Các trường hợp đồng dạng của hai tam giác vuông

Home Lớp 8 Toán lớp 8 - Sách Kết nối tri thức Bài 36: Các trường hợp đồng dạng của hai tam giác vuôngBài tập nâng cao

{"common":{"save":0,"post_id":"6647","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"6960","post_id":"6647","mon_id":"1158921","chapter_id":"1158939","question":"Cho tam giác ABC vuông t\u1ea1i A, k\u1ebb \u0111\u01b0\u1eddng cao AH, H ∈ BC. Bi\u1ebft AB = 3 cm ;<\/p>BC = 5 cm . Tính HB.<\/p><svg height=\"150\" width=\"230\"> <g><title><\/title><rect fill=\"#fff\" height=\"152\" id=\"canvas_background\" width=\"232\" 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><g id=\"svg_11\"> <g id=\"svg_6\"> <g id=\"svg_3\"> <path d=\"m60.97377,194.45512l0,-163l110.00001,163l-110.00001,0z\" fill=\"#fff\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\" transform=\"rotate(124 115.97377014160158,112.95511627197268) \"><\/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=\"79.31535\" x2=\"79\" y1=\"22.52273\" y2=\"113.52273\"><\/line> <\/g> <rect fill=\"none\" fill-opacity=\"null\" height=\"10\" id=\"svg_4\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\" width=\"10\" x=\"79.31535\" y=\"102.52273\"><\/rect> <rect fill=\"none\" fill-opacity=\"null\" height=\"10\" id=\"svg_5\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\" transform=\"rotate(35 80.31534576416014,28.522727966308604) \" width=\"10\" x=\"75.31535\" y=\"23.52273\"><\/rect> <\/g> <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=\"69.31535\" xml:space=\"preserve\" y=\"18.52273\">A<\/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=\"3.31535\" xml:space=\"preserve\" y=\"122.52273\">B<\/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=\"216.31535\" xml:space=\"preserve\" y=\"119.52273\">C<\/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=\"74.31535\" xml:space=\"preserve\" y=\"130.52273\">H<\/text> <\/g> <\/g> <\/svg><\/span><\/p>","options":["A.<\/strong> 1,6 cm","B.<\/strong> 1,7 cm","C.<\/strong> 1,8 cm","D.<\/strong> 1,9 cm"],"correct":"3","level":"3","hint":"","answer":"<svg height=\"150\" width=\"230\"> <g> <title><\/title> <rect fill=\"#fff\" height=\"152\" id=\"canvas_background\" width=\"232\" 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> <g id=\"svg_11\"> <g id=\"svg_6\"> <g id=\"svg_3\"> <path d=\"m60.97377,194.45512l0,-163l110.00001,163l-110.00001,0z\" fill=\"#fff\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\" transform=\"rotate(124 115.97377014160158,112.95511627197268) \"><\/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=\"79.31535\" x2=\"79\" y1=\"22.52273\" y2=\"113.52273\"><\/line> <\/g> <rect fill=\"none\" fill-opacity=\"null\" height=\"10\" id=\"svg_4\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\" width=\"10\" x=\"79.31535\" y=\"102.52273\"><\/rect> <rect fill=\"none\" fill-opacity=\"null\" height=\"10\" id=\"svg_5\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\" transform=\"rotate(35 80.31534576416014,28.522727966308604) \" width=\"10\" x=\"75.31535\" y=\"23.52273\"><\/rect> <\/g> <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=\"69.31535\" xml:space=\"preserve\" y=\"18.52273\">A<\/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=\"3.31535\" xml:space=\"preserve\" y=\"122.52273\">B<\/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=\"216.31535\" xml:space=\"preserve\" y=\"119.52273\">C<\/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=\"74.31535\" xml:space=\"preserve\" y=\"130.52273\">H<\/text> <\/g> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_13\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-31 33.64631271362299,102.7045440673828) \" x=\"30.31535\" xml:space=\"preserve\" y=\"109.52273\">)<\/text> <\/g> <\/svg><\/span><\/p>Xét tam giác ABC vuông t\u1ea1i A và tam giác HBA vuông t\u1ea1i H có<\/p>$\\widehat{B}$<\/span> là góc chung<\/p>⇒  \u25b3ABC$\\backsim$<\/span>\u25b3HBA  (g.g).<\/p>⇒ $\\dfrac{AB}{BC}=\\dfrac{HB}{AB}$<\/span>  hay  $\\dfrac{3}{HB}=\\dfrac{5}{3}$<\/span> ⇒ HB = $\\dfrac{3.3}{5}$<\/span> = 1,8 cm.<\/p>\u0110áp án \u0111úng là   C.<\/strong> 1,8 cm.<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-09-10 02:36:12","option_type":"txt","len":0},{"id":"6964","post_id":"6647","mon_id":"1158921","chapter_id":"1158939","question":"Cho tam giác ABC vuông t\u1ea1i A, k\u1ebb \u0111\u01b0\u1eddng cao AH, H ∈ BC. Bi\u1ebft AB = 3 cm ;<\/p>BC = 5 cm . Tính HC.<\/p><svg height=\"150\" width=\"230\"> <g><title><\/title><rect fill=\"#fff\" height=\"152\" id=\"canvas_background\" width=\"232\" 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><g id=\"svg_11\"> <g id=\"svg_6\"> <g id=\"svg_3\"> <path d=\"m60.97377,194.45512l0,-163l110.00001,163l-110.00001,0z\" fill=\"#fff\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\" transform=\"rotate(124 115.97377014160158,112.95511627197268) \"><\/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=\"79.31535\" x2=\"79\" y1=\"22.52273\" y2=\"113.52273\"><\/line> <\/g> <rect fill=\"none\" fill-opacity=\"null\" height=\"10\" id=\"svg_4\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\" width=\"10\" x=\"79.31535\" y=\"102.52273\"><\/rect> <rect fill=\"none\" fill-opacity=\"null\" height=\"10\" id=\"svg_5\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\" transform=\"rotate(35 80.31534576416014,28.522727966308604) \" width=\"10\" x=\"75.31535\" y=\"23.52273\"><\/rect> <\/g> <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=\"69.31535\" xml:space=\"preserve\" y=\"18.52273\">A<\/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=\"3.31535\" xml:space=\"preserve\" y=\"122.52273\">B<\/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=\"216.31535\" xml:space=\"preserve\" y=\"119.52273\">C<\/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=\"74.31535\" xml:space=\"preserve\" y=\"130.52273\">H<\/text> <\/g> <\/g> <\/svg><\/span><\/p>","options":["A.<\/strong> 3,3cm","B.<\/strong> 3,2 cm","C.<\/strong> 3,1 cm","D.<\/strong> 3 cm"],"correct":"2","level":"3","hint":"","answer":"<svg height=\"150\" width=\"230\"> <g> <title><\/title> <rect fill=\"#fff\" height=\"152\" id=\"canvas_background\" width=\"232\" 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> <g id=\"svg_11\"> <g id=\"svg_6\"> <g id=\"svg_3\"> <path d=\"m60.97377,194.45512l0,-163l110.00001,163l-110.00001,0z\" fill=\"#fff\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\" transform=\"rotate(124 115.97377014160158,112.95511627197268) \"><\/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=\"79.31535\" x2=\"79\" y1=\"22.52273\" y2=\"113.52273\"><\/line> <\/g> <rect fill=\"none\" fill-opacity=\"null\" height=\"10\" id=\"svg_4\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\" width=\"10\" x=\"79.31535\" y=\"102.52273\"><\/rect> <rect fill=\"none\" fill-opacity=\"null\" height=\"10\" id=\"svg_5\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\" transform=\"rotate(35 80.31534576416014,28.522727966308604) \" width=\"10\" x=\"75.31535\" y=\"23.52273\"><\/rect> <\/g> <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=\"69.31535\" xml:space=\"preserve\" y=\"18.52273\">A<\/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=\"3.31535\" xml:space=\"preserve\" y=\"122.52273\">B<\/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=\"216.31535\" xml:space=\"preserve\" y=\"119.52273\">C<\/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=\"74.31535\" xml:space=\"preserve\" y=\"130.52273\">H<\/text> <\/g> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_13\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-31 33.64631271362299,102.7045440673828) \" x=\"30.31535\" xml:space=\"preserve\" y=\"109.52273\">)<\/text> <\/g> <\/svg><\/span><\/p>Xét tam giác ABC vuông t\u1ea1i A và tam giác HBA vuông t\u1ea1i H có<\/p>$\\widehat{B}$<\/span> là góc chung<\/p>⇒  \u25b3ABC$\\backsim$<\/span>\u25b3HBA  (g.g).<\/p>⇒ $\\dfrac{AB}{BC}=\\dfrac{HB}{AB}$<\/span>  hay  $\\dfrac{3}{HB}=\\dfrac{5}{3}$<\/span> ⇒ HB = $\\dfrac{3.3}{5}$<\/span> = 1,8 cm.<\/p>Ta có:  HC = BC – HB = 5 – 1,8 = 3,2 cm.<\/p>\u0110áp án \u0111úng là   B.<\/strong> 3,2 cm.<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-09-10 02:44:33","option_type":"txt","len":0},{"id":"6966","post_id":"6647","mon_id":"1158921","chapter_id":"1158939","question":"Cho hình v\u1ebd, k\u1ebft lu\u1eadn \u0111úng là<\/p><svg height=\"180\" width=\"200\"> <g><title><\/title><rect fill=\"#fff\" height=\"182\" id=\"canvas_background\" width=\"202\" 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_17\"> <g id=\"svg_11\"> <g id=\"svg_8\"> <g id=\"svg_5\"> <rect fill=\"#ffffff\" height=\"165\" id=\"svg_4\" stroke=\"#ffffff\" stroke-width=\"1.5\" width=\"239\" x=\"0.31535\" y=\"6.52273\"><\/rect> <g id=\"svg_3\"> <line fill=\"none\" id=\"svg_1\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"111.31535\" x2=\"10.31535\" y1=\"14.52273\" y2=\"142.52273\"><\/line> <line fill=\"none\" id=\"svg_2\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"9.31535\" x2=\"202.31535\" y1=\"142.52273\" y2=\"143\"><\/line> <\/g> <\/g> <line fill=\"none\" id=\"svg_6\" stroke=\"#000000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-width=\"1.5\" x1=\"94.31535\" x2=\"94.31535\" y1=\"35.52273\" y2=\"143.52273\"><\/line> <line fill=\"none\" id=\"svg_7\" stroke=\"#000000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-width=\"1.5\" x1=\"128.31535\" x2=\"57.31535\" y1=\"142.52273\" y2=\"82.52273\"><\/line> <\/g> <rect fill=\"none\" fill-opacity=\"null\" height=\"10\" id=\"svg_9\" stroke=\"#000000\" stroke-opacity=\"null\" stroke-width=\"1.5\" width=\"10\" x=\"84.31535\" y=\"132.52273\"><\/rect> <rect fill=\"none\" fill-opacity=\"null\" height=\"10\" id=\"svg_10\" stroke=\"#000000\" stroke-opacity=\"null\" stroke-width=\"1.5\" transform=\"rotate(-53 58.3153533935547,89.5227279663086) \" width=\"10\" x=\"53.31535\" y=\"84.52273\"><\/rect> <\/g> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_12\" stroke=\"#000000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"-0.68465\" xml:space=\"preserve\" y=\"161.52273\">O<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_13\" stroke=\"#000000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"79.31535\" xml:space=\"preserve\" y=\"32.52273\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_14\" stroke=\"#000000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"121.31535\" xml:space=\"preserve\" y=\"160.52273\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_15\" stroke=\"#000000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"83.31535\" xml:space=\"preserve\" y=\"162.52273\">M<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_16\" stroke=\"#000000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"40.31535\" xml:space=\"preserve\" y=\"79.52273\">N<\/text> <\/g> <\/g> <\/svg><\/span><\/p>","options":["A.<\/strong> OA . ON = OB . OM","B.<\/strong> OA . OM = OB . ON","C.<\/strong> OM . ON = OA . OB","D.<\/strong> OM . MN = OA . OB"],"correct":"1","level":"3","hint":"","answer":"Xét tam giác MOA vuông t\u1ea1i M và tam giác NOB vuông t\u1ea1i N có<\/p>$\\widehat{O}$<\/span> là góc chung<\/p>⇒ $\\triangle MOA \\backsim \\triangle NOB$<\/span>  (g.g).<\/p>⇒ $\\dfrac{OM}{OA}=\\dfrac{ON}{OB}$<\/span>  hay   A.<\/strong> OA . ON = OB . OM <\/span>.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-09-10 02:57:12","option_type":"txt","len":2}]}