Tính chất đường phân giác của tam giác

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Bài 17 - Tính chất đường phân giác của tam giác

{"common":{"save":0,"post_id":"6583","level":1,"total":10,"point":10,"point_extra":0},"segment":[{"id":"6206","post_id":"6583","mon_id":"1158921","chapter_id":"1158932","question":"Cho tam giác ABC có AD là \u0111\u01b0\u1eddng phân giác c\u1ee7a góc BAC (D∈BC). Khi \u0111ó ta có t\u1ec9 l\u1ec7 th\u1ee9c nào d\u01b0\u1edbi \u0111ây?<\/p><svg height=\"220\" width=\"320\"> <g><title><\/title><rect fill=\"#fff\" height=\"222\" id=\"canvas_background\" width=\"322\" 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><path d=\"m74.7762,28.70004l208.96355,165.00001l-261.99999,0z\" fill=\"#ffff00\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\"><\/path> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_2\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"73.95453\" x2=\"129.95453\" y1=\"27.88636\" y2=\"192.88635\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_3\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(86.56979370117188 77.95452880859375,64.52272033691405) \" x=\"73.95453\" xml:space=\"preserve\" y=\"72.88635\">)<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_4\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(53.4637565612793 98.95452880859374,58.52272033691407) \" x=\"94.95453\" xml:space=\"preserve\" y=\"66.88635\">)<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_5\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"55.95453\" xml:space=\"preserve\" y=\"27.88636\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_6\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"1.95453\" xml:space=\"preserve\" y=\"202.88635\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_7\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"283.95452\" xml:space=\"preserve\" y=\"197.88635\">C<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_8\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"120.95453\" xml:space=\"preserve\" y=\"217.88635\">D<\/text> <\/g> <\/svg><\/span><\/p>","options":["A.<\/strong> $\\dfrac{DB}{DC}=\\dfrac{AC}{AB}$<\/span>","B.<\/strong> $\\dfrac{DB}{DC}=\\dfrac{AB}{AC}$<\/span>","C.<\/strong> $\\dfrac{DB}{AC}=\\dfrac{DC}{AB}$<\/span>","D.<\/strong> $\\dfrac{DB}{DC}=\\dfrac{BC}{AB}$<\/span>"],"correct":"2","level":"1","hint":"Tính ch\u1ea5t \u0111\u01b0\u1eddng phân giác trong tam giác:<\/strong><\/p>Trong tam giác, \u0111\u01b0\u1eddng phân giác c\u1ee7a m\u1ed9t góc chia c\u1ea1nh \u0111\u1ed1i di\u1ec7n thành hai \u0111o\u1ea1n th\u1eb3ng t\u1ec9 l\u1ec7 v\u1edbi hai c\u1ea1nh k\u1ec1 hai \u0111o\u1ea1n \u1ea5y.<\/p>","answer":"Vì AD là \u0111\u01b0\u1eddng phân giác c\u1ee7a góc BAC và D∈BC nên theo tính ch\u1ea5t \u0111\u01b0\u1eddng phân giác trong tam giác, ta có: <\/p>$\\dfrac{DB}{DC}=\\dfrac{AB}{AC}$<\/span><\/p>Ch\u1ecdn B.<\/strong> $\\dfrac{DB}{DC}=\\dfrac{AB}{AC}$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-08-06 01:26:31","option_type":"math","len":0},{"id":"6208","post_id":"6583","mon_id":"1158921","chapter_id":"1158932","question":"Cho tam giác ABC có BE là \u0111\u01b0\u1eddng phân giác c\u1ee7a góc ABC (E∈AC). Khi \u0111ó ta có t\u1ec9 l\u1ec7 th\u1ee9c nào d\u01b0\u1edbi \u0111ây?<\/p><svg height=\"180\" width=\"290\"> <g><title><\/title><rect fill=\"#fff\" height=\"182\" id=\"canvas_background\" width=\"292\" 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><path d=\"m190.24976,28.54505l77,134l-240,-1l163,-133z\" fill=\"#aaffff\" id=\"svg_2\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\"><\/path> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_3\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"4.95453\" xml:space=\"preserve\" y=\"169.88635\">B<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_4\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"180.95453\" xml:space=\"preserve\" y=\"25.88636\">A<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_5\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"268.95452\" xml:space=\"preserve\" y=\"166.88635\">C<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_6\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"232.95453\" xml:space=\"preserve\" y=\"93.88636\">E<\/text> <line fill=\"none\" id=\"svg_7\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"27.95453\" x2=\"228.95453\" y1=\"160.88635\" y2=\"94.88635\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_8\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-26.29534149169922 81.95452880859386,128.52272033691406) \" x=\"77.95453\" xml:space=\"preserve\" y=\"136.88635\">)<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_9\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-11.409579277038574 102.45246887207031,147.31086730957037) matrix(1.1250178813934324,0,0,1.111794829368591,-23.496246478476678,-18.077545974083478) \" x=\"107.95453\" xml:space=\"preserve\" y=\"156.88635\">)<\/text> <\/g> <\/svg><\/span><\/p>","options":["A.<\/strong> $\\dfrac{CE}{AE}=\\dfrac{AB}{BC}$<\/span>","B.<\/strong> $\\dfrac{CE}{AE}=\\dfrac{BC}{AC}$<\/span>","C.<\/strong> $\\dfrac{CE}{AE}=\\dfrac{AB}{AC}$<\/span>","D.<\/strong> $\\dfrac{CE}{AE}=\\dfrac{BC}{AB}$<\/span>"],"correct":"4","level":"1","hint":"Tính ch\u1ea5t \u0111\u01b0\u1eddng phân giác trong tam giác:<\/strong><\/p>Trong tam giác, \u0111\u01b0\u1eddng phân giác c\u1ee7a m\u1ed9t góc chia c\u1ea1nh \u0111\u1ed1i di\u1ec7n thành hai \u0111o\u1ea1n th\u1eb3ng t\u1ec9 l\u1ec7 v\u1edbi hai c\u1ea1nh k\u1ec1 hai \u0111o\u1ea1n \u1ea5y.<\/p>","answer":"Vì BE là \u0111\u01b0\u1eddng phân giác c\u1ee7a góc ABC và E∈AC nên theo tính ch\u1ea5t \u0111\u01b0\u1eddng phân giác trong tam giác, ta có: <\/p>$\\dfrac{CE}{AE}=\\dfrac{BC}{AB}$<\/span><\/p>Ch\u1ecdn D.<\/strong> $\\dfrac{CE}{AE}=\\dfrac{BC}{AB}$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-08-06 01:32:35","option_type":"math","len":0},{"id":"6209","post_id":"6583","mon_id":"1158921","chapter_id":"1158932","question":"Cho tam giác MNP có PD là \u0111\u01b0\u1eddng phân giác c\u1ee7a góc MPN (D∈MN). Khi \u0111ó ta có t\u1ec9 l\u1ec7 th\u1ee9c nào d\u01b0\u1edbi \u0111ây?<\/p><svg height=\"200\" width=\"290\"> <g><title><\/title><rect fill=\"#fff\" height=\"202\" id=\"canvas_background\" width=\"292\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_9\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g><title><\/title><g id=\"svg_10\"> <path d=\"m197.43475,28.58003l70.00001,147l-249.00001,1l179,-148z\" fill=\"#ffaaff\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\"><\/path> <line fill=\"none\" id=\"svg_2\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"266.95452\" x2=\"124.95453\" y1=\"175.88635\" y2=\"87.88636\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_3\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"268.95452\" xml:space=\"preserve\" y=\"187.88635\">P<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_4\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"203.95453\" xml:space=\"preserve\" y=\"23.88636\">M<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_5\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"-0.04547\" xml:space=\"preserve\" y=\"187.88635\">N<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_6\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"matrix(1,0,0,1.1856445615978115,0,-9.431273285694708) \" x=\"105.95453\" xml:space=\"preserve\" y=\"85.45212\">D<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_7\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(26.595590591430664 222.95060729980474,159.77145385742185) matrix(1,0,0,1.112702965736389,62,-57.75663331494979) \" x=\"156.95453\" xml:space=\"preserve\" y=\"204.08893\">(<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_8\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(56.720191955566406 241.9506225585937,141.7714538574219) matrix(1,0,0,1.112702965736389,62,-57.75663331494979) \" x=\"175.95453\" xml:space=\"preserve\" y=\"187.91211\">(<\/text> <\/g> <\/g> <\/svg><\/span><\/p>","options":["A.<\/strong> $\\dfrac{PM}{PN}=\\dfrac{DN}{DM}$<\/span>","B.<\/strong> $\\dfrac{PN}{PM}=\\dfrac{DN}{MN}$<\/span>","C.<\/strong> $\\dfrac{PM}{DM}=\\dfrac{PN}{DN}$<\/span>","D.<\/strong> $\\dfrac{PM}{MN}=\\dfrac{DM}{DN}$<\/span>"],"correct":"3","level":"1","hint":"Tính ch\u1ea5t \u0111\u01b0\u1eddng phân giác trong tam giác:<\/strong><\/p>Trong tam giác, \u0111\u01b0\u1eddng phân giác c\u1ee7a m\u1ed9t góc chia c\u1ea1nh \u0111\u1ed1i di\u1ec7n thành hai \u0111o\u1ea1n th\u1eb3ng t\u1ec9 l\u1ec7 v\u1edbi hai c\u1ea1nh k\u1ec1 hai \u0111o\u1ea1n \u1ea5y.<\/p>","answer":"Vì PD là \u0111\u01b0\u1eddng phân giác c\u1ee7a góc MPN và D∈MN nên theo tính ch\u1ea5t \u0111\u01b0\u1eddng phân giác trong tam giác, ta có: <\/p>$\\dfrac{PM}{PN}=\\dfrac{DM}{DN}$<\/span> suy ra $\\dfrac{PM}{DM}=\\dfrac{PN}{DN}$<\/span><\/p>Ch\u1ecdn C.<\/strong> $\\dfrac{PM}{DM}=\\dfrac{PN}{DN}$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-08-06 01:38:53","option_type":"math","len":0}]}