Đường trung bình của tam giác

Home Lớp 8 Toán lớp 8 - Sách Kết nối tri thức Bài 16 - Đường trung bình của tam giácBài tập nâng cao

{"common":{"save":0,"post_id":"6582","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"6232","post_id":"6582","mon_id":"1158921","chapter_id":"1158932","question":"Cho tam giác ABC có M, N, P l\u1ea7n l\u01b0\u1ee3t là trung \u0111i\u1ec3m c\u1ee7a AB, AC, BC. Bi\u1ebft AB = 4 cm, AC = 6 cm, BC = 8 cm.<\/p>Tính chu vi c\u1ee7a tam giác MNP.<\/p>","options":["A.<\/strong> 6 cm","B.<\/strong> 8 cm","C.<\/strong> 7 cm","D.<\/strong> 9 cm"],"correct":"4","level":"3","hint":"","answer":"<svg height=\"160\" width=\"245\"> <g> <title><\/title> <rect fill=\"#fff\" height=\"162\" id=\"canvas_background\" width=\"247\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" height=\"100%\" id=\"canvasGrid\" overflow=\"visible\" width=\"100%\" x=\"0\" y=\"0\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g> <title><\/title> <g id=\"svg_16\"> <g id=\"svg_3\"> <path d=\"m17.03377,135.50825l122,-116.00001l86,116.00001l-174,0z\" fill=\"#fff\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\"><\/path> <path d=\"m80.03379,134.50825l58.65385,-58.00001l41.34616,58.00001l-83.65386,0z\" fill=\"#fff\" id=\"svg_2\" stroke=\"#000\" stroke-width=\"1.5\" transform=\"rotate(-180 130.03379821777344,105.50824737548827) \"><\/path> <\/g> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_4\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"106.31535\" xml:space=\"preserve\" y=\"54.52273\">\\<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_5\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"42.31535\" xml:space=\"preserve\" y=\"114.52273\">\\<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_6\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"155.31535\" xml:space=\"preserve\" y=\"54.52273\">\/\/<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_7\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"197.31535\" xml:space=\"preserve\" y=\"110.52273\">\/\/<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_8\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"63.31535\" xml:space=\"preserve\" y=\"140.52273\">x<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_9\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"168.31535\" xml:space=\"preserve\" y=\"140.52273\">x<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_10\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"133.31535\" xml:space=\"preserve\" y=\"19.52273\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_11\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"60.31535\" xml:space=\"preserve\" y=\"77.52273\">M<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_12\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"183.31535\" xml:space=\"preserve\" y=\"79.52273\">N<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_13\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"115.31535\" xml:space=\"preserve\" y=\"154.52273\">P<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_14\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"2.31535\" xml:space=\"preserve\" y=\"144.52273\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_15\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"229.31535\" xml:space=\"preserve\" y=\"142.52273\">C<\/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 AC, P là trung \u0111i\u1ec3m c\u1ee7a BC<\/p>⇒ MN, NP, PM là các \u0111\u01b0\u1eddng trung bình c\u1ee7a tam giác ABC <\/p>⇒ MN = $\\dfrac{1}{2}$<\/span>BC, NP = $\\dfrac{1}{2}$<\/span>AB, PM = $\\dfrac{1}{2}$<\/span>AC.<\/p>Chu vi tam giác MNP là <\/p>MN + NP + PM = $\\dfrac{1}{2}$<\/span>BC + $\\dfrac{1}{2}$<\/span>AB + $\\dfrac{1}{2}$<\/span>AC<\/p>                         = $\\dfrac{1}{2}$<\/span>(BC + AB + AC) = $\\dfrac{1}{2}$<\/span>(8 + 4 + 6) = $\\dfrac{1}{2}$<\/span>.18 = 9 cm.<\/p>\u0110áp án \u0111úng là   D.<\/strong> 9 cm.<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-08-06 03:20:02","option_type":"txt","len":0},{"id":"6234","post_id":"6582","mon_id":"1158921","chapter_id":"1158932","question":"Cho tam giác ABC có M, N, P l\u1ea7n l\u01b0\u1ee3t là trung \u0111i\u1ec3m c\u1ee7a AB, AC, BC. Bi\u1ebft AB = 10 cm, AC = 14 cm, BC = 12 cm.<\/p>Hãy tính chu vi c\u1ee7a tam giác MNP.<\/p>","options":["A.<\/strong> 17 cm","B.<\/strong> 18 cm","C.<\/strong> 19 cm","D.<\/strong> 20 cm"],"correct":"2","level":"3","hint":"D\u1ef1a vào tính ch\u1ea5t \u0111\u01b0\u1eddng trung bình trong tam giác \u0111\u1ec3 tính \u0111\u1ed9 dài các c\u1ea1nh MN, NP, MP.<\/p>","answer":"<svg height=\"160\" width=\"245\"> <g> <title><\/title> <rect fill=\"#fff\" height=\"162\" id=\"canvas_background\" width=\"247\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" height=\"100%\" id=\"canvasGrid\" overflow=\"visible\" width=\"100%\" x=\"0\" y=\"0\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g> <title><\/title> <g id=\"svg_16\"> <g id=\"svg_3\"> <path d=\"m17.03377,135.50825l122,-116.00001l86,116.00001l-174,0z\" fill=\"#fff\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\"><\/path> <path d=\"m80.03379,134.50825l58.65385,-58.00001l41.34616,58.00001l-83.65386,0z\" fill=\"#fff\" id=\"svg_2\" stroke=\"#000\" stroke-width=\"1.5\" transform=\"rotate(-180 130.03379821777344,105.50824737548827) \"><\/path> <\/g> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_4\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"106.31535\" xml:space=\"preserve\" y=\"54.52273\">\\<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_5\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"42.31535\" xml:space=\"preserve\" y=\"114.52273\">\\<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_6\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"155.31535\" xml:space=\"preserve\" y=\"54.52273\">\/\/<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_7\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"197.31535\" xml:space=\"preserve\" y=\"110.52273\">\/\/<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_8\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"63.31535\" xml:space=\"preserve\" y=\"140.52273\">x<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_9\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"168.31535\" xml:space=\"preserve\" y=\"140.52273\">x<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_10\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"133.31535\" xml:space=\"preserve\" y=\"19.52273\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_11\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"60.31535\" xml:space=\"preserve\" y=\"77.52273\">M<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_12\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"183.31535\" xml:space=\"preserve\" y=\"79.52273\">N<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_13\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"115.31535\" xml:space=\"preserve\" y=\"154.52273\">P<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_14\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"2.31535\" xml:space=\"preserve\" y=\"144.52273\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_15\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"229.31535\" xml:space=\"preserve\" y=\"142.52273\">C<\/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 AC, P là trung \u0111i\u1ec3m c\u1ee7a BC<\/p>⇒ MN, NP, PM là các \u0111\u01b0\u1eddng trung bình c\u1ee7a tam giác ABC <\/p>⇒ MN = $\\dfrac{1}{2}$<\/span>BC, NP = $\\dfrac{1}{2}$<\/span>AB, PM = $\\dfrac{1}{2}$<\/span>AC.<\/p>Chu vi tam giác MNP là <\/p>MN + NP + PM = $\\dfrac{1}{2}$<\/span>BC + $\\dfrac{1}{2}$<\/span>AB + $\\dfrac{1}{2}$<\/span>AC<\/p>                         = $\\dfrac{1}{2}$<\/span>(BC + AB + AC) = $\\dfrac{1}{2}$<\/span>(12 + 10 + 14) = $\\dfrac{1}{2}$<\/span>.36 = 18 cm.<\/p>\u0110áp án \u0111úng là   B.<\/strong> 18 cm.<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-08-06 03:25:45","option_type":"txt","len":0},{"id":"6236","post_id":"6582","mon_id":"1158921","chapter_id":"1158932","question":"Cho tam giác ABC có M, N, P l\u1ea7n l\u01b0\u1ee3t là trung \u0111i\u1ec3m c\u1ee7a AB, AC, BC. Bi\u1ebft chu vi tam giác ABC là 20 cm.<\/p>Tính chu vi c\u1ee7a tam giác MNP. <\/p>","options":["A.<\/strong> 10 cm","B.<\/strong> 20 cm","C.<\/strong> 5 cm","D.<\/strong> 15 cm"],"correct":"1","level":"3","hint":"","answer":"<svg height=\"160\" width=\"245\"> <g> <title><\/title> <rect fill=\"#fff\" height=\"162\" id=\"canvas_background\" width=\"247\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" height=\"100%\" id=\"canvasGrid\" overflow=\"visible\" width=\"100%\" x=\"0\" y=\"0\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g> <title><\/title> <g id=\"svg_16\"> <g id=\"svg_3\"> <path d=\"m17.03377,135.50825l122,-116.00001l86,116.00001l-174,0z\" fill=\"#fff\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\"><\/path> <path d=\"m80.03379,134.50825l58.65385,-58.00001l41.34616,58.00001l-83.65386,0z\" fill=\"#fff\" id=\"svg_2\" stroke=\"#000\" stroke-width=\"1.5\" transform=\"rotate(-180 130.03379821777344,105.50824737548827) \"><\/path> <\/g> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_4\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"106.31535\" xml:space=\"preserve\" y=\"54.52273\">\\<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_5\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"42.31535\" xml:space=\"preserve\" y=\"114.52273\">\\<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_6\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"155.31535\" xml:space=\"preserve\" y=\"54.52273\">\/\/<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_7\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"197.31535\" xml:space=\"preserve\" y=\"110.52273\">\/\/<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_8\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"63.31535\" xml:space=\"preserve\" y=\"140.52273\">x<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_9\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"168.31535\" xml:space=\"preserve\" y=\"140.52273\">x<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_10\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"133.31535\" xml:space=\"preserve\" y=\"19.52273\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_11\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"60.31535\" xml:space=\"preserve\" y=\"77.52273\">M<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_12\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"183.31535\" xml:space=\"preserve\" y=\"79.52273\">N<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_13\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"115.31535\" xml:space=\"preserve\" y=\"154.52273\">P<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_14\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"2.31535\" xml:space=\"preserve\" y=\"144.52273\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_15\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"229.31535\" xml:space=\"preserve\" y=\"142.52273\">C<\/text> <\/g> <\/g> <\/svg><\/span><\/p>Vì chu vi tam giác ABC là 20 cm nên BC + AB + AC = 20 cm.<\/p>Xét tam giác ABC có M là trung \u0111i\u1ec3m c\u1ee7a AB, N là trung \u0111i\u1ec3m c\u1ee7a AC, P là trung \u0111i\u1ec3m c\u1ee7a BC<\/p>⇒ MN, NP, PM là các \u0111\u01b0\u1eddng trung bình c\u1ee7a tam giác ABC <\/p>⇒ MN = $\\dfrac{1}{2}$<\/span>BC, NP = $\\dfrac{1}{2}$<\/span>AB, PM = $\\dfrac{1}{2}$<\/span>AC.<\/p>Chu vi tam giác MNP là <\/p>MN + NP + PM = $\\dfrac{1}{2}$<\/span>BC + $\\dfrac{1}{2}$<\/span>AB + $\\dfrac{1}{2}$<\/span>AC<\/p>                         = $\\dfrac{1}{2}$<\/span>(BC + AB + AC) = $\\dfrac{1}{2}$<\/span>.20 = 10 cm.<\/p>\u0110áp án \u0111úng là   A.<\/strong> 10 cm.<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-08-06 03:28:47","option_type":"txt","len":0}]}