Bài ôn tập chương 9 - Quan hệ giữa các yếu tố trong một tam giác

Home Toán lớp 7 - tập 2 Chương 9: Quan hệ giữa các yếu tố trong một tam giác Ôn tập chương 9 - Quan hệ giữa các yếu tố trong một tam giácBài tập nâng cao

{"common":{"save":0,"post_id":"5847","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"8782","post_id":"5847","mon_id":"1158532","chapter_id":"1158662","question":"Cho ba \u0111i\u1ec3m A, B, C. Kh\u1eb3ng \u0111\u1ecbnh nào sau \u0111ây là \u0111úng?<\/p>","options":["A.<\/strong> $AB + BC \\ge AC$<\/span>","B. <\/strong>$AB + BC < AC$<\/span>","C. <\/strong>$AB + BC \\le AC$<\/span>","D.<\/strong> $AB + BC = AC$<\/span>"],"correct":"1","level":"3","hint":"","answer":"Tr\u01b0\u1eddng h\u1ee3p 1: A, B, C không th\u1eb3ng hàng<\/span><\/p><svg height=\"100\" width=\"190\"> <g><title><\/title><rect fill=\"#fff\" height=\"102\" id=\"canvas_background\" width=\"192\" 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_5\"> <path d=\"m55.61213,145.11524l0,-128.03786l71.29674,128.03786l-71.29674,0z\" fill=\"#fff\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\" transform=\"rotate(118.54293823242188 91.260498046875,81.0963134765625) \"><\/path> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_2\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"34.9\" xml:space=\"preserve\" y=\"16.2375\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_3\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"-0.1\" xml:space=\"preserve\" y=\"85.2375\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_4\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"170.9\" xml:space=\"preserve\" y=\"84.2375\">C<\/text> <\/g> <\/g> <\/svg><\/span><\/p>Khi \u0111ó ba \u0111i\u1ec3m A, B, C l\u1eadp thành m\u1ed9t tam giác nên theo b\u1ea5t \u0111\u1eb3ng th\u1ee9c trong tam giác ta có: AB + BC > AC  (1)<\/span><\/p>Tr\u01b0\u1eddng h\u1ee3p 2: A, B, C th\u1eb3ng hàng<\/p>+ N\u1ebfu B n\u1eb1m gi\u1eefa A và C thì AB + BC = AC (2)<\/span><\/p><svg height=\"50\" width=\"230\"> <g><title><\/title><rect fill=\"#fff\" height=\"52\" id=\"canvas_background\" width=\"232\" 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_5\"> <line fill=\"none\" id=\"svg_1\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"12.9\" x2=\"203.9\" y1=\"32\" y2=\"32.2375\"><\/line> <ellipse cx=\"12.9\" cy=\"32.7375\" fill=\"#ff0000\" id=\"svg_2\" rx=\"2\" ry=\"2\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <ellipse cx=\"85.9\" cy=\"32.7375\" fill=\"#ff0000\" id=\"svg_3\" rx=\"2\" ry=\"2\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <ellipse cx=\"205.9\" cy=\"32.7375\" fill=\"#ff0000\" id=\"svg_4\" rx=\"2\" ry=\"2\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <\/g> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_6\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"5.9\" xml:space=\"preserve\" y=\"21.2375\">A<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_7\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"80.9\" xml:space=\"preserve\" y=\"21.2375\">B<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_8\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"199.9\" xml:space=\"preserve\" y=\"23.2375\">C<\/text> <\/g> <\/svg><\/span><\/p>+ N\u1ebfu C n\u1eb1m gi\u1eefa A và B thì AB + BC > AC (3)<\/span><\/p><svg height=\"50\" width=\"230\"> <g><title><\/title><rect fill=\"#fff\" height=\"52\" id=\"canvas_background\" width=\"232\" 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_5\"> <line fill=\"none\" id=\"svg_1\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"12.9\" x2=\"203.9\" y1=\"32\" y2=\"32.2375\"><\/line> <ellipse cx=\"12.9\" cy=\"32.7375\" fill=\"#ff0000\" id=\"svg_2\" rx=\"2\" ry=\"2\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <ellipse cx=\"85.9\" cy=\"32.7375\" fill=\"#ff0000\" id=\"svg_3\" rx=\"2\" ry=\"2\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <ellipse cx=\"205.9\" cy=\"32.7375\" fill=\"#ff0000\" id=\"svg_4\" rx=\"2\" ry=\"2\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <\/g> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_6\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"5.9\" xml:space=\"preserve\" y=\"21.2375\">A<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_7\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"199.9\" xml:space=\"preserve\" y=\"22.2375\">B<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_8\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"80.9\" xml:space=\"preserve\" y=\"22.2375\">C<\/text> <\/g> <\/svg><\/span><\/p>+ N\u1ebfu A n\u1eb1m gi\u1eefa B và C thì AB + BC > AC (4)<\/span><\/p><svg height=\"50\" width=\"230\"> <g><title><\/title><rect fill=\"#fff\" height=\"52\" id=\"canvas_background\" width=\"232\" 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_5\"> <line fill=\"none\" id=\"svg_1\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"12.9\" x2=\"203.9\" y1=\"32\" y2=\"32.2375\"><\/line> <ellipse cx=\"12.9\" cy=\"32.7375\" fill=\"#ff0000\" id=\"svg_2\" rx=\"2\" ry=\"2\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <ellipse cx=\"85.9\" cy=\"32.7375\" fill=\"#ff0000\" id=\"svg_3\" rx=\"2\" ry=\"2\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <ellipse cx=\"205.9\" cy=\"32.7375\" fill=\"#ff0000\" id=\"svg_4\" rx=\"2\" ry=\"2\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <\/g> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_6\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"80.9\" xml:space=\"preserve\" y=\"23.2375\">A<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_7\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"6.9\" xml:space=\"preserve\" y=\"23.2375\">B<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_8\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"198.9\" xml:space=\"preserve\" y=\"25.2375\">C<\/text> <\/g> <\/svg><\/span><\/p>T\u1eeb (1), (2), (3) và (4) ta luôn có AB + BC = AC ho\u1eb7c AB + BC > AC, t\u1ee9c là $AB + BC \\ge AC$<\/span><\/p>\u0110áp án \u0111úng là  A.<\/strong> $AB + BC \\ge AC$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"1","date":"2022-06-06 03:59:36","option_type":"math","len":0},{"id":"8785","post_id":"5847","mon_id":"1158532","chapter_id":"1158662","question":"Cho tam giác ABC có AH là \u0111\u01b0\u1eddng cao và AH là \u0111\u01b0\u1eddng trung tuy\u1ebfn xu\u1ea5t phát t\u1eeb \u0111\u1ec9nh A. Khi \u0111ó kh\u1eb3ng \u0111\u1ecbnh nào sau \u0111ây là \u0111úng?<\/p>","options":["A.<\/strong> AH là \u0111\u01b0\u1eddng phân giác xu\u1ea5t phát t\u1eeb \u0111\u1ec9nh A","B. <\/strong>Tam giác ABC cân \u1edf A","C. $\\widehat{BAH}=\\widehat{HAC}$<\/span><\/strong>","D.<\/strong> C\u1ea3 A, B, C \u0111\u1ec1u \u0111úng"],"correct":"4","level":"3","hint":"","answer":"Ta có hình v\u1ebd:<\/p><svg height=\"170\" width=\"260\"> <g> <title><\/title> <rect fill=\"#fff\" height=\"172\" id=\"canvas_background\" width=\"262\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_11\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g> <title><\/title> <g id=\"svg_7\"> <path d=\"m9.6205,135.22443l114.5,-108.99999l114.5,108.99999l-229.00001,0l0.00001,0z\" fill=\"#fff\" 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=\"123.9\" x2=\"124\" y1=\"25.2375\" y2=\"136.2375\"><\/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=\"104.9\" xml:space=\"preserve\" y=\"23.2375\">A<\/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=\"119.9\" xml:space=\"preserve\" y=\"163.2375\">H<\/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=\"3.9\" xml:space=\"preserve\" y=\"164.2375\">B<\/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=\"239.9\" xml:space=\"preserve\" y=\"161.2375\">C<\/text> <\/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=\"65.9\" x2=\"71.9\" y1=\"125.2375\" y2=\"145.2375\"><\/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=\"164.9\" x2=\"172.9\" y1=\"124.2375\" y2=\"145.2375\"><\/line> <rect fill=\"#fff\" fill-opacity=\"null\" height=\"14\" id=\"svg_10\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\" width=\"13\" x=\"123.9\" y=\"121.2375\"><\/rect> <\/g> <\/svg><\/span><\/p>Vì AH là \u0111\u01b0\u1eddng cao nên AH &perp; BC<\/p>Vì AH là \u0111\u01b0\u1eddng trung tuy\u1ebfn xu\u1ea5t phát t\u1eeb \u0111\u1ec9nh A nên H là trung \u0111i\u1ec3m c\u1ee7a BC.<\/p>Xét ΔABH và ΔACH có:<\/p>AH là c\u1ea1nh chung<\/p>$\\widehat{AHB}=\\widehat{AHC}=90^0$<\/span><\/p>HB = HC (vì H là trung \u0111i\u1ec3m c\u1ee7a BC)<\/p>Suy ra ΔABH = ΔACH (c.g.c)<\/p>Suy ra $\\widehat{BAH}=\\widehat{HAC}$<\/span><\/span> <\/strong>(hai góc t\u01b0\u01a1ng \u1ee9ng) hay AH là \u0111\u01b0\u1eddng phân giác c\u1ee7a góc A<\/span><\/p>AB = AC (hai c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) hay ΔABC là tam giác cân \u1edf A<\/span><\/p>V\u1eady \u0111áp án \u0111úng là  D.<\/strong> C\u1ea3 A, B, C \u0111\u1ebfu \u0111úng<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"3","date":"2022-06-06 04:12:17","option_type":"math","len":0},{"id":"8786","post_id":"5847","mon_id":"1158532","chapter_id":"1158662","question":"Ch\u1ecdn câu \u0111úng.<\/p>","options":["A.<\/strong> Ba \u0111\u01b0\u1eddng trung tuy\u1ebfn trong tam giác \u0111\u1ed3ng quy t\u1ea1i m\u1ed9t \u0111i\u1ec3m. \u0110i\u1ec3m \u0111ó g\u1ecdi là tr\u1ecdng tâm tam giác","B. <\/strong>Ba \u0111\u01b0\u1eddng phân giác trong tam giác \u0111\u1ed3ng quy t\u1ea1i m\u1ed9t \u0111i\u1ec3m. \u0110i\u1ec3m \u0111ó g\u1ecdi là tr\u1ecdng tâm tam giác.","C. <\/strong>Ba \u0111\u01b0\u1eddng cao trong tam giác \u0111\u1ed3ng quy t\u1ea1i m\u1ed9t \u0111i\u1ec3m. \u0110i\u1ec3m \u0111ó g\u1ecdi là tr\u1ef1c tâm tam giác.","D.<\/strong> Ba \u0111\u01b0\u1eddng trung tr\u1ef1c trong tam giác \u0111\u1ed3ng quy t\u1ea1i m\u1ed9t \u0111i\u1ec3m. \u0110i\u1ec3m \u0111ó g\u1ecdi là tr\u1ef1c tâm tam giác."],"correct":"[\"1\",\"3\"]","level":"3","hint":"","answer":"Các \u0111áp án \u0111úng là <\/p>A.<\/strong> Ba \u0111\u01b0\u1eddng trung tuy\u1ebfn trong tam giác \u0111\u1ed3ng quy t\u1ea1i m\u1ed9t \u0111i\u1ec3m. \u0110i\u1ec3m \u0111ó g\u1ecdi là tr\u1ecdng tâm tam giác.<\/span><\/p>C. <\/strong>Ba \u0111\u01b0\u1eddng cao trong tam giác \u0111\u1ed3ng quy t\u1ea1i m\u1ed9t \u0111i\u1ec3m. \u0110i\u1ec3m \u0111ó g\u1ecdi là tr\u1ef1c tâm tam giác.<\/span><\/p>","type":"checkbox","extra_type":"classic-checkbox","time":"0","user_id":"131","test":"1","date":"2022-06-06 04:15:21","option_type":"txt","len":3}]}