{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" Trong m\u1ed9t tam gi\u00e1c giao \u0111i\u1ec3m c\u1ee7a ba \u0111\u01b0\u1eddng trung tuy\u1ebfn g\u1ecdi l\u00e0: ","select":["A. Tr\u1ecdng t\u00e2m c\u1ee7a tam gi\u00e1c ","B. Tr\u1ef1c t\u00e2m c\u1ee7a tam gi\u00e1c","C. T\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c","D. T\u00e2m \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp tam gi\u00e1c"],"hint":"","explain":" Ba \u0111\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a m\u1ed9t tam gi\u00e1c c\u00f9ng \u0111i qua m\u1ed9t \u0111i\u1ec3m, \u0111i\u1ec3m \u0111\u00f3 l\u00e0 tr\u1ecdng t\u00e2m c\u1ee7a tam gi\u00e1c <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: A <\/span> ","column":2}]}],"id_ques":2011},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"Ba \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a m\u1ed9t tam gi\u00e1c \u0111\u1ed3ng quy t\u1ea1i m\u1ed9t \u0111i\u1ec3m \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0: ","select":["A. Tr\u1ecdng t\u00e2m c\u1ee7a tam gi\u00e1c ","B. Tr\u1ef1c t\u00e2m c\u1ee7a tam gi\u00e1c","C. T\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c","D. T\u00e2m \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp tam gi\u00e1c"],"hint":"","explain":" Ba \u0111\u01b0\u1eddng trung trung tr\u1ef1c c\u1ee7a tam gi\u00e1c c\u00f9ng \u0111i qua m\u1ed9t \u0111i\u1ec3m, \u0111i\u1ec3m n\u00e0y c\u00e1ch \u0111\u1ec1u ba \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c <br\/> N\u00ean giao \u0111i\u1ec3m c\u1ee7a ba \u0111\u01b0\u1eddng trung tr\u1ef1c ch\u00ednh l\u00e0 t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: C<\/span> ","column":2}]}],"id_ques":2012},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"T\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c l\u00e0 \u0111i\u1ec3m c\u1eaft nhau c\u1ee7a: ","select":["A. Ba \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a c\u00e1c c\u1ea1nh ","B. Ba \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a c\u00e1c g\u00f3c","C. Ba \u0111\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a tam gi\u00e1c","D. Ba \u0111\u01b0\u1eddng cao c\u1ee7a tam gi\u00e1c"],"hint":"","explain":" T\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c l\u00e0 \u0111i\u1ec3m c\u00e1ch \u0111\u1ec1u ba \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c <br\/> Do \u0111\u00f3 t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c ch\u00ednh l\u00e0 giao \u0111i\u1ec3m ba \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a c\u00e1c c\u1ea1nh <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: A<\/span> ","column":2}]}],"id_ques":2013},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"C\u00e1c ph\u00e2n gi\u00e1c trong c\u1ee7a m\u1ed9t tam gi\u00e1c c\u1eaft nhau \u1edf m\u1ed9t \u0111i\u1ec3m g\u1ecdi l\u00e0: ","select":["A. Tr\u1ecdng t\u00e2m c\u1ee7a tam gi\u00e1c ","B. Tr\u1ef1c t\u00e2m c\u1ee7a tam gi\u00e1c","C. T\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c","D. T\u00e2m \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp tam gi\u00e1c"],"hint":"","explain":" Ba \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c trong c\u1ee7a tam gi\u00e1c c\u1eaft nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m, \u0111i\u1ec3m n\u00e0y c\u00e1ch \u0111\u1ec1u ba c\u1ea1nh c\u1ee7a tam gi\u00e1c <br\/> N\u00ean giao \u0111i\u1ec3m c\u1ee7a ba \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c trong c\u1ee7a tam gi\u00e1c ch\u00ednh l\u00e0 t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp tam gi\u00e1c <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D<\/span> ","column":2}]}],"id_ques":2014},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"H\u00e3y ch\u1ecdn tam gi\u00e1c c\u00f3 tr\u1ef1c t\u00e2m v\u00e0 t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c \u0111\u00f3 tr\u00f9ng nhau. ","select":["A. Tam gi\u00e1c vu\u00f4ng ","B. Tam gi\u00e1c th\u01b0\u1eddng","C. Tam gi\u00e1c c\u00e2n","D. Tam gi\u00e1c \u0111\u1ec1u"],"hint":"","explain":" Tam gi\u00e1c c\u00f3 tr\u1ef1c t\u00e2m v\u00e0 t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c \u0111\u00f3 tr\u00f9ng nhau l\u00e0 tam gi\u00e1c \u0111\u1ec1u (theo nh\u1eadn x\u00e9t SGK - Tr.82) <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D <\/span> ","column":2}]}],"id_ques":2015},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00fang hay sai","title_trans":"","temp":"true_false","correct":[["t","f","t","t"]],"list":[{"point":5,"image":"","col_name":["Kh\u1eb3ng \u0111\u1ecbnh","\u0110\u00fang","Sai"],"arr_ques":[" \u0110\u01b0\u1eddng vu\u00f4ng g\u00f3c l\u00e0 \u0111\u01b0\u1eddng ng\u1eafn nh\u1ea5t so v\u1edbi \u0111\u01b0\u1eddng xi\u00ean xu\u1ea5t ph\u00e1t t\u1eeb m\u1ed9t \u0111i\u1ec3m \u0111\u1ebfn m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng"," Trong hai \u0111\u01b0\u1eddng xi\u00ean, \u0111\u01b0\u1eddng n\u00e0o l\u1edbn h\u01a1n th\u00ec c\u00f3 h\u00ecnh chi\u1ebfu nh\u1ecf h\u01a1n "," Hai \u0111\u01b0\u1eddng xi\u00ean b\u1eb1ng nhau th\u00ec hai h\u00ecnh chi\u1ebfu c\u1ee7a ch\u00fang b\u1eb1ng nhau ","Hai \u0111\u01b0\u1eddng xi\u00ean c\u00f3 ch\u00e2n c\u00e1ch \u0111\u1ec1u ch\u00e2n c\u1ee7a \u0111\u01b0\u1eddng vu\u00f4ng g\u00f3c th\u00ec b\u1eb1ng nhau"],"hint":"","explain":["\u0110\u00daNG theo quan h\u1ec7 gi\u1eefa \u0111\u01b0\u1eddng vu\u00f4ng g\u00f3c v\u00e0 \u0111\u01b0\u1eddng xi\u00ean","SAI: \u0110\u01b0\u1eddng xi\u00ean n\u00e0o l\u1edbn h\u01a1n th\u00ec c\u00f3 h\u00ecnh chi\u1ebfu l\u1edbn h\u01a1n ","\u0110\u00daNG ","\u0110\u00daNG: Hai h\u00ecnh chi\u1ebfu b\u1eb1ng nhau th\u00ec hai \u0111\u01b0\u1eddng xi\u00ean b\u1eb1ng nhau "]}]}],"id_ques":2016},{"time":24,"part":[{"title":"N\u1ed1i t\u1eeb ho\u1eb7c c\u1ee5m t\u1eeb \u1edf c\u1ed9t b\u00ean tr\u00e1i v\u1edbi c\u1ed9t b\u00ean ph\u1ea3i \u0111\u1ec3 \u0111\u01b0\u1ee3c c\u00e2u ho\u00e0n ch\u1ec9nh","title_trans":"N\u1ed1i t\u1eeb ho\u1eb7c c\u1ee5m t\u1eeb \u1edf c\u1ed9t b\u00ean tr\u00e1i v\u1edbi c\u1ed9t b\u00ean ph\u1ea3i \u0111\u1ec3 \u0111\u01b0\u1ee3c c\u00e2u ho\u00e0n ch\u1ec9nh","audio":"","temp":"matching","correct":[["3","1","4","2"]],"list":[{"point":5,"image":"","left":["\u0110i\u1ec3m n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a m\u1ed9t \u0111o\u1ea1n th\u1eb3ng","\u0110i\u1ec3m n\u1eb1m tr\u00ean tia ph\u00e2n gi\u00e1c c\u1ee7a m\u1ed9t g\u00f3c","Giao \u0111i\u1ec3m ba \u0111\u01b0\u1eddng trung tr\u1ef1c trong m\u1ed9t tam gi\u00e1c","Giao \u0111i\u1ec3m ba \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c trong m\u1ed9t tam gi\u00e1c"],"right":["th\u00ec c\u00e1ch \u0111\u1ec1u hai c\u1ea1nh c\u1ee7a g\u00f3c \u0111\u00f3","th\u00ec c\u00e1ch \u0111\u1ec1u ba c\u1ea1nh c\u1ee7a tam gi\u00e1c \u0111\u00f3","th\u00ec c\u00e1ch \u0111\u1ec1u hai \u0111\u1ea7u \u0111o\u1ea1n th\u1eb3ng \u0111\u00f3","th\u00ec c\u00e1ch \u0111\u1ec1u ba \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c \u0111\u00f3"],"top":100,"hint":"","explain":" <span class='basic_left'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0: <br\/> \u0110i\u1ec3m n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a m\u1ed9t \u0111o\u1ea1n th\u1eb3ng th\u00ec c\u00e1ch \u0111\u1ec1u hai \u0111\u1ea7u \u0111o\u1ea1n th\u1eb3ng \u0111\u00f3 <br\/> \u0110i\u1ec3m n\u1eb1m tr\u00ean tia ph\u00e2n gi\u00e1c c\u1ee7a m\u1ed9t g\u00f3c th\u00ec c\u00e1ch \u0111\u1ec1u hai c\u1ea1nh c\u1ee7a m\u1ed9t g\u00f3c <br\/> Giao \u0111i\u1ec3m ba \u0111\u01b0\u1eddng trung tr\u1ef1c trong m\u1ed9t tam gi\u00e1c th\u00ec c\u00e1ch \u0111\u1ec1u ba \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c \u0111\u00f3 <br\/> Giao \u0111i\u1ec3m ba \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c trong m\u1ed9t tam gi\u00e1c th\u00ec c\u00e1ch \u0111\u1ec1u ba c\u1ea1nh c\u1ee7a tam gi\u00e1c \u0111\u00f3 <\/span> "}]}],"id_ques":2017},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00fang hay sai","title_trans":"","temp":"true_false","correct":[["t","t","f","t"]],"list":[{"point":5,"image":"","col_name":["Kh\u1eb3ng \u0111\u1ecbnh","\u0110\u00fang","Sai"],"arr_ques":[" Trong m\u1ed9t tam gi\u00e1c m\u1ed9t c\u1ea1nh nh\u1ecf h\u01a1n t\u1ed5ng \u0111\u1ed9 d\u00e0i hai c\u1ea1nh kia"," Trong m\u1ed9t tam gi\u00e1c vu\u00f4ng c\u1ea1nh d\u00e0i nh\u1ea5t l\u00e0 c\u1ea1nh huy\u1ec1n "," Trong m\u1ed9t tam gi\u00e1c \u0111\u1ed1i di\u1ec7n v\u1edbi c\u1ea1nh l\u1edbn nh\u1ea5t l\u00e0 g\u00f3c t\u00f9 "," M\u1ed9t tam gi\u00e1c c\u00e2n g\u00f3c \u1edf \u0111\u1ec9nh nh\u1ecf h\u01a1n $60^{o}$ th\u00ec c\u1ea1nh \u0111\u00e1y nh\u1ecf nh\u1ea5t "],"hint":"","explain":["\u0110\u00daNG theo b\u1ea5t \u0111\u1eb3ng th\u1ee9c tam gi\u00e1c","\u0110\u00daNG v\u00ec trong tam gi\u00e1c g\u00f3c l\u1edbn nh\u1ea5t l\u00e0 g\u00f3c vu\u00f4ng n\u00ean c\u1ea1nh \u0111\u1ed1i di\u1ec7n v\u1edbi g\u00f3c vu\u00f4ng l\u00e0 c\u1ea1nh l\u1edbn nh\u1ea5t ","SAI v\u00ec trong tam gi\u00e1c nh\u1ecdn th\u00ec \u0111\u1ed1i di\u1ec7n v\u1edbi c\u1ea1nh l\u1edbn nh\u1ea5t l\u00e0 g\u00f3c nh\u1ecdn","\u0110\u00daNG: V\u00ec t\u1ed5ng ba g\u00f3c trong tam gi\u00e1c b\u1eb1ng $180^{o}$ n\u00ean n\u1ebfu g\u00f3c \u1edf \u0111\u1ec9nh nh\u1ecf h\u01a1n $60^{o}$ th\u00ec t\u1ed5ng hai g\u00f3c \u1edf \u0111\u00e1y l\u1edbn h\u01a1n $120^{o}$ <br\/> N\u00ean m\u1ed7i g\u00f3c \u1edf \u0111\u00e1y l\u1edbn h\u01a1n $60^{o}$ <br\/> $\\Rightarrow$ G\u00f3c \u1edf \u0111\u1ec9nh l\u00e0 g\u00f3c nh\u1ecf nh\u1ea5t n\u00ean c\u1ea1nh \u0111\u00e1y nh\u1ecf nh\u1ea5t (quan h\u1ec7 gi\u1eefa g\u00f3c v\u00e0 c\u1ea1nh \u0111\u1ed1i di\u1ec7n trong tam gi\u00e1c) "]}]}],"id_ques":2018},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"Cho tam gi\u00e1c $ABC$ c\u00f3 $\\widehat{A} = 70^{o}, \\widehat{B} = 50^{o}$. Khi \u0111\u00f3: ","select":["A. $AC > BC$ ","B. $AB > AC$","C. $AB = BC$ ","D. $AB < AC$ "],"hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> T\u00ednh $\\widehat{C}$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> So s\u00e1nh c\u00e1c g\u00f3c c\u1ee7a $\\triangle{ABC}$ r\u1ed3i so s\u00e1nh c\u00e1c c\u1ea1nh c\u1ee7a $\\triangle{ABC}$ <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai24/lv1/img\/H7C3B24_D01.png' \/><\/center> <br\/> Trong $\\triangle{ABC}$ c\u00f3 $\\widehat{A} + \\widehat{B} + \\widehat{C} = 180^{o}$ (t\u1ed5ng ba g\u00f3c trong m\u1ed9t tam gi\u00e1c) <br\/> $ \\begin{align} \\Rightarrow \\widehat{C} &= 180^{o} - (\\widehat{A} + \\widehat{B}) \\\\ &= 180^{o} - (70^{o} + 50^{o}) \\\\ &= 60^{o} \\end{align} $ <br\/> V\u00ec $50^{o} < 60^{o} < 70^{o}$ n\u00ean $\\widehat{B} < \\widehat{C} < \\widehat{A}$ <br\/> $\\Rightarrow$ $AC < AB < BC$ (quan h\u1ec7 gi\u1eefa g\u00f3c v\u00e0 c\u1ea1nh \u0111\u1ed1i di\u1ec7n trong $\\triangle{ABC}$) <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: B. $AB > AC$ <\/span> ","column":2}]}],"id_ques":2019},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"Cho tam gi\u00e1c $ABC$ c\u00e2n \u1edf $A$, trung tuy\u1ebfn $AM$, tr\u1ecdng t\u00e2m $G$. Bi\u1ebft $AB = 5cm$, $BM = 4cm$. Khi \u0111\u00f3 \u0111\u1ed9 d\u00e0i $AG$ l\u00e0: ","select":["A. $\\dfrac{5}{3}cm$ ","B. $4cm$","C. $2cm$ ","D. $3cm$ "],"hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> T\u00ednh $AM$ d\u1ef1a v\u00e0o \u0111\u1ecbnh l\u00fd Pitago <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ednh $AG$ d\u1ef1a v\u00e0o t\u00ednh ch\u1ea5t tr\u1ecdng t\u00e2m <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai24/lv1/img\/H7C3B24_D02.png' \/><\/center> <br\/> $\\blacktriangleright$ $\\triangle{ABC}$ c\u00e2n t\u1ea1i $A$ c\u00f3 $AM$ l\u00e0 trung tuy\u1ebfn n\u00ean $AM$ c\u0169ng l\u00e0 \u0111\u01b0\u1eddng cao (t\u00ednh ch\u1ea5t tam gi\u00e1c c\u00e2n) <br\/> $\\triangle{ABM}$ vu\u00f4ng t\u1ea1i $M$ c\u00f3: <br\/> $AM^2 + BM^2 = AB^2$ (\u0111\u1ecbnh l\u00fd Pitago) <br\/> $\\begin{align} \\Rightarrow AM^2 &= AB^2 - BM^2 \\\\ &= 5^2 - 4^2 \\\\ &= 9 \\end{align}$ <br\/> $\\Rightarrow$ $AM = 3(cm)$ <br\/> $\\blacktriangleright$ V\u00ec $AM$ l\u00e0 trung tuy\u1ebfn, $G$ l\u00e0 tr\u1ecdng t\u00e2m n\u00ean $AG = \\dfrac{2}{3}AM = \\dfrac{2}{3}.3 = 2(cm)$ <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: C. $2cm$ <\/span> ","column":2}]}],"id_ques":2020},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":" Trong c\u00e1c b\u1ed9 ba \u0111o\u1ea1n th\u1eb3ng c\u00f3 \u0111\u1ed9 d\u00e0i sau, b\u1ed9 ba n\u00e0o <b> kh\u00f4ng <\/b> v\u1ebd \u0111\u01b0\u1ee3c m\u1ed9t tam gi\u00e1c? ","select":["A. $10, 41, 42$ ","B. $6, 7, 2$","C. $8, 8, 5$ ","D. $8, 8, 17$ "],"hint":"S\u1eed d\u1ee5ng b\u1ea5t \u0111\u1eb3ng th\u1ee9c tam gi\u00e1c ho\u1eb7c h\u1ec7 qu\u1ea3","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> X\u00e1c \u0111\u1ecbnh s\u1ed1 l\u1edbn nh\u1ea5t trong b\u1ed9 ba s\u1ed1 \u0111\u00e3 cho <br\/> <b> B\u01b0\u1edbc 2: <\/b> So s\u00e1nh t\u1ed5ng hai s\u1ed1 c\u00f2n l\u1ea1i v\u1edbi s\u1ed1 l\u1edbn nh\u1ea5t <br\/> N\u1ebfu c\u00f3 $a + b > c$ th\u00ec b\u1ed9 ba s\u1ed1 \u0111\u00f3 c\u00f3 th\u1ec3 v\u1ebd \u0111\u01b0\u1ee3c m\u1ed9t tam gi\u00e1c ($c$ l\u00e0 s\u1ed1 l\u1edbn nh\u1ea5t) <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> \u00c1p d\u1ee5ng b\u1ea5t \u0111\u1eb3ng th\u1ee9c tam gi\u00e1c cho c\u00e1c b\u1ed9 ba \u0111o\u1ea1n th\u1eb3ng, ta c\u00f3: <br\/> $\\blacktriangleright$ $10 + 41 > 42$ n\u00ean b\u1ed9 ba \u0111o\u1ea1n th\u1eb3ng c\u00f3 \u0111\u1ed9 d\u00e0i $10, 41, 42$ c\u00f3 th\u1ec3 v\u1ebd \u0111\u01b0\u1ee3c m\u1ed9t tam gi\u00e1c <br\/> $\\blacktriangleright$ $6 + 2 > 7$ n\u00ean b\u1ed9 ba \u0111o\u1ea1n th\u1eb3ng c\u00f3 \u0111\u1ed9 d\u00e0i $6, 7, 2$ c\u00f3 th\u1ec3 v\u1ebd \u0111\u01b0\u1ee3c m\u1ed9t tam gi\u00e1c <br\/> $\\blacktriangleright$ $8 + 5 > 8$ n\u00ean b\u1ed9 ba \u0111o\u1ea1n th\u1eb3ng c\u00f3 \u0111\u1ed9 d\u00e0i $8, 8, 5$ c\u00f3 th\u1ec3 v\u1ebd \u0111\u01b0\u1ee3c m\u1ed9t tam gi\u00e1c <br\/> $\\blacktriangleright$ $8 + 8 < 17$ n\u00ean b\u1ed9 ba \u0111o\u1ea1n th\u1eb3ng c\u00f3 \u0111\u1ed9 d\u00e0i $8, 8, 17$ kh\u00f4ng th\u1ec3 v\u1ebd \u0111\u01b0\u1ee3c m\u1ed9t tam gi\u00e1c <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang ph\u1ea3i ch\u1ecdn l\u00e0: D. $8, 8, 17$ <\/span> ","column":2}]}],"id_ques":2021},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"Cho tam gi\u00e1c $MNP$ c\u00f3 $\\widehat{N} = 100^{o}$. C\u00e1c \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{M}$ v\u00e0 $\\widehat{P}$ c\u1eaft nhau t\u1ea1i $O$. S\u1ed1 \u0111o c\u1ee7a g\u00f3c $MOP$ l\u00e0: ","select":["A. $140^{o}$ ","B. $130^{o}$","C. $120^{o}$ ","D. $110^{o}$ "],"hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> T\u00ednh s\u1ed1 \u0111o $\\widehat{M} + \\widehat{P}$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ednh s\u1ed1 \u0111o $\\widehat{OMP} + \\widehat{OPM}$ <br\/> <b> B\u01b0\u1edbc 3: <\/b> T\u00ednh s\u1ed1 \u0111o $\\widehat{MOP}$ <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai24/lv1/img\/H7C3B24_D03.png' \/><\/center> <br\/> $\\blacktriangleright$ Trong $\\triangle{MNP}$ c\u00f3: $\\widehat{M} + \\widehat{N} + \\widehat{P} = 180^{o}$ (t\u1ed5ng ba g\u00f3c trong m\u1ed9t tam gi\u00e1c) <br\/> $ \\begin{align} \\Rightarrow \\widehat{M} + \\widehat{P} &= 180^{o} - \\widehat{N} \\\\ &= 180^{o} - 100^{o} \\\\ &= 80^{o} \\end{align}$ <br\/> $\\blacktriangleright$ V\u00ec $MO, PO$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{M}$ v\u00e0 $\\widehat{P}$ <br\/> $\\Rightarrow$ $\\widehat{M_{1}} + \\widehat{P_{1}} = \\dfrac{\\widehat{M} + \\widehat{P}}{2} = \\dfrac{80^{o}}{2} = 40^{o}$ <br\/> $\\blacktriangleright$ Trong $\\triangle{MOP}$ c\u00f3 $\\widehat{M_{1}} + \\widehat{MOP} + \\widehat{P_{1}} = 180^{o}$ <br\/> $ \\begin{align} \\Rightarrow \\widehat{MOP} &= 180^{o} - (\\widehat{M_{1}} + \\widehat{P_{1}}) \\\\ &= 180^{o} - 40^{o} \\\\ &= 140^{o} \\end{align}$ <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: A. $140^{o}$ <\/span> ","column":2}]}],"id_ques":2022},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"Cho tam gi\u00e1c $ABC$ c\u00e2n \u1edf $A$ c\u00f3 $\\widehat{BAC} = 70^{o}$. C\u00e1c \u0111\u01b0\u1eddng cao $BI$ v\u00e0 $CK$ c\u1eaft nhau t\u1ea1i $H$. Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y <b> sai<\/b>? ","select":["A. $\\widehat{ABI} = \\widehat{ACK} = 20^{o}$ ","B. $\\widehat{IBC} + \\widehat{KCB} = 110^{o} $","C. $\\widehat{BHC} = 110^{o}$ ","D. $BI = CK$ "],"hint":"","explain":" <span class='basic_left'> <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai24/lv1/img\/H7C3B24_D04.png' \/><\/center> <br\/> $\\blacktriangleright$ $\\widehat{A}$ v\u00e0 $\\widehat{C_{2}}$ l\u00e0 hai g\u00f3c ph\u1ee5 nhau n\u00ean $\\widehat{C_{2}} = 90^{o} - \\widehat{A} = 90^{o} - 70^{o} = 20^{o}$ <br\/> $\\widehat{B_{2}} = \\widehat{C_{2}} = 20^{o}$ (c\u00f9ng ph\u1ee5 v\u1edbi $\\widehat{A}$) (1) <br\/> $\\Rightarrow$ <b> \u0110\u00e1p \u00e1n A \u0111\u00fang <\/b> <br\/> $\\blacktriangleright$ $\\triangle{ABC}$ c\u00e2n t\u1ea1i $A$ n\u00ean $\\widehat{ABC} = \\widehat{ACB}$ (t\u00ednh ch\u1ea5t) <br\/> M\u00e0 $\\widehat{A} + \\widehat{B} + \\widehat{C} = 180^{o}$ (t\u1ed5ng ba g\u00f3c trong m\u1ed9t tam gi\u00e1c) <br\/> $\\Rightarrow$ $\\widehat{B} + \\widehat{C} = 180^{o} - \\widehat{A} = 180^{o} - 70^{o} = 110^{o}$ <br\/> $ \\begin{align} \\Rightarrow \\widehat{IBC} + \\widehat{KCB} &= \\widehat{B} + \\widehat{C} - (\\widehat{B_{2}} + \\widehat{C_{2}}) \\\\ &= 110^{o} - (20^{o} + 20^{o}) \\\\ &= 70^{o} \\end{align} $ <br\/> $\\Rightarrow$ <b> \u0110\u00e1p \u00e1n B sai <\/b> <br\/> $\\blacktriangleright$ $\\triangle{BHC}$ c\u00f3 $\\widehat{B_{1}} + \\widehat{C_{1}} + \\widehat{BHC} = 180^{o}$ (t\u1ed5ng ba g\u00f3c trong m\u1ed9t tam gi\u00e1c) <br\/> $\\Rightarrow$ $\\widehat{BHC} = 180^{o} - (\\widehat{B_{1}} + \\widehat{C_{1}}) = 180^{o} - 70^{o} = 110^{o}$ <br\/> $\\Rightarrow$ <b> \u0110\u00e1p \u00e1n C \u0111\u00fang <\/b> <br\/> $\\blacktriangleright$ $\\triangle{BIC} = \\triangle{CKB}$ (c\u1ea1nh huy\u1ec1n - g\u00f3c nh\u1ecdn) v\u00ec: <br\/> $\\begin{cases} \\widehat{KBC} = \\widehat{ICB} (\\triangle{ABC} \\hspace{0,2cm} \\text{c\u00e2n}) \\\\ BC \\hspace{0,2cm} \\text{chung} \\end{cases}$ <br\/> $\\Rightarrow$ $BI = CK$ (hai c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) <br\/> $\\Rightarrow$ <b> \u0110\u00e1p \u00e1n D \u0111\u00fang <\/b> <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n sai l\u00e0: B <\/span> ","column":2}]}],"id_ques":2023},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"Cho tam gi\u00e1c $ABC$ c\u00e2n t\u1ea1i $A$ c\u00f3 $\\widehat{A} = 110^{o}$. Tr\u00ean c\u1ea1nh $BC$ l\u1ea5y \u0111i\u1ec3m $D$ bi\u1ebft $\\widehat{ADC} = 105^{o}$. T\u1eeb $C$ k\u1ebb \u0111\u01b0\u1eddng th\u1eb3ng song song v\u1edbi $AD$ c\u1eaft $BA$ \u1edf $E$. H\u00e3y so s\u00e1nh c\u00e1c c\u1ea1nh c\u1ee7a $\\triangle{ACE}$. ","select":["A. $AE > AC > CE$ ","B. $AE < AC < CE$","C. $AE < AC = CE$ ","D. $AE > AC = CE$ "],"hint":"","explain":" <span class='basic_left'> <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai24/lv1/img\/H7C3B24_D05.png' \/><\/center> <br\/> $\\blacktriangleright$ $\\triangle{ABC}$ c\u00e2n \u1edf $A$ n\u00ean $\\widehat{ABC} = \\widehat{ACB}$ <br\/> $\\widehat{A} + \\widehat{ABC} + \\widehat{ACB} = 180^{o}$ (t\u1ed5ng ba g\u00f3c trong m\u1ed9t tam gi\u00e1c) <br\/> $\\Rightarrow$ $\\widehat{ABC} = \\widehat{ACB} = \\dfrac{180^{o} - \\widehat{A}}{2} = \\dfrac{180^{o} - 110^{o}}{2} = 35^{o}$ <br\/> $\\blacktriangleright$ Trong $\\triangle{ADC}$ c\u00f3: <br\/> $\\widehat{DAC} + \\widehat{ADC} + \\widehat{ACD} = 180^{o}$ (t\u1ed5ng ba g\u00f3c trong m\u1ed9t tam gi\u00e1c) <br\/> $\\Rightarrow$ $\\widehat{DAC} = 180^{o} - (\\widehat{ADC} + \\widehat{ACD}) = 180^{o} - (105^{o} + 35^{o}) = 40^{o}$ <br\/> $\\Rightarrow$ $\\widehat{BAD} = \\widehat{BAC} - \\widehat{DAC} = 110^{o} - 40^{o} = 70^{o}$ <br\/> $\\widehat{CAE}$ v\u00e0 $\\widehat{BAC}$ l\u00e0 hai g\u00f3c k\u1ec1 b\u00f9 n\u00ean: <br\/> $\\widehat{CAE} = 180^{o} - \\widehat{BAC} = 180^{o} - 110^{o} = 70^{o}$ <br\/> $\\blacktriangleright$ V\u00ec $CE \/\/ AD$ n\u00ean $\\widehat{AEC} = \\widehat{BAD} = 70^{o}$ (hai g\u00f3c \u0111\u1ed3ng v\u1ecb) <br\/> $\\widehat{ACE} = \\widehat{CAD} = 40^{o}$ (hai g\u00f3c so le trong) <br\/> $\\blacktriangleright$ Trong $\\triangle{ACE}$ c\u00f3 $\\widehat{ACE} < \\widehat{CAE} = \\widehat{AEC}$ <br\/> $\\Rightarrow$ $AE < AC = CE$ (quan h\u1ec7 gi\u1eefa g\u00f3c v\u00e0 c\u1ea1nh \u0111\u1ed1i di\u1ec7n trong $\\triangle{ACE}$) <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: C <\/span> ","column":2}]}],"id_ques":2024},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"Ba \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c $ABC$ c\u1eaft nhau t\u1ea1i $O$. Ph\u00e1t bi\u1ec3u n\u00e0o sau \u0111\u00e2y l\u00e0 \u0111\u00fang? ","select":["A. $AO$ lu\u00f4n vu\u00f4ng g\u00f3c v\u1edbi $BC$","B. $AO$ lu\u00f4n \u0111i qua trung \u0111i\u1ec3m c\u1ee7a $BC$","C. $OA = OB = OC$ ","D. $O$ c\u00e1ch \u0111\u1ec1u ba c\u1ea1nh c\u1ee7a tam gi\u00e1c "],"hint":"","explain":" <span class='basic_left'> <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai24/lv1/img\/H7C3B24_D06.png' \/><\/center> <br\/> G\u1ecdi $AM, BN, CP$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a c\u00e1c g\u00f3c $A, B, C$ <br\/> $\\blacktriangleright$ $AO$ l\u00e0 \u0111\u01b0\u1eddng cao \u1ee9ng v\u1edbi c\u1ea1nh $BC$ khi $\\triangle{ABC}$ c\u00e2n t\u1ea1i $A$ ho\u1eb7c \u0111\u1ec1u (t\u00ednh ch\u1ea5t tam gi\u00e1c c\u00e2n) <br\/> $\\Rightarrow$ <b> \u0110\u00e1p \u00e1n A sai <\/b> <br\/> $\\blacktriangleright$ $AO$ l\u00e0 \u0111\u01b0\u1eddng trung tuy\u1ebfn \u1ee9ng v\u1edbi c\u1ea1nh $BC$ khi v\u00e0 ch\u1ec9 khi $\\triangle{ABC}$ c\u00e2n t\u1ea1i $A$ ho\u1eb7c \u0111\u1ec1u (t\u00ednh ch\u1ea5t tam gi\u00e1c c\u00e2n) <br\/> $\\Rightarrow$ <b> \u0110\u00e1p \u00e1n B sai <\/b> <br\/> $\\blacktriangleright$ $AM, BN, CP$ c\u1eaft nhau t\u1ea1i $O$ n\u00ean $OA = OB = OC$ khi v\u00e0 ch\u1ec9 khi $\\triangle{ABC}$ \u0111\u1ec1u (t\u00ednh ch\u1ea5t tam gi\u00e1c \u0111\u1ec1u) <br\/> $\\Rightarrow$ <b> \u0110\u00e1p \u00e1n C sai <\/b> <br\/> $\\blacktriangleright$ V\u00ec $O$ l\u00e0 giao \u0111i\u1ec3m ba \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c n\u00ean $O$ c\u00e1ch \u0111\u1ec1u ba c\u1ea1nh c\u1ee7a tam gi\u00e1c (t\u00ednh ch\u1ea5t ba \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a m\u1ed9t tam gi\u00e1c) <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D <\/span> ","column":2}]}],"id_ques":2025},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"Tam gi\u00e1c $ABC$ c\u00f3 trung tuy\u1ebfn $AM$ th\u00ec: ","select":["A. $AM$ chia \u0111\u00f4i g\u00f3c $BAC$ ","B. $AM \\perp AC$","C. $AM \\perp BC$ ","D. $AM$ chia tam gi\u00e1c th\u00e0nh hai ph\u1ea7n c\u00f3 di\u1ec7n t\u00edch b\u1eb1ng nhau "],"hint":"","explain":" <span class='basic_left'> <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai24/lv1/img\/H7C3B24_D07.png' \/><\/center> <br\/> K\u1ebb $AH \\perp BC$ <br\/> V\u00ec $AM$ l\u00e0 \u0111\u01b0\u1eddng trung tuy\u1ebfn, n\u00ean theo \u0111\u1ecbnh ngh\u0129a th\u00ec \u0111\u01b0\u1eddng trung tuy\u1ebfn l\u00e0 \u0111\u01b0\u1eddng \u0111i qua m\u1ed9t \u0111\u1ec9nh v\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh \u0111\u1ed1i di\u1ec7n n\u00ean $M$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $BC$ <br\/> $\\Rightarrow$ <b> C\u00e1c \u0111\u00e1p \u00e1n A, B, C sai <\/b> <br\/>V\u00ec $M$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $BC$ $\\Rightarrow$ $MB = MC$ (1) <br\/> Di\u1ec7n t\u00edch tam gi\u00e1c $AMB$ l\u00e0: $S_{\\triangle{AMB}} = \\dfrac{1}{2}AH.BM$ (2) <br\/> Di\u1ec7n t\u00edch tam gi\u00e1c $AMC$ l\u00e0: $S_{\\triangle{AMC}} = \\dfrac{1}{2}AH . CM$ (3) <br\/> T\u1eeb (1), (2), (3) $\\Rightarrow$ $S_{\\triangle{AMB}} = S_{\\triangle{AMC}}$ <br\/> $\\Rightarrow$ <b> \u0110\u00e1p \u00e1n D \u0111\u00fang <\/b> <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D <\/span> ","column":2}]}],"id_ques":2026},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["50"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"Cho tam gi\u00e1c $ABC$ c\u00e2n t\u1ea1i $A$. Hai \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AB$ v\u00e0 $AC$ c\u1eaft nhau t\u1ea1i $O$. Bi\u1ebft $\\widehat{BAC} = 40^{o}$. T\u00ednh $\\widehat{OBC}$. <br\/> <b> \u0110\u00e1p \u00e1n l\u00e0: <\/b> $\\widehat{OBC} = $ _input_ $^{o}$ ","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> T\u00ednh $\\widehat{OAM}$ b\u1eb1ng c\u00e1ch ch\u1ee9ng minh $\\widehat{OAM} = \\widehat{OAN}$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ednh $\\widehat{OBM}$ b\u1eb1ng c\u00e1ch ch\u1ee9ng minh $\\widehat{OBM} = \\widehat{OAM}$ <br\/> <b> B\u01b0\u1edbc 3: <\/b> T\u00ednh g\u00f3c $ABC$ r\u1ed3i t\u00ednh $\\widehat{OBC}$ <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai24/lv1/img\/H7C3B24_D08.png' \/><\/center> G\u1ecdi $M, N$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$ v\u00e0 $AC$ <br\/> $\\triangle{ABC}$ c\u00e2n t\u1ea1i $A$ n\u00ean $AB = AC$ (t\u00ednh ch\u1ea5t) <br\/> L\u1ea1i c\u00f3 $M, N$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB, AC$ n\u00ean $AM = MB = AN = NC$ <br\/> $\\blacktriangleright$ X\u00e9t hai tam gi\u00e1c vu\u00f4ng $AMO$ v\u00e0 $ANO$ c\u00f3: <br\/> $\\begin{cases} AO \\hspace{0,2cm} \\text{chung} \\\\ AM = AN (cmt) \\end{cases}$ <br\/> $\\Rightarrow$ $\\triangle{AMO} = \\triangle{ANO}$ (c\u1ea1nh huy\u1ec1n - c\u1ea1nh g\u00f3c vu\u00f4ng) <br\/> $\\Rightarrow$ $\\widehat{A_{1}} = \\widehat{A_{2}} = \\dfrac{1}{2}\\widehat{A} = \\dfrac{1}{2}.40^{o} = 20^{o}$ (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng) <br\/> $\\blacktriangleright$ X\u00e9t hai tam gi\u00e1c vu\u00f4ng $\\triangle{AOM}$ v\u00e0 $\\triangle{BOM}$ c\u00f3: <br\/> $\\begin{cases} AM = MB \\\\ MO \\hspace{0,2cm} \\text{chung} \\end{cases}$ <br\/> $\\Rightarrow$ $\\triangle{AOM} = \\triangle{BOM}$ (hai c\u1ea1nh g\u00f3c vu\u00f4ng) <br\/> $\\widehat{B_{2}} = \\widehat{A_{2}} = 20^{o}$ (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng) <br\/> $\\blacktriangleright$ $\\triangle{ABC}$ c\u00e2n t\u1ea1i $A$ n\u00ean $\\widehat{ABC} = \\widehat{ACB}$ (t\u00ednh ch\u1ea5t) <br\/> L\u1ea1i c\u00f3: $\\widehat{BAC} + \\widehat{ABC} + \\widehat{ACB} = 180^{o}$ (t\u1ed5ng ba g\u00f3c trong m\u1ed9t tam gi\u00e1c) <br\/> $\\Rightarrow$ $\\widehat{ABC} + \\widehat{ACB} = 180^{o} - \\widehat{BAC} = 180^{o} - 40^{o} = 140^{o}$ <br\/> $\\Rightarrow$ $\\widehat{ABC} = \\widehat{ACB} = \\dfrac{140^{o}}{2} = 70^{o}$ <br\/> $\\Rightarrow$ $\\widehat{B_{1}} = \\widehat{ABC} - \\widehat{B_{1}} = 70^{o} - 20^{o} = 50^{o}$ hay $\\widehat{OBC} = 50^{o}$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n l\u00e0: $50$ <\/span>"}]}],"id_ques":2027},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["<"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"Cho tam gi\u00e1c $ABC$ \u0111\u1ec1u. G\u1ecdi $M$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $BC$. Tr\u00ean c\u1ea1nh $AB$ l\u1ea5y \u0111i\u1ec3m $D$. Tia $DM$ c\u1eaft $AC$ t\u1ea1i $E$. H\u00e3y so s\u00e1nh $MD$ v\u00e0 $ME$. <br\/> <b> \u0110\u00e1p \u00e1n l\u00e0: <\/b> $MD$ _input_ $ME$ ","hint":"D\u1ef1a v\u00e0o quan h\u1ec7 gi\u1eefa g\u00f3c v\u00e0 c\u1ea1nh \u0111\u1ed1i di\u1ec7n trong m\u1ed9t tam gi\u00e1c","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> So s\u00e1nh $MD$ v\u00e0 $MB$ d\u1ef1a v\u00e0o quan h\u1ec7 gi\u1eefa g\u00f3c v\u00e0 c\u1ea1nh \u0111\u1ed1i di\u1ec7n trong $\\triangle{DMB}$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> So s\u00e1nh $MC$ v\u00e0 $ME$ d\u1ef1a v\u00e0o quan h\u1ec7 gi\u1eefa g\u00f3c v\u00e0 c\u1ea1nh \u0111\u1ed1i di\u1ec7n trong $\\triangle{CME}$ <br\/> <b> B\u01b0\u1edbc 3: <\/b> So s\u00e1nh $MD$ v\u00e0 $ME$ <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai24/lv1/img\/H7C3B24_D09.png' \/><\/center> <br\/> $\\blacktriangleright$ $\\triangle{ABC}$ \u0111\u1ec1u n\u00ean $\\widehat{BAC} = \\widehat{B} = 60^{o}$ <br\/> $\\triangle{ADE}$ c\u00f3 $\\widehat{D_{1}}$ l\u00e0 g\u00f3c ngo\u00e0i t\u1ea1i \u0111\u1ec9nh $D$ n\u00ean $\\widehat{D_{1}} > \\widehat{A} = 60^{o}$ <br\/> $\\blacktriangleright$ X\u00e9t $\\triangle{DBM}$ c\u00f3 $\\widehat{D_{1}} > \\widehat{B} = 60^{o}$ <br\/> $\\Rightarrow$ $MB > MD$ (quan h\u1ec7 gi\u1eefa g\u00f3c v\u00e0 c\u1ea1nh \u0111\u1ed1i di\u1ec7n trong $\\triangle{DMB}$) (1) <br\/> $\\blacktriangleright$ X\u00e9t $\\triangle{CME}$ c\u00f3 $\\widehat{C} = 180^{o} - \\widehat{ACB} = 180^{o} - 60^{o} = 120^{o}$ (hai g\u00f3c k\u1ec1 b\u00f9) <br\/> $\\Rightarrow$ $ME$ l\u00e0 c\u1ea1nh l\u1edbn nh\u1ea5t (\u0111\u1ed1i di\u1ec7n v\u1edbi g\u00f3c $C$ l\u00e0 g\u00f3c t\u00f9) <br\/> $\\Rightarrow$ $ME > MC$ (2) <br\/> M\u1eb7t kh\u00e1c $MB = MC$ n\u00ean t\u1eeb (1) v\u00e0 (2) $\\Rightarrow$ $ME > MD$ <br\/> <span class='basic_pink'> V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0 d\u1ea5u $<$ <\/span>"}]}],"id_ques":2028},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["15"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"M\u1ed9t b\u00f4ng sen c\u00e1ch m\u1eb7t h\u1ed3 $2dm$, sau khi b\u1ecb gi\u00f3 th\u1ed5i nghi\u00eang \u0111i, b\u00f4ng sen ch\u1ea1m m\u1eb7t n\u01b0\u1edbc c\u00e1ch th\u00e2n c\u00e2y \u1edf v\u1ecb tr\u00ed c\u0169 l\u00e0 $8dm$. T\u00ednh \u0111\u1ed9 s\u00e2u c\u1ee7a h\u1ed3 n\u01a1i c\u00f3 b\u00f4ng sen \u0111\u00f3. <br\/> <b> \u0110\u00e1p \u00e1n l\u00e0: <\/b> _input_ $dm$ ","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pitago \u0111\u1ec3 t\u00ednh chi\u1ec1u cao b\u00f4ng sen t\u1eeb g\u1ed1c t\u1edbi m\u1eb7t n\u01b0\u1edbc c\u0169ng ch\u00ednh l\u00e0 \u0111\u1ed9 s\u00e2u c\u1ee7a h\u1ed3 <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai24/lv1/img\/H7C3B24_D10.png' \/><\/center> <br\/> $\\blacktriangleright$ G\u1ecdi $OA$ l\u00e0 chi\u1ec1u cao c\u1ee7a b\u00f4ng sen t\u1eeb g\u1ed1c t\u1edbi ng\u1ecdn <br\/> $OB = x$ l\u00e0 \u0111\u1ed9 s\u00e2u c\u1ee7a h\u1ed3, $C$ l\u00e0 v\u1ecb tr\u00ed b\u00f4ng sen ch\u1ea1m m\u1eb7t n\u01b0\u1edbc khi b\u1ecb gi\u00f3 th\u1ed5i <br\/> Ta c\u00f3: $OC = OA =x + 2$ <br\/> \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pitago v\u00e0o tam gi\u00e1c vu\u00f4ng $BOC$, ta c\u00f3: <br\/> $\\begin{align} & x^2 + 8^2 = (x + 2)^2 \\\\ & x^2 + 64 = (x + 2)(x + 2) \\\\ & x^2 + 64 = x^2 + 2x + 2x + 4 \\\\ & x^2 + 64 = x^2 + 4x + 4 \\\\ & 4x = 60 \\\\ & x = 15(dm) \\end{align} $ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n l\u00e0: $15$ <\/span>"}]}],"id_ques":2029},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"Cho tam gi\u00e1c $ABC$, bi\u1ebft s\u1ed1 \u0111o c\u00e1c g\u00f3c t\u1ec9 l\u1ec7 v\u1edbi nhau theo t\u1ec9 s\u1ed1: $\\widehat{A} : \\widehat{B}: \\widehat{C} = 3 : 2 : 1$. H\u00e3y so s\u00e1nh ba c\u1ea1nh c\u1ee7a tam gi\u00e1c $ABC$. ","select":["A. $AB > AC > BC$ ","B. $AC > BC > AB$","C. $AC > AB > BC$ ","D. $BC > AC > AB$ "],"hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> T\u00ednh s\u1ed1 \u0111o c\u00e1c g\u00f3c c\u1ee7a tam gi\u00e1c $ABC$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> So s\u00e1nh c\u00e1c c\u1ea1nh c\u1ee7a $\\triangle{ABC}$ <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai24/lv1/img\/H7C3B24_D11.png' \/><\/center> <br\/>$\\blacktriangleright$ $\\triangle{ABC}$ c\u00f3 $\\widehat{A} + \\widehat{B} + \\widehat{C} = 180^{o}$ (t\u1ed5ng ba g\u00f3c trong m\u1ed9t tam gi\u00e1c) <br\/> V\u00e0 $\\widehat{A} : \\widehat{B} : \\widehat{C} = 3 : 2 : 1$ $\\Rightarrow$ $\\dfrac{\\widehat{A}}{3} = \\dfrac{\\widehat{B}}{2} = \\dfrac{\\widehat{C}}{1}$ <br\/> $\\Rightarrow$ $\\dfrac{\\widehat{A}}{3} = \\dfrac{\\widehat{B}}{2} = \\dfrac{\\widehat{C}}{1} = \\dfrac{\\widehat{A} + \\widehat{B} + \\widehat{C}}{3 + 2 + 1} = \\dfrac{180^{o}}{6} = 30^{o} $ (t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau) <br\/> $\\Rightarrow$ $\\widehat{A} = 90^{o}; \\widehat{B} = 60^{o}; \\widehat{C} = 30^{o}$ <br\/> $\\blacktriangleright$ V\u00ec $90^{o} > 60^{o} > 30^{o}$ n\u00ean $\\widehat{A} > \\widehat{B} > \\widehat{C}$ <br\/> $\\Rightarrow$ $BC > AC > AB$ (quan h\u1ec7 gi\u1eefa g\u00f3c v\u00e0 c\u1ea1nh \u0111\u1ed1i di\u1ec7n trong m\u1ed9t tam gi\u00e1c) <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D <\/span> ","column":2}]}],"id_ques":2030}],"lesson":{"save":0,"level":1}}