Hai mặt phẳng song song

Home Lớp 11 Toán lớp 11 - Sách kết nối tri thức Bài 13. Hai mặt phẳng song song.Bài tập nâng cao

{"common":{"save":0,"post_id":"7077","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5131","post_id":"7077","mon_id":"1158924","chapter_id":"1159156","question":"Cho hình l\u0103ng tr\u1ee5 ABC.A'B'C'. G\u1ecdi H là trung \u0111i\u1ec3m c\u1ee7a A'B'. \u0110\u01b0\u1eddng th\u1eb3ng B'C song song v\u1edbi m\u1eb7t ph\u1eb3ng nào sau \u0111ây?<\/p>","options":["A.<\/strong> (AHC')","B.<\/strong> (AA'H)","C.<\/strong> (HAB)","D.<\/strong> (HA'C)"],"correct":"1","level":"3","hint":"","answer":"<svg height=\"270\" width=\"300\"> <g> <title><\/title> <rect fill=\"#fff\" height=\"272\" id=\"canvas_background\" width=\"302\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_12\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g> <title><\/title> <line fill=\"none\" id=\"svg_2\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"2\" x1=\"76.5\" x2=\"44.5\" y1=\"84\" y2=\"242\"><\/line> <line fill=\"none\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"2\" x1=\"215\" x2=\"181\" y1=\"83.25\" 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id=\"svg_9\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"2\" x1=\"147\" x2=\"181\" y1=\"84.25\" y2=\"242.25\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_10\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"2\" x1=\"276\" x2=\"146\" y1=\"24.25\" y2=\"84.25\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_11\" stroke=\"#bf0000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"3\" x1=\"183\" x2=\"276\" y1=\"242.25\" y2=\"25.25\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_13\" stroke=\"#000\" stroke-dasharray=\"5,5\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"2\" x1=\"241\" x2=\"44\" y1=\"181.25\" y2=\"242.25\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_14\" stroke=\"#ff0000\" stroke-dasharray=\"5,5\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"3\" x1=\"242\" x2=\"76\" y1=\"182.25\" y2=\"83.25\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_15\" stroke=\"#ff0000\" stroke-dasharray=\"5,5\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"3\" x1=\"115\" x2=\"241\" y1=\"242.25\" y2=\"180.25\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_16\" stroke=\"#000000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"2\" x1=\"74\" x2=\"217\" y1=\"83.25\" y2=\"84.25\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_17\" stroke=\"#000000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"2\" x1=\"276\" x2=\"212\" y1=\"24.25\" y2=\"87.25\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_18\" stroke=\"#000000\" stroke-opacity=\"null\" text-anchor=\"start\" x=\"60\" xml:space=\"preserve\" y=\"81.25\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_19\" stroke=\"#000000\" stroke-opacity=\"null\" text-anchor=\"start\" x=\"277\" xml:space=\"preserve\" y=\"26.25\">C<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_20\" stroke=\"#000000\" stroke-opacity=\"null\" text-anchor=\"start\" x=\"246\" xml:space=\"preserve\" y=\"191.25\">C'<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_21\" stroke=\"#000000\" stroke-opacity=\"null\" text-anchor=\"start\" x=\"23\" xml:space=\"preserve\" y=\"245.25\">A'<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_22\" stroke=\"#000000\" stroke-opacity=\"null\" text-anchor=\"start\" x=\"106\" xml:space=\"preserve\" y=\"260.25\">H<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_23\" stroke=\"#000000\" stroke-opacity=\"null\" text-anchor=\"start\" x=\"186\" xml:space=\"preserve\" y=\"257.25\">B'<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_24\" stroke=\"#000000\" stroke-opacity=\"null\" stroke-width=\"null\" text-anchor=\"start\" x=\"136\" xml:space=\"preserve\" y=\"80.25\">M<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_25\" stroke=\"#000000\" stroke-opacity=\"null\" stroke-width=\"null\" text-anchor=\"start\" x=\"203\" xml:space=\"preserve\" y=\"82.25\">B<\/text> <\/g> <\/svg><\/span><\/p>G\u1ecdi M là trung \u0111i\u1ec3m c\u1ee7a AB suy ra MB' \/\/ AH ⇒ MB' \/\/ (AHC') (1).<\/p>Vì MH là \u0111\u01b0\u1eddng trung bình c\u1ee7a hình bình hành ABB'A' nên MH song song và b\u1eb1ng BB'. Suy ra MH song song và b\u1eb1ng CC'. Do \u0111ó MHC'C là hình bình hành.<\/p>T\u1eeb \u0111ó suy ra MC \/\/ HC' ⇒ MC \/\/ (AHC')  (2).<\/p>T\u1eeb (1) và (2) suy ra (B'MC) \/\/ (AHC') ⇒ B'C \/\/ (AHC').<\/p>Ch\u1ecdn A.<\/strong> (AHC').<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-02-17 02:35:57","option_type":"txt","len":1},{"id":"5132","post_id":"7077","mon_id":"1158924","chapter_id":"1159156","question":"Cho hình l\u0103ng tr\u1ee5 ABC.A'B'C'. G\u1ecdi H là trung \u0111i\u1ec3m c\u1ee7a A'B'. \u0110\u01b0\u1eddng th\u1eb3ng B'C song song v\u1edbi m\u1eb7t ph\u1eb3ng nào sau \u0111ây?<\/p>","options":["A.<\/strong> CB","B.<\/strong> CB'","C.<\/strong> BB'","D.<\/strong> BA'"],"correct":"2","level":"3","hint":"","answer":"<svg height=\"270\" width=\"300\"> <g> <title><\/title> <rect fill=\"#fff\" height=\"272\" id=\"canvas_background\" width=\"302\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_12\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g> <title><\/title> <line fill=\"none\" id=\"svg_2\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"2\" x1=\"76.5\" x2=\"44.5\" y1=\"84\" y2=\"242\"><\/line> <line fill=\"none\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"2\" x1=\"215\" x2=\"181\" y1=\"83.25\" y2=\"242.25\"><\/line> <line fill=\"none\" id=\"svg_4\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"2\" x1=\"78\" x2=\"276\" y1=\"82.25\" y2=\"25.25\"><\/line> <line fill=\"none\" id=\"svg_5\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"2\" x1=\"45\" x2=\"183\" y1=\"242.25\" y2=\"242.25\"><\/line> <line fill=\"none\" id=\"svg_6\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"2\" x1=\"275\" x2=\"241\" y1=\"26.25\" y2=\"183.25\"><\/line> <line fill=\"none\" id=\"svg_7\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"2\" x1=\"182\" x2=\"242\" y1=\"243.25\" y2=\"181.25\"><\/line> <line fill=\"none\" id=\"svg_8\" stroke=\"#ff0000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"3\" x1=\"77\" x2=\"114\" y1=\"83.25\" y2=\"244.25\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_9\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"2\" x1=\"147\" x2=\"181\" y1=\"84.25\" y2=\"242.25\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_10\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"2\" x1=\"276\" x2=\"146\" y1=\"24.25\" y2=\"84.25\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_11\" stroke=\"#bf0000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"3\" x1=\"183\" x2=\"276\" y1=\"242.25\" y2=\"25.25\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_13\" stroke=\"#000\" stroke-dasharray=\"5,5\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"2\" x1=\"241\" x2=\"44\" y1=\"181.25\" y2=\"242.25\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_14\" stroke=\"#ff0000\" stroke-dasharray=\"5,5\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"3\" x1=\"242\" x2=\"76\" y1=\"182.25\" y2=\"83.25\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_15\" stroke=\"#ff0000\" stroke-dasharray=\"5,5\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"3\" x1=\"115\" x2=\"241\" y1=\"242.25\" y2=\"180.25\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_16\" stroke=\"#000000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"2\" x1=\"74\" x2=\"217\" y1=\"83.25\" y2=\"84.25\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_17\" stroke=\"#000000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"2\" x1=\"276\" x2=\"212\" y1=\"24.25\" y2=\"87.25\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_18\" stroke=\"#000000\" stroke-opacity=\"null\" text-anchor=\"start\" x=\"60\" xml:space=\"preserve\" y=\"81.25\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_19\" stroke=\"#000000\" stroke-opacity=\"null\" text-anchor=\"start\" x=\"277\" xml:space=\"preserve\" y=\"26.25\">C<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_20\" stroke=\"#000000\" stroke-opacity=\"null\" text-anchor=\"start\" x=\"246\" xml:space=\"preserve\" y=\"191.25\">C'<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_21\" stroke=\"#000000\" stroke-opacity=\"null\" text-anchor=\"start\" x=\"23\" xml:space=\"preserve\" y=\"245.25\">A'<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_22\" stroke=\"#000000\" stroke-opacity=\"null\" text-anchor=\"start\" x=\"106\" xml:space=\"preserve\" y=\"260.25\">H<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_23\" stroke=\"#000000\" stroke-opacity=\"null\" text-anchor=\"start\" x=\"186\" xml:space=\"preserve\" y=\"257.25\">B'<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_24\" stroke=\"#000000\" stroke-opacity=\"null\" stroke-width=\"null\" text-anchor=\"start\" x=\"136\" xml:space=\"preserve\" y=\"80.25\">M<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_25\" stroke=\"#000000\" stroke-opacity=\"null\" stroke-width=\"null\" text-anchor=\"start\" x=\"203\" xml:space=\"preserve\" y=\"82.25\">B<\/text> <\/g> <\/svg><\/span><\/p>G\u1ecdi M là trung \u0111i\u1ec3m c\u1ee7a AB suy ra MB' \/\/ AH ⇒ MB' \/\/ (AHC') (1).<\/p>Vì MH là \u0111\u01b0\u1eddng trung bình c\u1ee7a hình bình hành ABB'A' nên MH song song và b\u1eb1ng BB'. Suy ra MH song song và b\u1eb1ng CC'. Do \u0111ó MHC'C là hình bình hành.<\/p>T\u1eeb \u0111ó suy ra MC \/\/ HC' ⇒ MC \/\/ (AHC')  (2).<\/p>T\u1eeb (1) và (2) suy ra (B'MC) \/\/ (AHC') ⇒ B'C \/\/ (AHC').<\/p>Ch\u1ecdn B.<\/strong> CB'.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-02-17 02:37:22","option_type":"txt","len":0},{"id":"5133","post_id":"7077","mon_id":"1158924","chapter_id":"1159156","question":"Cho hình l\u0103ng tr\u1ee5 ABC.A'B'C'. Trong các kh\u1eb3ng \u0111\u1ecbnh sau, kh\u1eb3ng \u0111\u1ecbnh nào sai<\/strong>?<\/p>","options":["A.<\/strong> (ABC) \/\/ (A'B'C')","B.<\/strong> AA' \/\/ (BCC')","C.<\/strong> AB \/\/ (A'B'C')","D.<\/strong> AA'B'B là hình ch\u1eef nh\u1eadt"],"correct":"4","level":"3","hint":"","answer":"M\u1eb7t bên AA'B'B là hình bình hành. Nó là hình ch\u1eef nh\u1eadt n\u1ebfu ABC.A'B'C' là hình l\u0103ng tr\u1ee5 \u0111\u1ee9ng.<\/p>Kh\u1eb3ng \u0111\u1ecbnh sai <\/strong>là  <\/span>D.<\/strong> AA'B'B là hình ch\u1eef nh\u1eadt.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-02-17 02:43:13","option_type":"txt","len":2}]}