Tứ giác - Bài tập nâng cao

Home Lớp 8 Toán lớp 8 - Sách Kết nối tri thứcBài tập nâng cao

{"common":{"save":0,"post_id":"6561","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"6018","post_id":"6561","mon_id":"1158921","chapter_id":"1158929","question":"T\u1ee9 giác ABCD có BA = BC, DA = DC và $\\widehat{B}=80^0,\\widehat{D}=120^0$<\/span>. Tính các góc A và góc C.<\/p><svg height=\"210\" width=\"242\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\"> <g><title><\/title><rect fill=\"#fff\" height=\"212\" id=\"canvas_background\" width=\"244\" 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><image height=\"210\" id=\"svg_1\" stroke=\"null\" width=\"242\" x=\"0.5\" 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\" y=\"1.5\"><\/image> <line fill=\"none\" id=\"svg_7\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"14.36175\" x2=\"142.44439\" y1=\"74.27889\" y2=\"65.0646\"><\/line> <\/g> <\/g> <\/svg><\/span><\/p>Xét $\\Delta$<\/span>ABD và $\\Delta$<\/span>CBD có: BD là c\u1ea1nh chung, BA = BC, DA = DC.<\/p>Suy ra $\\Delta$<\/span>ABD = $\\Delta$<\/span>CBD (c.c.c)<\/p>Suy ra $\\widehat{BAD}=\\widehat{BCD}$<\/span> (hai góc t\u01b0\u01a1ng \u1ee9ng) hay $\\widehat{A}=\\widehat{C}$<\/span><\/p>Theo \u0111\u1ecbnh lí v\u1ec1 t\u1ed5ng các góc trong m\u1ed9t t\u1ee9 giác, ta có:<\/p> $\\widehat{A}+\\widehat{B}+\\widehat{C}+\\widehat{D}=360^0$<\/span><\/p>$\\widehat{A}+80^0+\\widehat{A}+120^0=360^0$<\/span><\/p>           $2.\\widehat{A}=160^0$<\/span><\/p>           $\\widehat{A}=80^0$<\/span><\/p>Suy ra $\\widehat{C}=\\widehat{A}=80^0$<\/span><\/p>Ch\u1ecdn D.<\/strong> $\\widehat{A}=\\widehat{C}=80^0$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-07-17 07:09:04","option_type":"math","len":0},{"id":"6021","post_id":"6561","mon_id":"1158921","chapter_id":"1158929","question":"Cho t\u1ee9 giác MNPQ, bi\u1ebft $\\widehat{M}:\\widehat{N}:\\widehat{P}:\\widehat{Q}=4:3:2:1$<\/span>. Tính các góc c\u1ee7a t\u1ee9 giác MNPQ.<\/p>","options":["A.<\/strong> $\\widehat{M}=36^0,\\widehat{N}=108^0,\\widehat{P}=72^0,\\widehat{Q}=144^0$<\/span>","B.<\/strong> $\\widehat{M}=36^0,\\widehat{N}=72^0,\\widehat{P}=108^0,\\widehat{Q}=144^0$<\/span>","C.<\/strong> $\\widehat{M}=144^0,\\widehat{N}=108^0,\\widehat{P}=72^0,\\widehat{Q}=36^0$<\/span>","D.<\/strong> $\\widehat{M}=72^0,\\widehat{N}=108^0,\\widehat{P}=144^0,\\widehat{Q}=36^0$<\/span>"],"correct":"3","level":"3","hint":"","answer":"Vì $\\widehat{M}:\\widehat{N}:\\widehat{P}:\\widehat{Q}=4:3:2:1$<\/span> nên $\\dfrac{\\widehat{M}}{4}=\\dfrac{\\widehat{N}}{3}=\\dfrac{\\widehat{P}}{2}=\\dfrac{\\widehat{Q}}{1}$<\/span>. <\/p>Áp d\u1ee5ng tính ch\u1ea5t c\u1ee7a dãy t\u1ec9 s\u1ed1 b\u1eb1ng nhau ta có:<\/p>$\\dfrac{\\widehat{M}}{4}=\\dfrac{\\widehat{N}}{3}=\\dfrac{\\widehat{P}}{2}=\\dfrac{\\widehat{Q}}{1}$<\/span> $=\\dfrac{\\widehat{M}+\\widehat{N}+\\widehat{P}+\\widehat{Q}}{4+3+2+1}=\\dfrac{360^0}{10}=36^0$<\/span><\/p>Suy ra $\\widehat{M}=4.36^0=144^0,\\widehat{N}=3.36^0=108^0,\\widehat{P}=2.36^0=72^0,\\widehat{Q}=1.36^0=36^0$<\/span><\/p>Ch\u1ecdn C.<\/strong> $\\widehat{M}=144^0,\\widehat{N}=108^0,\\widehat{P}=72^0,\\widehat{Q}=36^0$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-07-17 07:26:00","option_type":"math","len":0},{"id":"6023","post_id":"6561","mon_id":"1158921","chapter_id":"1158929","question":"Cho t\u1ee9 giác MNPQ, bi\u1ebft $\\widehat{M}:\\widehat{N}:\\widehat{P}:\\widehat{Q}=2:2:2:3$<\/span>. Tính các góc c\u1ee7a t\u1ee9 giác MNPQ.<\/p>","options":["A.<\/strong> $\\widehat{M}=120^0,\\widehat{N}=80^0,\\widehat{P}=80^0,\\widehat{Q}=80^0$<\/span>","B.<\/strong> $\\widehat{M}=80^0,\\widehat{N}=80^0,\\widehat{P}=120^0,\\widehat{Q}=80^0$<\/span>","C.<\/strong> $\\widehat{M}=80^0,\\widehat{N}=120^0,\\widehat{P}=80^0,\\widehat{Q}=80^0$<\/span>","D.<\/strong> $\\widehat{M}=80^0,\\widehat{N}=80^0,\\widehat{P}=80^0,\\widehat{Q}=120^0$<\/span>"],"correct":"4","level":"3","hint":"","answer":"Vì $\\widehat{M}:\\widehat{N}:\\widehat{P}:\\widehat{Q}=2:2:2:3$<\/span> nên $\\dfrac{\\widehat{M}}{2}=\\dfrac{\\widehat{N}}{2}=\\dfrac{\\widehat{P}}{2}=\\dfrac{\\widehat{Q}}{3}$<\/span>. <\/p>Áp d\u1ee5ng tính ch\u1ea5t c\u1ee7a dãy t\u1ec9 s\u1ed1 b\u1eb1ng nhau ta có:<\/p>$\\dfrac{\\widehat{M}}{2}=\\dfrac{\\widehat{N}}{2}=\\dfrac{\\widehat{P}}{2}=\\dfrac{\\widehat{Q}}{3}$<\/span> $=\\dfrac{\\widehat{M}+\\widehat{N}+\\widehat{P}+\\widehat{Q}}{2+2+2+3}=\\dfrac{360^0}{9}=40^0$<\/span><\/p>Suy ra $\\widehat{M}=2.40^0=80^0,\\widehat{N}=2.40^0=80^0,\\widehat{P}=2.40^0=80^0,\\widehat{Q}=3.40^0=120^0$<\/span><\/p>Ch\u1ecdn D.<\/strong> $\\widehat{M}=80^0,\\widehat{N}=80^0,\\widehat{P}=80^0,\\widehat{Q}=120^0$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-07-17 07:30:40","option_type":"math","len":0}]}