Quiz — Fiche méthodes - Similitudes.pdf

Question 1 sur 10 20:00

[{"id":34940,"question":"Quelle transformation n'est PAS une similitude ?","option_a":"Une homothétie de rapport 2","option_b":"Une rotation d'angle 90°","option_c":"Une translation de vecteur u","option_d":"Une projection orthogonale sur une droite","option_e":"","option_f":"","bonne_reponse":"d","explication":"Une projection orthogonale ne conserve pas les distances ni les angles, contrairement aux similitudes qui préservent les rapports de distances.","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 homothétie de rapport 2\", \"b\": \"Une rotation d'angle 90°\", ","_debug_options_count":4},{"id":34941,"question":"Une similitude indirecte inverse l'orientation des angles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les similitudes indirectes (comme les symétries axiales) modifient l'orientation des angles, contrairement aux similitudes directes qui les conservent.","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":34942,"question":"Le rapport d'une similitude est toujours positif.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le rapport d'une similitude peut être négatif si la similitude inclut une symétrie axiale (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":34943,"question":"Si une similitude transforme A en A' et B en B', alors le rapport de la similitude est égal à :","option_a":"A'B' \/ AB","option_b":"AB \/ A'B'","option_c":"A'B' + AB","option_d":"A'B' - AB","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le rapport d'une similitude est défini comme le rapport des distances entre les points images et les points originaux (A'B' \/ AB).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A'B' \/ AB\", \"b\": \"AB \/ A'B'\", \"c\": \"A'B' + AB\", \"d\": \"A'B' - AB\"}","_debug_options_count":4},{"id":34944,"question":"La composition d'une rotation de 30° et d'une homothétie de rapport 2 est une similitude de rapport :","option_a":"2","option_b":"30","option_c":"60","option_d":"15","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le rapport de la composition est le produit des rapports (2 pour l'homothétie, 1 pour la rotation), soit 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\": \"2\", \"b\": \"30\", \"c\": \"60\", \"d\": \"15\"}}","_debug_options_count":4},{"id":34945,"question":"Toute similitude conserve les angles orientés.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Seules les similitudes directes conservent les angles orientés. Les similitudes indirectes les inversent.","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":34946,"question":"Si une similitude transforme un triangle équilatéral en un triangle rectangle, alors son rapport est :","option_a":"√2","option_b":"1\/2","option_c":"2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"b","explication":"Un triangle équilatéral transformé en triangle rectangle a ses côtés divisés par 2 (hypoténuse = côté original), donc le rapport est 1\/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\": \"√2\", \"b\": \"1\/2\", \"c\": \"2\", \"d\": \"1\"}}","_debug_options_count":4},{"id":34947,"question":"Une similitude de rapport 1 est nécessairement une isométrie.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une similitude de rapport 1 est une isométrie, mais elle peut aussi être une similitude indirecte (comme une symétrie axiale).","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":34948,"question":"Quelle propriété n'est PAS caractéristique d'une similitude ?","option_a":"Conservation des rapports de distances","option_b":"Conservation des angles","option_c":"Conservation des aires","option_d":"Transformation d'une droite en droite","option_e":"","option_f":"","bonne_reponse":"c","explication":"Les similitudes conservent les rapports de distances et transforment les droites en droites, mais elles ne conservent pas les aires (sauf si le rapport est 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"Conservation des rapports de distances\", \"b\": \"Conservation des a","_debug_options_count":4},{"id":34949,"question":"Si une similitude transforme un cercle de rayon 3 en un cercle de rayon 6, alors son rapport est :","option_a":"2","option_b":"3","option_c":"1\/2","option_d":"18","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le rapport d'une similitude est le rapport des rayons des cercles images et originaux (6 \/ 3 = 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\": \"2\", \"b\": \"3\", \"c\": \"1\/2\", \"d\": \"18\"}}","_debug_options_count":4}]