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 trung bình

{"common":{"save":0,"post_id":"6645","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"6940","post_id":"6645","mon_id":"1158921","chapter_id":"1158939","question":"Cho tam giác ABC có các \u0111\u01b0\u1eddng cao AD và BE, D ∈ BC, E ∈ AC. K\u1ebft lu\u1eadn \u0111úng là<\/p><svg height=\"210\" width=\"240\"> <g><title><\/title><rect fill=\"#fff\" height=\"212\" id=\"canvas_background\" width=\"242\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_16\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g><title><\/title><g id=\"svg_15\"> <g id=\"svg_9\"> <g id=\"svg_4\"> <line fill=\"none\" id=\"svg_1\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"63.31535\" x2=\"17.31535\" y1=\"25.52273\" y2=\"182.52273\"><\/line> <line fill=\"none\" id=\"svg_2\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"17.31535\" x2=\"215.31535\" y1=\"182.52273\" y2=\"182.52273\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"62.31535\" x2=\"214.31535\" y1=\"26.52273\" y2=\"182.52273\"><\/line> <\/g> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_5\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"63.31535\" x2=\"63.31535\" y1=\"26.52273\" y2=\"181.52273\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_6\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"17.31535\" x2=\"119.31534\" y1=\"182.52273\" y2=\"84.52273\"><\/line> <rect fill=\"none\" fill-opacity=\"null\" height=\"12\" id=\"svg_7\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\" width=\"12\" x=\"63.31535\" y=\"170.52273\"><\/rect> <rect fill=\"none\" fill-opacity=\"null\" height=\"12\" id=\"svg_8\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\" transform=\"rotate(-43 109.31535339355472,84.52272796630858) \" width=\"12\" x=\"103.31535\" y=\"78.52273\"><\/rect> <\/g> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_10\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"53.31535\" xml:space=\"preserve\" y=\"23.52273\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_11\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"56.31535\" xml:space=\"preserve\" y=\"199.52273\">D<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_12\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"2.31535\" xml:space=\"preserve\" y=\"192.52273\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_13\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"217.31535\" xml:space=\"preserve\" y=\"188.52273\">C<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_14\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"121.31535\" xml:space=\"preserve\" y=\"80.52273\">E<\/text> <\/g> <\/g> <\/svg><\/span><\/p>","options":["A.<\/strong> $\\dfrac{EC}{DC}=\\dfrac{CB}{DA}$<\/span>","B.<\/strong> $\\dfrac{EC}{DC}=\\dfrac{EB}{DA}$<\/span>","C.<\/strong> $\\dfrac{CB}{CA}=\\dfrac{DA}{EB}$<\/span>","D.<\/strong> $\\dfrac{EB}{DA}=\\dfrac{DC}{EC}$<\/span>"],"correct":"2","level":"2","hint":"","answer":"<svg height=\"210\" width=\"240\"> <g> <title><\/title> <rect fill=\"#fff\" height=\"212\" id=\"canvas_background\" width=\"242\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_16\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g> <title><\/title> <g id=\"svg_15\"> <g id=\"svg_9\"> <g id=\"svg_4\"> <line fill=\"none\" id=\"svg_1\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"63.31535\" x2=\"17.31535\" y1=\"25.52273\" y2=\"182.52273\"><\/line> <line fill=\"none\" id=\"svg_2\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"17.31535\" x2=\"215.31535\" y1=\"182.52273\" y2=\"182.52273\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"62.31535\" x2=\"214.31535\" y1=\"26.52273\" y2=\"182.52273\"><\/line> <\/g> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_5\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"63.31535\" x2=\"63.31535\" y1=\"26.52273\" y2=\"181.52273\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_6\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"17.31535\" x2=\"119.31534\" y1=\"182.52273\" y2=\"84.52273\"><\/line> <rect fill=\"none\" fill-opacity=\"null\" height=\"12\" id=\"svg_7\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\" width=\"12\" x=\"63.31535\" y=\"170.52273\"><\/rect> <rect fill=\"none\" fill-opacity=\"null\" height=\"12\" id=\"svg_8\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\" transform=\"rotate(-43 109.31535339355472,84.52272796630858) \" width=\"12\" x=\"103.31535\" y=\"78.52273\"><\/rect> <\/g> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_10\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"53.31535\" xml:space=\"preserve\" y=\"23.52273\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_11\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"56.31535\" xml:space=\"preserve\" y=\"199.52273\">D<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_12\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"2.31535\" xml:space=\"preserve\" y=\"192.52273\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_13\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"217.31535\" xml:space=\"preserve\" y=\"188.52273\">C<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_14\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"121.31535\" xml:space=\"preserve\" y=\"80.52273\">E<\/text> <\/g> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_17\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(23 187.31393432617202,168.34092712402347) \" x=\"183.31535\" xml:space=\"preserve\" y=\"176.52273\">(<\/text> <\/g> <\/svg><\/span><\/p>Xét tam giác ECB vuông t\u1ea1i E và tam giác DCA vuông t\u1ea1i D <\/p>$\\widehat{C}$<\/span>  là góc chung<\/p>⇒ \u25b3ECB$\\backsim$<\/span>\u25b3DCA  (g.g)<\/p>T\u1eeb \u0111ó suy ra   B.<\/strong> $\\dfrac{EC}{DC}=\\dfrac{EB}{DA}$<\/span> .<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-09-10 01:37:31","option_type":"math","len":0},{"id":"6942","post_id":"6645","mon_id":"1158921","chapter_id":"1158939","question":"Cho tam giác ABC vuông t\u1ea1i A và tam giác DEF vuông t\u1ea1i D. Bi\u1ebft AC = 3 cm ; BC = 4,5 cm ; DE = 2 cm ; EF = 3 cm. K\u1ebft lu\u1eadn \u0111úng là  <\/p>","options":["A.<\/strong> \u25b3FDE$\\backsim$<\/span>\u25b3ACB","B.<\/strong> \u25b3DEF$\\backsim$<\/span>\u25b3BAC","C.<\/strong> \u25b3ABC$\\backsim$<\/span>\u25b3DEF","D.<\/strong> \u25b3ABC$\\backsim$<\/span>\u25b3DFE"],"correct":"4","level":"2","hint":"","answer":"Xét tam giác ABC vuông t\u1ea1i A và tam giác DEF vuông t\u1ea1i D có<\/p>$\\dfrac{BC}{EF}=\\dfrac{AC}{DE} $<\/span>  $\\bigg(\\dfrac{4,5}{3}=\\dfrac{3}{2}\\bigg)$<\/span> <\/p>⇒  D.<\/strong> \u25b3ABC$\\backsim$<\/span>\u25b3DFE <\/span> (c\u1ea1nh huy\u1ec1n - c\u1ea1nh góc vuông).<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-09-10 01:43:27","option_type":"math","len":0},{"id":"6943","post_id":"6645","mon_id":"1158921","chapter_id":"1158939","question":"Cho tam giác ABC vuông t\u1ea1i A và tam giác MNP vuông t\u1ea1i M. Bi\u1ebft AC = 3 cm ; BC = 4,5 cm ; MP = 4 cm ; NP = 6 cm. K\u1ebft lu\u1eadn \u0111úng là <\/p>","options":["A.<\/strong> \u25b3NMP$\\backsim$<\/span>\u25b3BCA","B.<\/strong> \u25b3PMN$\\backsim$<\/span>\u25b3BCA","C.<\/strong> \u25b3ABC$\\backsim$<\/span>\u25b3MNP","D.<\/strong> \u25b3ABC$\\backsim$<\/span>\u25b3MPN"],"correct":"3","level":"2","hint":"","answer":"Xét tam giác ABC vuông t\u1ea1i A và tam giác MNP vuông t\u1ea1i M có<\/p>$\\dfrac{AC}{MP}=\\dfrac{BC}{NP}$<\/span>  $\\bigg(\\dfrac{3}{4}=\\dfrac{4,5}{6}\\bigg)$<\/span> <\/p>⇒  C.<\/strong> \u25b3ABC$\\backsim$<\/span>\u25b3MNP <\/span> (c\u1ea1nh huy\u1ec1n - c\u1ea1nh góc vuông).<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-09-10 01:48:36","option_type":"math","len":0}]}