Bài tập cuối chương 4 - Bài tập nâng cao

Home Lớp 8 Toán lớp 8 - Sách Kết nối tri thức Bài tập cuối chương 4Bài tập nâng cao

{"common":{"save":0,"post_id":"6588","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"6304","post_id":"6588","mon_id":"1158921","chapter_id":"1158932","question":"Cho t\u1ee9 giác ABCD có M, N, P, Q l\u1ea7n l\u01b0\u1ee3t là trung \u0111i\u1ec3m c\u1ee7a AB, BC, CD, DA. T\u1ee9 giác MNPQ là hình gì?<\/p>","options":["A.<\/strong> Hình bình hành","B.<\/strong> Hình thang cân","C.<\/strong> Hình thoi","D.<\/strong> Hình vuông"],"correct":"1","level":"3","hint":"","answer":"<svg height=\"230\" width=\"230\"> <g> <title><\/title> <rect fill=\"#fff\" height=\"232\" id=\"canvas_background\" width=\"232\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_1\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g> <title><\/title> <g id=\"svg_34\"> <g id=\"svg_25\"> <g id=\"svg_23\"> <g id=\"svg_14\"> <g id=\"svg_7\"> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"55.31535\" x2=\"199.31535\" y1=\"41.52273\" y2=\"41.52273\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_4\" stroke=\"#000\" stroke-linecap=\"null\" 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stroke-width=\"1.5\" x1=\"22.31535\" x2=\"198.31535\" y1=\"119.52273\" y2=\"42.52273\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_10\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"126.31535\" x2=\"198.31535\" y1=\"42.52274\" y2=\"124.52274\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_11\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"55.31535\" x2=\"198.31535\" y1=\"42.52274\" y2=\"197.52274\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_12\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"127.31535\" x2=\"38.31535\" y1=\"41.52273\" y2=\"81.52273\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_13\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" 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id=\"svg_18\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"4.31535\" xml:space=\"preserve\" y=\"127.52273\">D<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_19\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"123.31535\" xml:space=\"preserve\" y=\"35.52273\">M<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_20\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"204.31535\" xml:space=\"preserve\" y=\"127.52273\">N<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_21\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"96.31535\" xml:space=\"preserve\" y=\"173.52273\">P<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_22\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"19.31535\" xml:space=\"preserve\" y=\"78.52273\">Q<\/text> <\/g> <rect fill=\"none\" height=\"214\" id=\"svg_24\" stroke-width=\"1.5\" width=\"281\" x=\"7.31535\" y=\"10.52273\"><\/rect> <\/g> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"16\" id=\"svg_26\" stroke=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"matrix(0.8078423142433167,0,0,1,15.241053287032173,0) \" x=\"85.50467\" xml:space=\"preserve\" y=\"45.52273\">|<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"16\" id=\"svg_27\" stroke-width=\"0\" text-anchor=\"start\" x=\"157.31535\" xml:space=\"preserve\" y=\"45.52273\">|<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"16\" id=\"svg_28\" stroke-width=\"0\" text-anchor=\"start\" x=\"194.31535\" xml:space=\"preserve\" y=\"90.52273\">=<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"16\" id=\"svg_29\" stroke-width=\"0\" text-anchor=\"start\" x=\"194.31535\" xml:space=\"preserve\" y=\"162.52273\">=<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"16\" id=\"svg_30\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(17 61.769889831543054,137.06819152832028) \" x=\"56.31535\" xml:space=\"preserve\" y=\"142.52273\">X<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"16\" id=\"svg_31\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(17 156.76989746093741,180.06819152832034) \" x=\"151.31535\" xml:space=\"preserve\" y=\"185.52273\">X<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"14\" id=\"svg_32\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-64 30.776992797851584,96.52273559570314) \" x=\"25.31535\" xml:space=\"preserve\" y=\"101.52273\">|||<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"14\" id=\"svg_33\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-64 46.776992797851555,60.52273559570312) \" x=\"41.31535\" xml:space=\"preserve\" y=\"65.52273\">|||<\/text> <\/g> <\/g> <\/svg><\/span><\/p>Xét tam giác ABC có M là trung \u0111i\u1ec3m c\u1ee7a AB, N là trung \u0111i\u1ec3m c\u1ee7a BC.<\/p>Suy ra MN là \u0111\u01b0\u1eddng trung bình c\u1ee7a tam giác ABC.<\/p>Suy ra MN \/\/ AC ; MN = $\\dfrac{1}{2}$<\/span>AC   (1)<\/p>Xét tam giác ADC có P là trung \u0111i\u1ec3m c\u1ee7a CD, Q là trung \u0111i\u1ec3m c\u1ee7a DA<\/p>Suy ra PQ là \u0111\u01b0\u1eddng trung bình c\u1ee7a tam giác ADC <\/p>Suy ra PQ \/\/ AC ; PQ =  $\\dfrac{1}{2}$<\/span>AC   (2)<\/p>T\u1eeb (1) và (2) suy ra MN \/\/ PQ ( \/\/ AC) ; MN = PQ = ( $\\dfrac{1}{2}$<\/span>AC )<\/p>Suy ra t\u1ee9 giác MNPQ là hình bình hành.<\/p>(T\u1ee9 giác có hai c\u1ea1nh \u0111\u1ed1i v\u1eeba song song v\u1eeba b\u1eb1ng nhau là hình bình hành).<\/p>\u0110áp án \u0111úng   A.<\/strong> Hình bình hành.<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-08-13 02:32:11","option_type":"txt","len":2},{"id":"6307","post_id":"6588","mon_id":"1158921","chapter_id":"1158932","question":"Cho t\u1ee9 giác ABCD có M, N, P, Q l\u1ea7n l\u01b0\u1ee3t là trung \u0111i\u1ec3m c\u1ee7a AB, BC, CD, DA. T\u1ee9 giác ABCD c\u1ea7n có thêm \u0111i\u1ec1u ki\u1ec7n gì \u0111\u1ec3 t\u1ee9 giác MNPQ là hình thoi?<\/p>","options":["A.<\/strong> AB = CD","B.<\/strong> AC = BD","C.<\/strong> AB \/\/ CD","D.<\/strong> AD \/\/ BC"],"correct":"2","level":"3","hint":"","answer":"<svg height=\"230\" width=\"230\"> <g> <title><\/title> <rect fill=\"#fff\" height=\"232\" id=\"canvas_background\" width=\"232\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_1\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g> <title><\/title> <g id=\"svg_34\"> <g id=\"svg_25\"> <g id=\"svg_23\"> <g id=\"svg_14\"> <g id=\"svg_7\"> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"55.31535\" x2=\"199.31535\" y1=\"41.52273\" y2=\"41.52273\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_4\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"55.31535\" x2=\"23.31535\" y1=\"41.52273\" y2=\"118.52273\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_5\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"23\" x2=\"199\" y1=\"118.52273\" y2=\"198.52273\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_6\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"199\" x2=\"199.31535\" y1=\"41.52273\" y2=\"199\"><\/line> <\/g> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_8\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"38.31535\" x2=\"110.31534\" y1=\"80.52274\" y2=\"158.52274\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_9\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"22.31535\" x2=\"198.31535\" y1=\"119.52273\" y2=\"42.52273\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_10\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"126.31535\" x2=\"198.31535\" y1=\"42.52274\" y2=\"124.52274\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_11\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"55.31535\" x2=\"198.31535\" y1=\"42.52274\" y2=\"197.52274\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_12\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"127.31535\" x2=\"38.31535\" y1=\"41.52273\" y2=\"81.52273\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_13\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"198.31535\" x2=\"110.31535\" y1=\"123.52273\" y2=\"158.52273\"><\/line> <\/g> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_15\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"39.31535\" xml:space=\"preserve\" y=\"38.52273\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_16\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"201.31535\" xml:space=\"preserve\" y=\"34.52273\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_17\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"199.31535\" xml:space=\"preserve\" y=\"210.52273\">C<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_18\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"4.31535\" xml:space=\"preserve\" y=\"127.52273\">D<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_19\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"123.31535\" xml:space=\"preserve\" y=\"35.52273\">M<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_20\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"204.31535\" xml:space=\"preserve\" y=\"127.52273\">N<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_21\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"96.31535\" xml:space=\"preserve\" y=\"173.52273\">P<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_22\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"19.31535\" xml:space=\"preserve\" y=\"78.52273\">Q<\/text> <\/g> <rect fill=\"none\" height=\"214\" id=\"svg_24\" stroke-width=\"1.5\" width=\"281\" x=\"7.31535\" y=\"10.52273\"><\/rect> <\/g> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"16\" id=\"svg_26\" stroke=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"matrix(0.8078423142433167,0,0,1,15.241053287032173,0) \" x=\"85.50467\" xml:space=\"preserve\" y=\"45.52273\">|<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"16\" id=\"svg_27\" stroke-width=\"0\" text-anchor=\"start\" x=\"157.31535\" xml:space=\"preserve\" y=\"45.52273\">|<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"16\" id=\"svg_28\" stroke-width=\"0\" text-anchor=\"start\" x=\"194.31535\" xml:space=\"preserve\" y=\"90.52273\">=<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"16\" id=\"svg_29\" stroke-width=\"0\" text-anchor=\"start\" x=\"194.31535\" xml:space=\"preserve\" y=\"162.52273\">=<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"16\" id=\"svg_30\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(17 61.769889831543054,137.06819152832028) \" x=\"56.31535\" xml:space=\"preserve\" y=\"142.52273\">X<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"16\" id=\"svg_31\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(17 156.76989746093741,180.06819152832034) \" x=\"151.31535\" xml:space=\"preserve\" y=\"185.52273\">X<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"14\" id=\"svg_32\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-64 30.776992797851584,96.52273559570314) \" x=\"25.31535\" xml:space=\"preserve\" y=\"101.52273\">|||<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"14\" id=\"svg_33\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-64 46.776992797851555,60.52273559570312) \" x=\"41.31535\" xml:space=\"preserve\" y=\"65.52273\">|||<\/text> <\/g> <\/g> <\/svg><\/span><\/p>Xét tam giác ABC có M là trung \u0111i\u1ec3m c\u1ee7a AB, N là trung \u0111i\u1ec3m c\u1ee7a BC<\/p>Suy ra MN là \u0111\u01b0\u1eddng trung bình c\u1ee7a tam giác ABC <\/p>Suy ra MN \/\/ AC ; MN = $\\dfrac{1}{2}$<\/span>AC   (1)<\/p>Xét tam giác ADC có P là trung \u0111i\u1ec3m c\u1ee7a CD, Q là trung \u0111i\u1ec3m c\u1ee7a DA<\/p>Suy ra PQ là \u0111\u01b0\u1eddng trung bình c\u1ee7a tam giác ADC <\/p>Suy ra PQ \/\/ AC ; PQ =  $\\dfrac{1}{2}$<\/span>AC   (2)<\/p>T\u1eeb (1) và (2) suy ra MN \/\/ PQ ( \/\/ AC) ; MN = PQ = ( $\\dfrac{1}{2}$<\/span>AC )<\/p>Suy ra t\u1ee9 giác MNPQ là hình bình hành .<\/p>(T\u1ee9 giác có hai c\u1ea1nh \u0111\u1ed1i v\u1eeba song song v\u1eeba b\u1eb1ng nhau là hình bình hành).<\/p>Xét tam giác ABD có M là trung \u0111i\u1ec3m c\u1ee7a AB, Q là trung \u0111i\u1ec3m c\u1ee7a AD<\/p>Suy ra MQ là \u0111\u01b0\u1eddng trung bình c\u1ee7a tam giác ABD <\/p>Suy ra MQ =  $\\dfrac{1}{2}$<\/span>BD  <\/p>\u0110\u1ec3 hình bình hành MNPQ là hình thoi thì <\/p>MN = MQ  (hình bình hành có hai c\u1ea1nh k\u1ec1 b\u1eb1ng nhau là hình thoi).<\/p>hay  $\\dfrac{1}{2}$<\/span>AC = $\\dfrac{1}{2}$<\/span>BD suy ra AC = BD.<\/p>\u0110áp án \u0111úng là   B.<\/strong> AC = BD.<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-08-13 02:38:40","option_type":"txt","len":1},{"id":"6309","post_id":"6588","mon_id":"1158921","chapter_id":"1158932","question":"Cho t\u1ee9 giác ABCD có M, N, P, Q l\u1ea7n l\u01b0\u1ee3t là trung \u0111i\u1ec3m c\u1ee7a AB, BC, CD, DA. T\u1ee9 giác ABCD c\u1ea7n có thêm \u0111i\u1ec1u ki\u1ec7n gì \u0111\u1ec3 t\u1ee9 giác MNPQ là hình ch\u1eef nh\u1eadt?<\/p>","options":["A.<\/strong> AC = BC","B.<\/strong> AB = DC","C.<\/strong> AB $\\bot$<\/span> BC","D.<\/strong> AC $\\bot$<\/span> BD"],"correct":"4","level":"3","hint":"","answer":"<svg height=\"230\" width=\"230\"> <g> <title><\/title> <rect fill=\"#fff\" height=\"232\" id=\"canvas_background\" width=\"232\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_1\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g> <title><\/title> <g id=\"svg_34\"> <g id=\"svg_25\"> <g id=\"svg_23\"> <g id=\"svg_14\"> <g id=\"svg_7\"> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"55.31535\" x2=\"199.31535\" y1=\"41.52273\" y2=\"41.52273\"><\/line> <line 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stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"198.31535\" x2=\"110.31535\" y1=\"123.52273\" y2=\"158.52273\"><\/line> <\/g> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_15\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"39.31535\" xml:space=\"preserve\" y=\"38.52273\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_16\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"201.31535\" xml:space=\"preserve\" y=\"34.52273\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_17\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"199.31535\" xml:space=\"preserve\" y=\"210.52273\">C<\/text> <text fill=\"#000000\" 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xml:space=\"preserve\" y=\"173.52273\">P<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_22\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"19.31535\" xml:space=\"preserve\" y=\"78.52273\">Q<\/text> <\/g> <rect fill=\"none\" height=\"214\" id=\"svg_24\" stroke-width=\"1.5\" width=\"281\" x=\"7.31535\" y=\"10.52273\"><\/rect> <\/g> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"16\" id=\"svg_26\" stroke=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"matrix(0.8078423142433167,0,0,1,15.241053287032173,0) \" x=\"85.50467\" xml:space=\"preserve\" y=\"45.52273\">|<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"16\" id=\"svg_27\" stroke-width=\"0\" text-anchor=\"start\" x=\"157.31535\" xml:space=\"preserve\" y=\"45.52273\">|<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"16\" id=\"svg_28\" stroke-width=\"0\" text-anchor=\"start\" x=\"194.31535\" xml:space=\"preserve\" y=\"90.52273\">=<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"16\" id=\"svg_29\" stroke-width=\"0\" text-anchor=\"start\" x=\"194.31535\" xml:space=\"preserve\" y=\"162.52273\">=<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"16\" id=\"svg_30\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(17 61.769889831543054,137.06819152832028) \" x=\"56.31535\" xml:space=\"preserve\" y=\"142.52273\">X<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"16\" id=\"svg_31\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(17 156.76989746093741,180.06819152832034) \" x=\"151.31535\" xml:space=\"preserve\" y=\"185.52273\">X<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"14\" id=\"svg_32\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-64 30.776992797851584,96.52273559570314) \" x=\"25.31535\" xml:space=\"preserve\" y=\"101.52273\">|||<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"14\" id=\"svg_33\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-64 46.776992797851555,60.52273559570312) \" x=\"41.31535\" xml:space=\"preserve\" y=\"65.52273\">|||<\/text> <\/g> <\/g> <\/svg><\/span><\/p>Xét tam giác ABC có M là trung \u0111i\u1ec3m c\u1ee7a AB, N là trung \u0111i\u1ec3m c\u1ee7a BC<\/p>suy ra MN là \u0111\u01b0\u1eddng trung bình c\u1ee7a tam giác ABC <\/p>suy ra MN \/\/ AC ; MN = $\\dfrac{1}{2}$<\/span>AC   (1)<\/p>Xét tam giác ADC có P là trung \u0111i\u1ec3m c\u1ee7a CD, Q là trung \u0111i\u1ec3m c\u1ee7a DA<\/p>suy ra PQ là \u0111\u01b0\u1eddng trung bình c\u1ee7a tam giác ADC <\/p>suy ra PQ \/\/ AC ; PQ =  $\\dfrac{1}{2}$<\/span>AC   (2)<\/p>T\u1eeb (1) và (2) suy ra MN \/\/ PQ ( \/\/ AC) ; MN = PQ = ( $\\dfrac{1}{2}$<\/span>AC )<\/p>suy ra t\u1ee9 giác MNPQ là hình bình hành.<\/p>(T\u1ee9 giác có hai c\u1ea1nh \u0111\u1ed1i v\u1eeba song song v\u1eeba b\u1eb1ng nhau là hình bình hành).<\/p>Xét tam giác ABD có M là trung \u0111i\u1ec3m c\u1ee7a AB, Q là trung \u0111i\u1ec3m c\u1ee7a AD<\/p>suy ra MQ là \u0111\u01b0\u1eddng trung bình c\u1ee7a tam giác ABD <\/p>suy ra MQ \/\/ BD  <\/p>\u0110\u1ec3 hình bình hành MNPQ là hình ch\u1eef nh\u1eadt thì<\/p>$\\widehat{QMN}$<\/span> = 90°  (hình bình hành có m\u1ed9t góc vuông là hình ch\u1eef nh\u1eadt).<\/p>hay  MN $\\bot$<\/span> MQ  mà MN \/\/ AC ; MQ \/\/ BD<\/p>suy ra AC $\\bot$<\/span> BD.<\/p>\u0110áp án \u0111úng là   D.<\/strong> AC $\\bot$<\/span> BD.<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-08-13 02:44:35","option_type":"math","len":0}]}