e":"","option_f":"","bonne_reponse":"b","explication":"Cette transformation est une homothétie de centre A et de rapport 2, car elle conserve les directions et multiplie les distances par 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Une translation de vecteur AB\", \"b\": \"Une homothétie de centre A","_debug_options_count":4},{"id":17332,"question":"Deux triangles sont semblables si leurs angles sont égaux deux à deux.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Deux triangles sont semblables si leurs angles sont égaux deux à deux (critère d'angle-angle-angle). Cette propriété est caractéristique 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":17333,"question":"Quelle transformation ne conserve pas les angles ?","option_a":"Une rotation","option_b":"Une translation","option_c":"Une homothétie","option_d":"Une projection orthogonale","option_e":"","option_f":"","bonne_reponse":"d","explication":"Une projection orthogonale ne conserve pas les angles, contrairement aux rotations, translations et homothéties qui préservent les angles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"Une rotation\", \"b\": \"Une translation\", \"c\": \"Une homothétie\", \"d","_debug_options_count":4},{"id":17334,"question":"Le rapport de similitude entre deux figures est toujours positif.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le rapport de similitude peut être négatif si la similitude inverse l'orientation des figures (similitude indirecte).","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":17335,"question":"Quelle est la transformation qui associe à un point M son symétrique par rapport à une droite D ?","option_a":"Une rotation","option_b":"Une translation","option_c":"Une symétrie axiale","option_d":"Une homothétie","option_e":"","option_f":"","bonne_reponse":"c","explication":"La symétrie axiale par rapport à une droite D est la transformation qui associe à tout point M son symétrique M' par rapport à D.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"Une rotation\", \"b\": \"Une translation\", \"c\": \"Une symétrie axiale","_debug_options_count":4},{"id":17336,"question":"Une homothétie de rapport -1 est équivalente à une symétrie centrale.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une homothétie de rapport -1 est effectivement équivalente à une symétrie centrale, car elle inverse l'orientation et conserve les distances à un facteur près.","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":17337,"question":"Quelle transformation conserve les rapports de distances mais pas les angles ?","option_a":"Une rotation","option_b":"Une translation","option_c":"Une homothétie","option_d":"Une projection","option_e":"","option_f":"","bonne_reponse":"d","explication":"Une projection conserve les rapports de distances le long d'une droite, mais ne conserve pas les angles entre les droites.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"Une rotation\", \"b\": \"Une translation\", \"c\": \"Une homothétie\", \"d","_debug_options_count":4},{"id":17338,"question":"Deux cercles de rayons différents sont toujours semblables.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Tous les cercles sont semblables, car ils ont la même forme (angles égaux) et ne diffèrent que par leur taille (rapport de similitude égal au rapport des rayons).","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}]