Quan hệ giữa góc và cạnh đối diện trong một tam giác-Bài tập nâng cao

Home Toán lớp 7 - Sách KNTT Bài 31: Quan hệ giữa góc và cạnh đối diện trong một tam giácBài tập nâng cao

{"common":{"save":0,"post_id":"5832","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"8651","post_id":"5832","mon_id":"1158532","chapter_id":"1158662","question":"Cho tam giác ABC , D là m\u1ed9t \u0111i\u1ec3m n\u1eb1m trên c\u1ea1nh AC sao cho AD = AB. H\u1ecfi k\u1ebft lu\u1eadn nào sau \u0111ây là \u0111úng?<\/p><svg height=\"220\" width=\"220\"> <g><title><\/title><rect fill=\"#fff\" height=\"222\" id=\"canvas_background\" width=\"222\" 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_21\"> <g id=\"svg_16\"> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_6\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"72.82639\" x2=\"19.82639\" y1=\"9.02083\" y2=\"201.02084\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_7\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"199.82639\" x2=\"72.82639\" y1=\"199.02083\" y2=\"8.02083\"><\/line> <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=\"20.82639\" x2=\"200.82639\" y1=\"200.02083\" y2=\"198.02083\"><\/line> <ellipse cx=\"182.32639\" cy=\"171.52083\" fill=\"#bf5f00\" id=\"svg_10\" rx=\"3\" ry=\"3\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\"><\/ellipse> <ellipse cx=\"73.32639\" cy=\"11.52083\" fill=\"#bf5f00\" id=\"svg_11\" rx=\"3\" ry=\"3\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\"><\/ellipse> <ellipse cx=\"21.32639\" cy=\"198.52083\" fill=\"#bf5f00\" id=\"svg_12\" rx=\"3\" ry=\"3\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\"><\/ellipse> <ellipse cx=\"199.32639\" cy=\"198.52083\" fill=\"#bf5f00\" id=\"svg_13\" rx=\"3\" ry=\"3\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\"><\/ellipse> <line fill=\"none\" id=\"svg_14\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"33.82639\" x2=\"55.82639\" y1=\"108.02083\" y2=\"112.02083\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_15\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"128.82639\" x2=\"145.82639\" y1=\"111.02083\" y2=\"98.02083\"><\/line> <\/g> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" id=\"svg_17\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"57.82639\" xml:space=\"preserve\" y=\"15.02083\">A<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" id=\"svg_18\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"3.82639\" xml:space=\"preserve\" y=\"208.02083\">B<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" id=\"svg_19\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"202.82639\" xml:space=\"preserve\" y=\"199.02083\">C<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" id=\"svg_20\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"182.82639\" xml:space=\"preserve\" y=\"167.02083\">D<\/text> <\/g> <\/g> <\/svg><\/span><\/p>","options":["A.<\/strong> Góc B > góc C","B.<\/strong> Góc B < góc C","C.<\/strong> Góc B = góc C","D.<\/strong> T\u1ea5t c\u1ea3 \u0111\u1ec1u sai"],"correct":"1","level":"3","hint":"So sánh hai canh AB và AC thông qua c\u1ea1nh AD.<\/p>","answer":"Vì D là m\u1ed9t \u0111i\u1ec3m n\u1eb1m trên c\u1ea1nh AC nên AD < AC<\/p>Mà AD = AB (gi\u1ea3 thi\u1ebft)<\/p>Suy ra AB < AC<\/p>Do \u0111ó  góc C < góc B hay góc B > góc C<\/p>\u0110áp án \u0111úng là   A.<\/strong> Góc B > góc C<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"1","date":"2022-06-03 03:33:56","option_type":"txt","len":2},{"id":"8655","post_id":"5832","mon_id":"1158532","chapter_id":"1158662","question":"Trong m\u1ed9t tam giác cân có m\u1ed9t góc b\u1eb1ng 100°. C\u1ea1nh l\u1edbn nh\u1ea5t c\u1ee7a tam giác \u0111ó là<\/p>","options":["A.<\/strong> C\u1ea1nh bên","B. <\/strong>C\u1ea1nh \u0111áy"],"correct":"2","level":"3","hint":"Tam giác cân có góc \u1edf \u0111\u1ec9nh có s\u1ed1 \u0111o là  a° thì hai góc \u1edf \u0111áy có s\u1ed1 \u0111o là  $\\dfrac{180^0-a^0}{2}$<\/span> .<\/p>Tam giác cân có m\u1ed9t góc \u1edf \u0111áy có s\u1ed1 \u0111o là  b° thì góc \u1edf \u0111\u1ec9nh có s\u1ed1 \u0111o là  $180^0-2b^0$<\/span> .<\/p>","answer":"Vì ta ch\u1ec9 bi\u1ebft tam giác \u0111ã cho có m\u1ed9t góc b\u1eb1ng 100° nên ta xét hai tr\u01b0\u1eddng h\u1ee3p:<\/p> + Tr\u01b0\u1eddng h\u1ee3p 1: Góc 100° là góc \u1edf \u0111\u1ec9nh<\/p>    Suy ra hai góc \u1edf \u0111áy có s\u1ed1 \u0111o là  $\\dfrac{180^0-100^0}{2}=40^0$<\/span>.<\/p>    Do \u0111ó góc \u1edf \u0111\u1ec9nh có s\u1ed1 \u0111o l\u1edbn nh\u1ea5t nên c\u1ea1nh \u0111áy là c\u1ea1nh l\u1edbn nh\u1ea5t (vì c\u1ea1nh \u0111\u1ed1i di\u1ec7n v\u1edbi góc \u1edf \u0111\u1ec9nh là c\u1ea1nh \u0111áy).<\/p> + Tr\u01b0\u1eddng h\u1ee3p 2: Góc 100° là góc \u1edf \u0111áy<\/p>    Suy ra góc \u1edf \u0111\u1ec9nh có s\u1ed1 \u0111o là  $180^0-2.100^0=-20^0$<\/span>  (vô lí vì s\u1ed1 \u0111o c\u1ee7a các góc trong m\u1ed9t tam giác ph\u1ea3i là m\u1ed9t s\u1ed1 d\u01b0\u01a1ng)<\/p>    Do \u0111ó không t\u1ed3n t\u1ea1i tam giác trong tr\u01b0\u1eddng h\u1ee3p này.<\/p>T\u1eeb c\u1ea3 hai tr\u01b0\u1eddng h\u1ee3p ta có tam giác \u0111ó là tam giác cân có góc \u1edf \u0111\u1ec9nh b\u1eb1ng 100° nên c\u1ea1nh l\u1edbn nh\u1ea5t c\u1ee7a tam giác \u0111ó là  c\u1ea1nh \u0111áy.<\/p>\u0110áp án \u0111úng là  B. <\/strong>C\u1ea1nh \u0111áy<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"1","date":"2022-06-03 04:03:01","option_type":"txt","len":2},{"id":"8658","post_id":"5832","mon_id":"1158532","chapter_id":"1158662","question":"Cho hình vuông ABCD, \u0111i\u1ec3m M là m\u1ed9t \u0111i\u1ec3m n\u1eb1m trên c\u1ea1nh AD (hình v\u1ebd). So sánh BM và CD.<\/p><svg height=\"200\" width=\"200\"> <g><title><\/title><rect fill=\"#fff\" height=\"202\" 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_9\"> <rect fill=\"#fff\" height=\"150\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\" width=\"150\" x=\"25.82639\" y=\"22.02083\"><\/rect> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" id=\"svg_2\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"12.82639\" xml:space=\"preserve\" y=\"18.02083\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" id=\"svg_3\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"177.82639\" xml:space=\"preserve\" y=\"20.02083\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" id=\"svg_4\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"180.82639\" xml:space=\"preserve\" y=\"184.02083\">C<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" id=\"svg_5\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"12.82639\" xml:space=\"preserve\" y=\"180.02083\">D<\/text> <ellipse cx=\"25.32639\" cy=\"70.52083\" fill=\"#ffaa56\" id=\"svg_6\" rx=\"2.5\" ry=\"3\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\"><\/ellipse> <line fill=\"none\" id=\"svg_7\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"25.82639\" x2=\"174.82639\" y1=\"72.02083\" y2=\"23.02083\"><\/line> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" id=\"svg_8\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"6.82639\" xml:space=\"preserve\" y=\"75.02083\">M<\/text> <\/g> <\/g> <\/svg><\/span><\/p>","options":["A.<\/strong> BM < CD","B.<\/strong> BM > CD","C. <\/strong>BM = CD","D.<\/strong> Không so sánh \u0111\u01b0\u1ee3c"],"correct":"2","level":"3","hint":"So sánh c\u1ea1nh BM và AB r\u1ed3i t\u1eeb \u0111ó so sánh BM và CD.<\/p>","answer":"Vì tam giác ABM vuông t\u1ea1i A nên BM là c\u1ea1nh huy\u1ec1n<\/p>Suy ra BM là c\u1ea1nh l\u1edbn nh\u1ea5t hay  BM > AB.<\/p>M\u1eb7t khác ABCD là hình vuông nên AB = CD.<\/p>Do \u0111ó BM > CD.<\/p>\u0110áp án \u0111úng là    B.<\/strong> BM > CD<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"1","date":"2022-06-03 04:17:42","option_type":"txt","len":2}]}