Bài tập cuối chương IX - Bài tập nâng cao

Home Lớp 8 Toán lớp 8 - Sách Kết nối tri thức Bài tập cuối chương 9Bài tập nâng cao

{"common":{"save":0,"post_id":"6670","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"7027","post_id":"6670","mon_id":"1158921","chapter_id":"1158939","question":"Bi\u1ebft $\u25b3MNP$<\/span> có MN = 6 cm ; NP = 4,8 cm ; MP = 3,6 cm. K\u1ebft lu\u1eadn \u0111úng là<\/p>","options":["A.<\/strong> \u25b3MNP không vuông.","B.<\/strong> \u25b3MNP vuông t\u1ea1i M.","C.<\/strong> \u25b3MNP vuông t\u1ea1i N.","D.<\/strong> \u25b3MNP vuông t\u1ea1i P."],"correct":"4","level":"3","hint":"","answer":"Xét tam giác MNP có<\/p>$MN^2=6^2=36$<\/span><\/p>$NP^2+MP^2=4,8^2+3,6^2=36$<\/span><\/p>⇒ $MN^2=NP^2+MP^2$<\/span><\/p>⇒ Tam giác MNP vuông t\u1ea1i P  (theo \u0111\u1ecbnh lí Pythagore \u0111\u1ea3o).<\/p>\u0110áp án \u0111úng là   D.<\/strong> \u25b3MNP vuông t\u1ea1i P.<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-09-13 02:05:06","option_type":"txt","len":2},{"id":"7028","post_id":"6670","mon_id":"1158921","chapter_id":"1158939","question":"Cho $\u25b3ABC\\backsim\u25b3DEF$<\/span> có t\u1ec9 s\u1ed1 chu vi là $\\dfrac{3}{4}$<\/span>  và DE – AB = 10 cm. \u0110\u1ed9 dài c\u1ee7a AB và DE l\u1ea7n l\u01b0\u1ee3t là<\/p>","options":["A.<\/strong> 40 cm và 30 cm.","B.<\/strong> 30 cm và 40 cm.","C.<\/strong> 35 cm và 45 cm.","D.<\/strong> 45 cm và 35 cm."],"correct":"2","level":"3","hint":"","answer":"Vì t\u1ec9 s\u1ed1 chu vi c\u1ee7a hai tam giác \u0111\u1ed3ng d\u1ea1ng b\u1eb1ng t\u1ec9 s\u1ed1 \u0111\u1ed3ng d\u1ea1ng nên $\u25b3ABC\\backsim\u25b3DEF$<\/span> theo t\u1ec9 s\u1ed1 là $\\dfrac{3}{4}$<\/span> .<\/p>⇒ $\\dfrac{AB}{DE}=\\dfrac{3}{4}$<\/span> ⇒ $\\dfrac{AB}{3}=\\dfrac{DE}{4}$<\/span> $=\\dfrac{DE-AB}{4-3}$<\/span> $=\\dfrac{10}{1}$<\/span> = 10<\/p>Ta có  $\\dfrac{AB}{3}=10$<\/span> ⇒ $AB = 3.10 = 30$<\/span> cm<\/p>$\\dfrac{DE}{4}=10$<\/span> ⇒ $DE=4.10 =40$<\/span> cm.<\/p>\u0110áp án \u0111úng là   B.<\/strong> 30 cm và 40 cm.<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-09-13 02:10:59","option_type":"txt","len":2},{"id":"7031","post_id":"6670","mon_id":"1158921","chapter_id":"1158939","question":"Cho hình v\u1ebd. Tính x và y.<\/p><svg height=\"220\" width=\"230\"> <g><title><\/title><rect fill=\"#fff\" height=\"222\" 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_20\"> <g id=\"svg_6\"> <line fill=\"none\" id=\"svg_1\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"87.31535\" x2=\"201.31534\" y1=\"30.52273\" y2=\"189.52273\"><\/line> <line fill=\"none\" id=\"svg_2\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"164.31535\" x2=\"16.31535\" y1=\"30.52273\" y2=\"187.52273\"><\/line> <line fill=\"none\" id=\"svg_4\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"87.31535\" x2=\"163.31535\" y1=\"30.52273\" y2=\"30.52273\"><\/line> <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=\"16.31535\" x2=\"201.31535\" y1=\"188.52273\" y2=\"188.52273\"><\/line> <\/g> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"18\" id=\"svg_7\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"132.31535\" xml:space=\"preserve\" y=\"84.52273\">I<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"18\" id=\"svg_8\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"75.31535\" xml:space=\"preserve\" y=\"26.52273\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"18\" id=\"svg_9\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"165.31535\" xml:space=\"preserve\" y=\"22.52273\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"18\" id=\"svg_10\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"4.31535\" xml:space=\"preserve\" y=\"202.52273\">C<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"18\" id=\"svg_11\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"202.31535\" xml:space=\"preserve\" y=\"200.52273\">D<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"18\" font-style=\"italic\" id=\"svg_12\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"120.31535\" xml:space=\"preserve\" y=\"26.52273\">x<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"18\" font-style=\"italic\" id=\"svg_13\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"148.31535\" xml:space=\"preserve\" y=\"58.52273\">y<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"18\" id=\"svg_14\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(54 94.3326950073242,56.15908813476564) \" x=\"76.31535\" xml:space=\"preserve\" y=\"62.52273\">4 cm<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"18\" id=\"svg_15\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-46 48.0826873779297,133.15908813476562) \" x=\"23.31535\" xml:space=\"preserve\" y=\"139.52273\">7,2 cm<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"18\" id=\"svg_16\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(53 176.3327026367187,133.15908813476562) \" x=\"158.31535\" xml:space=\"preserve\" y=\"139.52273\">8 cm<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"18\" id=\"svg_17\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"98.31535\" xml:space=\"preserve\" y=\"205.52273\">9 cm<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"18\" font-weight=\"bold\" id=\"svg_18\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(38 103.04261779785159,37.15908813476561) \" x=\"100.31535\" xml:space=\"preserve\" y=\"43.52273\">)<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"18\" font-weight=\"bold\" id=\"svg_19\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-147 185.04261779785156,182.15908813476562) \" x=\"182.31535\" xml:space=\"preserve\" y=\"188.52273\">)<\/text> <\/g> <\/g> <\/svg><\/span><\/p>","options":["A.<\/strong> x = 4,5 cm ; y = 3,6 cm.","B.<\/strong> x = 3,6 cm ; y = 4,5 cm.","C.<\/strong> x = 5,4 cm ; y = 6,3 cm.","D.<\/strong> x = 6,3 cm ; y = 5,4 cm."],"correct":"1","level":"3","hint":"","answer":"Xét tam giác IAB và tam giác IDC có<\/p>$\\widehat{AIB}=\\widehat{DIC}$<\/span> (hai góc \u0111\u1ed1i \u0111\u1ec9nh)<\/p>$\\widehat{BAI}=\\widehat{CDI}$<\/span>  (gi\u1ea3 thi\u1ebft)<\/p>⇒ $\u25b3IAB\\backsim\u25b3IDC$<\/span>  (g.g)<\/p>⇒ $\\dfrac{IA}{ID}=\\dfrac{AB}{DC}=\\dfrac{IB}{IC}$<\/span>  hay  $\\dfrac{4}{8}=\\dfrac{x}{9}=\\dfrac{y}{7,2}$<\/span> .<\/p>Ta có  $\\dfrac{4}{8}=\\dfrac{x}{9}$<\/span> ⇒ $x=\\dfrac{4.9}{8}$<\/span> = 4,5 cm.<\/p>$\\dfrac{4}{8}=\\dfrac{y}{7,2}$<\/span> ⇒ $y = \\dfrac{4.7,2}{8}$<\/span> = 3,6 cm.<\/p>\u0110áp án \u0111úng là   A.<\/strong> x = 4,5 cm ; y = 3,6 cm.<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-09-13 02:22:30","option_type":"txt","len":2}]}