Đa giác đều - Bài tập nâng cao

Home Lớp 9 Toán lớp 9 - Sách Kết nối tri thức Bài 30. Đa giác đềuBài tập nâng cao

{"common":{"save":0,"post_id":"7986","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"10637","post_id":"7986","mon_id":"1159278","chapter_id":"1159333","question":"T\u1ed5ng s\u1ed1 \u0111o các góc trong \u0111a giác n c\u1ea1nh là<\/p>","options":["A.<\/strong> n.180°","B.<\/strong> (n – 1).180°","C.<\/strong> (n – 2).180°","D.<\/strong> (n – 3).180°"],"correct":"3","level":"3","hint":"","answer":"Ch\u1ecdn C.<\/strong> (n – 2).180°.<\/span><\/p>\u0110a giác l\u1ed3i n c\u1ea1nh có s\u1ed1 \u0111\u01b0\u1eddng chéo xu\u1ea5t phát t\u1eeb m\u1ed9t \u0111\u1ec9nh là n – 3 \u0111\u01b0\u1eddng. S\u1ed1 tam giác không có \u0111i\u1ec3m trong chung c\u1ee7a n – giác là: n – 2 tam giác. T\u1ed5ng các góc trong c\u1ee7a n – giác l\u1ed3i b\u1eb1ng t\u1ed5ng các góc c\u1ee7a n – 2 tam giác. V\u1eady t\u1ed5ng các góc trong c\u1ee7a n – giác l\u1ed3i có s\u1ed1 \u0111o b\u1eb1ng (n – 2).180°<\/strong><\/span>.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2025-03-26 08:39:46","option_type":"txt","len":2},{"id":"10640","post_id":"7986","mon_id":"1159278","chapter_id":"1159333","question":"M\u1ed9t \u0111a giác có s\u1ed1 \u0111\u01b0\u1eddng chéo là 54 thì s\u1ed1 c\u1ea1nh c\u1ee7a \u0111a giác \u0111ó là<\/p>","options":["A.<\/strong> 12","B.<\/strong> 10","C.<\/strong> 14","D.<\/strong> 8"],"correct":"1","level":"3","hint":"","answer":"Ch\u1ecdn A.<\/strong> 12.<\/span><\/p>S\u1ed1 \u0111\u01b0\u1eddng chéo c\u1ee7a n - giác là $\\dfrac{(n-3)n}{2}$<\/span>.<\/p>Ta có $\\dfrac{(n-3)n}{2}=54$<\/span> hay $n^2-3n-108=0$<\/span>.<\/p>Suy ra n = 12 (nh\u1eadn) ho\u1eb7c n = –9 (lo\u1ea1i).<\/p>V\u1eady \u0111a giác có 54 \u0111\u01b0\u1eddng chéo thì có s\u1ed1 c\u1ea1nh là 12.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2025-03-26 08:44:03","option_type":"txt","len":0},{"id":"10644","post_id":"7986","mon_id":"1159278","chapter_id":"1159333","question":"Cho l\u1ee5c giác \u0111\u1ec1u ABCDEF. G\u1ecdi O là tâm c\u1ee7a l\u1ee5c giác \u0111\u1ec1u. Có bao nhiêu phép quay tâm O gi\u1eef nguyên tam giác ACE?<\/p>","options":["A.<\/strong> 1","B.<\/strong> 2","C.<\/strong> 4","D.<\/strong> 6"],"correct":"4","level":"3","hint":"","answer":"Ch\u1ecdn D.<\/strong> 6.<\/span><\/p><svg height=\"275\" width=\"300\"> <g><title><\/title><rect fill=\"#ffffff\" height=\"277\" id=\"canvas_background\" width=\"302\" 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><ellipse cx=\"149\" cy=\"136.5\" fill=\"none\" id=\"svg_2\" rx=\"133\" ry=\"133\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <path d=\"m17.3225,136.53144l56.57143,-109.50001l150.85715,0l56.57142,109.50001l-56.57142,109.50001l-150.85715,0l-56.57143,-109.50001z\" fill=\"none\" id=\"svg_3\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\"><\/path> <ellipse cx=\"149\" cy=\"136.5\" fill=\"#000000\" id=\"svg_4\" rx=\"2\" ry=\"2\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <line fill=\"none\" id=\"svg_5\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"72.5\" x2=\"281.5\" y1=\"27\" y2=\"136\"><\/line> <line fill=\"none\" id=\"svg_6\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"74.5\" x2=\"75\" y1=\"27\" y2=\"246\"><\/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=\"75.5\" x2=\"282.5\" y1=\"245\" y2=\"135\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_8\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(54 79.55738830566406,36.96906280517578) matrix(1.7993569374084477,0,0,1.220659001325643,-59.340034658028166,-7.296099131863486) \" x=\"73.19378\" xml:space=\"preserve\" y=\"44.39351\">)<\/text> <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=\"75.5\" xml:space=\"preserve\" y=\"67\">120<\/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=\"100.5\" xml:space=\"preserve\" y=\"55\">o<\/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=\"58.5\" xml:space=\"preserve\" y=\"20\">A<\/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=\"0.5\" xml:space=\"preserve\" y=\"141\">B<\/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=\"59.5\" xml:space=\"preserve\" y=\"259\">C<\/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\" x=\"226.5\" xml:space=\"preserve\" y=\"259\">D<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_16\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"284.5\" xml:space=\"preserve\" y=\"143\">E<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_17\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"228.5\" xml:space=\"preserve\" y=\"27\">F<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_19\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"151.5\" xml:space=\"preserve\" y=\"134\">O<\/text> <\/g> <\/svg><\/span><\/p>Ba \u0111\u1ec9nh A, C, E c\u1ee7a tam giác \u0111\u1ec1u ACE chia \u0111\u01b0\u1eddng tròn (O) thành ba cung b\u1eb1ng nhau và có s\u1ed1 \u0111o là s\u0111 $\\stackrel\\frown{AC}$<\/span> = s\u0111 $\\stackrel\\frown{CE}$<\/span> = s\u0111 $\\stackrel\\frown{EA}$<\/span> = 120° . V\u1eady có 3 phép quay tâm O tho\u1ea3 mãn yêu c\u1ea7u là quay 120°, 240° thu\u1eadn chi\u1ec1u ho\u1eb7c 120° ng\u01b0\u1ee3c chi\u1ec1u.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2025-03-26 09:01:58","option_type":"txt","len":0}]}