Bài tập cuối chương 3 - Bài tập nâng cao

Home Lớp 8 Toán lớp 8 - Sách Kết nối tri thức Bài tập cuối chương 3Bài tập nâng cao

{"common":{"save":0,"post_id":"6576","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"6131","post_id":"6576","mon_id":"1158921","chapter_id":"1158929","question":"Cho t\u1ee9 giác ABCD có $\\widehat{C}$<\/span> = 60°, $\\widehat{D}$<\/span> = 80°. G\u1ecdi E là giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng phân giác trong c\u1ee7a các góc A và B c\u1ee7a t\u1ee9 giác ABCD. Tính s\u1ed1 \u0111o góc AEB.<\/p>","options":["A.<\/strong> 70°","B.<\/strong> 80°","C.<\/strong> 110°","D.<\/strong> 140°"],"correct":"1","level":"3","hint":"","answer":"<svg height=\"160\" width=\"230\"> <g> <title><\/title> <rect fill=\"#fff\" height=\"162\" 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_23\"> <g id=\"svg_17\"> <g id=\"svg_10\"> <g id=\"svg_7\"> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"37.31535\" x2=\"140.31535\" y1=\"55.52273\" y2=\"16.52273\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_4\" stroke=\"#000\" stroke-linecap=\"null\" 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stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"140.31535\" x2=\"106.31535\" y1=\"16.52273\" y2=\"117.52273\"><\/line> <\/g> <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=\"49.31535\" xml:space=\"preserve\" y=\"64.52273\">)<\/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\" transform=\"rotate(59 42.646312713623054,70.70454406738281) \" x=\"39.31535\" xml:space=\"preserve\" y=\"77.52273\">)<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_13\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-34 126.14915466308592,29.613639831542955) \" x=\"123.31535\" xml:space=\"preserve\" y=\"35.52273\">(<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_14\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(75 143.1491546630859,33.61363983154298) \" x=\"140.31535\" xml:space=\"preserve\" y=\"39.52273\">)<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_15\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"50.31535\" xml:space=\"preserve\" y=\"55.52273\">_<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" id=\"svg_16\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"37.31535\" xml:space=\"preserve\" y=\"78.52273\">|<\/text> <\/g> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" id=\"svg_18\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"23.31535\" xml:space=\"preserve\" y=\"54.52273\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" id=\"svg_19\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"139.31535\" xml:space=\"preserve\" y=\"14.52273\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" id=\"svg_20\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"214.31535\" xml:space=\"preserve\" y=\"152.52273\">C<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" id=\"svg_21\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"0.31535\" xml:space=\"preserve\" y=\"152.52273\">D<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" id=\"svg_22\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"102.31535\" xml:space=\"preserve\" y=\"130.52273\">E<\/text> <\/g> <\/g> <\/svg><\/span><\/p>Ta có  $\\widehat{DAB}+\\widehat{CBA}+\\widehat{BCD}+\\widehat{ADC}$<\/span> = 360°  (\u0111\u1ecbnh lí t\u1ed5ng các góc trong t\u1ee9 giác).<\/p>           $\\widehat{DAB}+\\widehat{CBA}$<\/span> + 60° + 80° = 360°<\/p>           $\\widehat{DAB}+\\widehat{CBA}$<\/span> = 360° – 60° – 80°<\/p>           $\\widehat{DAB}+\\widehat{CBA}$<\/span> = 220°<\/p>Ta có  $\\widehat{DAE}=\\widehat{EAB}=\\dfrac{\\widehat{DAB}}{2}$<\/span>  (vì AE là tia phân giác c\u1ee7a góc DAB).<\/p>           $\\widehat{CBE}=\\widehat{EBA}=\\dfrac{\\widehat{CBA}}{2}$<\/span>  (vì BE là tia phân giác c\u1ee7a góc CBA).<\/p>Suy ra  $\\widehat{EAB}+\\widehat{EBA}$<\/span>  $=\\dfrac{\\widehat{DAB}}{2}+\\dfrac{\\widehat{CBA}}{2}$<\/span>  $=\\dfrac{\\widehat{DAB}+\\widehat{CBA}}{2}$<\/span>  $=\\dfrac{220^0}{2} $<\/span> = 110°.<\/p>Xét tam giác EAB có $\\widehat{AEB}+\\widehat{EAB}+\\widehat{EBA}$<\/span> = 180°  (\u0111\u1ecbnh lí t\u1ed5ng các góc trong tam giác)<\/p>                                  $\\widehat{AEB}$<\/span> + 110° = 180°<\/p>                                  $\\widehat{AEB}$<\/span>  = 180° – 110° = 70°<\/p>\u0110áp án \u0111úng là   A.<\/strong> 70°.<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-07-25 10:19:53","option_type":"txt","len":1},{"id":"6132","post_id":"6576","mon_id":"1158921","chapter_id":"1158929","question":"Cho tam giác ABC có AH là \u0111\u01b0\u1eddng cao (H ∈ BC). K\u1ebb HM \/\/ AC (M ∈ AB), HN \/\/ AB (N ∈ AC).<\/p>Tam giác ABC c\u1ea7n có thêm \u0111i\u1ec1u ki\u1ec7n nào sau \u0111ây \u0111\u1ec3 t\u1ee9 giác AMHN là hình thoi?<\/p>","options":["A.<\/strong> Tam giác ABC vuông t\u1ea1i A.","B.<\/strong> Tam giác ABC vuông t\u1ea1i B.","C.<\/strong> Tam giác ABC cân t\u1ea1i B.","D.<\/strong> Tam giác ABC cân t\u1ea1i A."],"correct":"4","level":"3","hint":"","answer":"<svg height=\"190\" width=\"290\"> <g> <title><\/title> <rect fill=\"#fff\" height=\"192\" id=\"canvas_background\" width=\"292\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_15\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g> <title><\/title> <g id=\"svg_14\"> <g id=\"svg_8\"> <g id=\"svg_6\"> <g id=\"svg_3\"> <path d=\"m19.10377,170.50824l152.5,-154l100.5,154l-202,0l-51,0z\" 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=\"171.31535\" x2=\"171.31535\" y1=\"16.52273\" y2=\"170.52273\"><\/line> <\/g> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_4\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"171.31535\" x2=\"109.31535\" y1=\"170.52273\" y2=\"79.52273\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_5\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"170.31535\" x2=\"233.31535\" y1=\"170.52273\" y2=\"109.52273\"><\/line> <\/g> <rect fill=\"none\" fill-opacity=\"null\" height=\"12\" id=\"svg_7\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\" width=\"12\" x=\"171.31535\" y=\"158.52273\"><\/rect> <\/g> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_9\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"157.31535\" xml:space=\"preserve\" y=\"15.52273\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_10\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"6.31535\" xml:space=\"preserve\" y=\"181.52273\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_11\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"272.31535\" xml:space=\"preserve\" y=\"183.52273\">C<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_12\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"93.31535\" xml:space=\"preserve\" y=\"75.52273\">M<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_13\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"235.31535\" xml:space=\"preserve\" y=\"110.52273\">N<\/text> <\/g> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_16\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"166.31535\" xml:space=\"preserve\" y=\"187.52273\">H<\/text> <\/g> <\/svg><\/span><\/p>Xét t\u1ee9 giác AMHN có AM \/\/ HN (AB \/\/ HN, M ∈ AB) ; AN \/\/ HM (AC \/\/ HM, N ∈ AC).<\/p>Suy ra t\u1ee9 giác AMHN là hình bình hành (t\u1ee9 giác có các c\u1ea1nh \u0111\u1ed1i song song là hình bình hành).<\/p>\u0110\u1ec3 hình bình hành AMHN là hình thoi thì <\/p>AH là tia phân giác c\u1ee7a góc MAN (hình bình hành có m\u1ed9t \u0111\u01b0\u1eddng chéo là \u0111\u01b0\u1eddng phân giác c\u1ee7a m\u1ed9t góc là hình thoi).<\/p>hay AH là tia phân giác c\u1ee7a góc BAC.<\/p>Mà AH là \u0111\u01b0\u1eddng cao c\u1ee7a tam giác ABC.<\/p>⇒ Tam giác ABC là tam giác cân t\u1ea1i A (n\u1ebfu m\u1ed9t tam giác có m\u1ed9t \u0111\u01b0\u1eddng cao v\u1eeba là \u0111\u01b0\u1eddng phân giác thì tam giác \u0111ó là tam giác cân).<\/p>\u0110áp án \u0111úng là   D.<\/strong> Tam giác ABC cân t\u1ea1i A.<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-07-25 10:27:25","option_type":"txt","len":2},{"id":"6135","post_id":"6576","mon_id":"1158921","chapter_id":"1158929","question":"Cho t\u1ee9 giác ABCD là hình thang cân có AB \/\/ CD và $\\widehat{A}=2\\widehat{D}$<\/span> + 30°. Tính s\u1ed1 \u0111o các góc c\u1ee7a hình thang cân \u0111ó.<\/p>","options":["A.<\/strong> $\\widehat{A}=\\widehat{B}$<\/span> = 130°; $\\widehat{C}=\\widehat{D}$<\/span> = 50°.","B.<\/strong> $\\widehat{A}=\\widehat{B}$<\/span> = 120°; $\\widehat{C}=\\widehat{D}$<\/span> = 45°.","C.<\/strong> $\\widehat{A}=\\widehat{B}$<\/span> = 140°; $\\widehat{C}=\\widehat{D}$<\/span> = 55°.","D.<\/strong> $\\widehat{A}=\\widehat{B}$<\/span> = 150°; $\\widehat{C}=\\widehat{D}$<\/span> = 60°."],"correct":"1","level":"3","hint":"","answer":"Vì AB \/\/ CD nên $\\widehat{A}+\\widehat{D}$<\/span> = 180°  (hai góc trong cùng phía).<\/p>              $2\\widehat{D}$<\/span> + 30° + $\\widehat{D}$<\/span> = 180°  (vì  $\\widehat{A}=2\\widehat{D}$<\/span> + 30° )<\/p>                      $3\\widehat{D}$<\/span> + 30° = 180°<\/p>                      $3\\widehat{D}$<\/span>           = 180° – 30°<\/p>                      $3\\widehat{D}$<\/span>           = 150°<\/p>                        $\\widehat{D}$<\/span>           = 150° : 3<\/p>                        $\\widehat{D}$<\/span>           = 50°<\/p>⇒  $\\widehat{A}=2\\widehat{D}$<\/span> + 30° = 2 . 50° + 30° = 130°.<\/p>Vì ABCD là hình thang cân nên   $\\widehat{A}=\\widehat{B}$<\/span> = 130°; $\\widehat{C}=\\widehat{D}$<\/span> = 50°.<\/p>(Hai góc k\u1ec1 c\u1ea1nh \u0111áy c\u1ee7a hình thang cân thì b\u1eb1ng nhau).<\/p>\u0110áp án \u0111úng là    A.<\/strong> $\\widehat{A}=\\widehat{B}$<\/span> = 130°; $\\widehat{C}=\\widehat{D}$<\/span> = 50°.<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-07-25 10:37:00","option_type":"math","len":0}]}