Quiz — serie Similitudes (LPTn).pdf

Question 1 sur 10 20:00

[{"id":15549,"question":"Quelle transformation n'est PAS une similitude ?","option_a":"Une homothétie","option_b":"Une rotation suivie d'une homothétie","option_c":"Une projection orthogonale","option_d":"Une translation suivie d'une homothétie","option_e":"","option_f":"","bonne_reponse":"c","explication":"La projection orthogonale ne conserve pas les angles ni les rapports de distances, contrairement aux similitudes.","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 homothétie\", \"b\": \"Une rotation suivie d'une homothétie\", \"","_debug_options_count":4},{"id":15550,"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 peut être négatif, ce qui correspond à une similitude indirecte (composée d'une homothétie et d'une symétrie).","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":15551,"question":"Si une similitude a un rapport k=2 et transforme un segment de longueur 3 en un segment de longueur...","option_a":"3","option_b":"6","option_c":"1.5","option_d":"4","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le rapport k=2 multiplie les longueurs par 2, donc 3 × 2 = 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"3\", \"b\": \"6\", \"c\": \"1.5\", \"d\": \"4\"}}","_debug_options_count":4},{"id":15552,"question":"Une similitude conserve les angles orientés.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les similitudes directes (rapport positif) conservent les angles orientés, mais les similitudes indirectes (rapport négatif) les inversent.","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":15553,"question":"Quelle est l'image d'un cercle de rayon r par une similitude de rapport k ?","option_a":"Un cercle de rayon r","option_b":"Un cercle de rayon k×r","option_c":"Un cercle de rayon r\/k","option_d":"Une ellipse","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une similitude transforme un cercle en un cercle dont le rayon est multiplié par le rapport k.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Un cercle de rayon r\", \"b\": \"Un cercle de rayon k×r\", \"c\": \"Un c","_debug_options_count":4},{"id":15554,"question":"Une translation est une similitude de rapport...","option_a":"0","option_b":"1","option_c":"2","option_d":"non défini","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une translation est une isométrie (similitude de rapport 1) car elle conserve les distances.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"2\", \"d\": \"non défini\"}}","_debug_options_count":4},{"id":15555,"question":"Si deux similitudes ont le même rapport et le même angle, elles sont égales.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Deux similitudes avec le même rapport et le même angle diffèrent éventuellement par une translation, donc ne sont pas forcément égales.","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":15556,"question":"Quelle transformation transforme un triangle équilatéral en un triangle équilatéral mais pas nécessairement superposable ?","option_a":"Une translation","option_b":"Une rotation","option_c":"Une homothétie","option_d":"Une symétrie axiale","option_e":"","option_f":"","bonne_reponse":"c","explication":"Une homothétie de rapport ≠1 transforme un triangle équilatéral en un triangle équilatéral de taille différente, sans superposition possible.","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 translation\", \"b\": \"Une rotation\", \"c\": \"Une homothétie\", \"d","_debug_options_count":4},{"id":15557,"question":"Le centre d'une similitude est toujours fixe.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Seul le centre d'une homothétie est fixe. Une similitude générale peut ne pas avoir de point fixe (exemple : translation).","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":15558,"question":"Quelle est la composée d'une rotation d'angle θ et d'une homothétie de rapport k ?","option_a":"Une translation","option_b":"Une similitude directe de rapport k et d'angle θ","option_c":"Une symétrie centrale","option_d":"Une homothétie de rapport k²","option_e":"","option_f":"","bonne_reponse":"b","explication":"La composée d'une rotation et d'une homothétie est une similitude directe de rapport k et d'angle θ.","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\", \"b\": \"Une similitude directe de rapport k et d'","_debug_options_count":4}]