{"segment":[{"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":["","\u0110\u00fang","Sai"],"arr_ques":[" Tam gi\u00e1c vu\u00f4ng n\u00e0y c\u00f3 m\u1ed9t g\u00f3c nh\u1ecdn b\u1eb1ng g\u00f3c nh\u1ecdn c\u1ee7a tam gi\u00e1c vu\u00f4ng kia th\u00ec hai tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng"," T\u1ec9 s\u1ed1 hai \u0111\u01b0\u1eddng cao t\u01b0\u01a1ng \u1ee9ng c\u1ee7a hai tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng b\u1eb1ng t\u1ec9 s\u1ed1 \u0111\u1ed3ng d\u1ea1ng "," T\u1ec9 s\u1ed1 di\u1ec7n t\u00edch hai tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng b\u1eb1ng t\u1ec9 s\u1ed1 \u0111\u1ed3ng d\u1ea1ng","Tam gi\u00e1c vu\u00f4ng n\u00e0y c\u00f3 hai c\u1ea1nh g\u00f3c vu\u00f4ng t\u1ec9 l\u1ec7 v\u1edbi hai c\u1ea1nh g\u00f3c vu\u00f4ng c\u1ee7a tam gi\u00e1c vu\u00f4ng kia l\u00e0 hai tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng"],"hint":"","explain":["\u0110\u00fang","<br\/>\u0110\u00fang ","<br\/> Sai v\u00ec: T\u1ec9 s\u1ed1 di\u1ec7n t\u00edch hai tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng b\u1eb1ng b\u00ecnh ph\u01b0\u01a1ng t\u1ec9 s\u1ed1 \u0111\u1ed3ng d\u1ea1ng","<br\/>\u0110\u00fang "]}]}],"id_ques":1740},{"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":" <span class='basic_left'> Cho hai tam gi\u00e1c vu\u00f4ng c\u00f3 \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh g\u00f3c vu\u00f4ng l\u1ea7n l\u01b0\u1ee3t l\u00e0: 4cm; 6cm v\u00e0 8cm; 12cm. Hai tam gi\u00e1c vu\u00f4ng \u0111\u00f3 c\u00f3 \u0111\u1ed3ng d\u1ea1ng hay kh\u00f4ng?<br\/><\/span>","select":[" A. C\u00f3 \u0111\u1ed3ng d\u1ea1ng"," B. Kh\u00f4ng \u0111\u1ed3ng d\u1ea1ng"],"hint":"","explain":"<span class='basic_left'>Ta c\u00f3:<br\/> $\\dfrac{4}{8} = \\dfrac{6}{12}$ (v\u00ec c\u00f9ng =$ \\dfrac{1}{2}$)<br\/>N\u00ean hai tam gi\u00e1c vu\u00f4ng \u0111\u00f3 c\u00f3 \u0111\u1ed3ng d\u1ea1ng v\u1edbi nhau<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: <span class='basic_pink'>A. C\u00f3 \u0111\u1ed3ng d\u1ea1ng<\/span><\/span><\/span>","column":2}]}],"id_ques":1741},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" <span class='basic_left'> Cho h\u00ecnh v\u1ebd nh\u01b0 sau:<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai17/lv1/img\/H8C3B4_D101.png' \/><\/center><br\/>$\\triangle$ $ABC$ v\u00e0 $\\triangle$ $DEF$ c\u00f3 \u0111\u1ed3ng d\u1ea1ng hay kh\u00f4ng?<\/span>","select":[" A. C\u00f3 \u0111\u1ed3ng d\u1ea1ng"," B. Kh\u00f4ng \u0111\u1ed3ng d\u1ea1ng"],"hint":"T\u00ednh $\\widehat{B}$ ho\u1eb7c $\\widehat{E}$","explain":"<span class='basic_left'>$\\triangle$ vu\u00f4ng $DEF$ c\u00f3: <br\/>$\\widehat{E} + \\widehat{F} = 90^o$ (hai g\u00f3c ph\u1ee5 nhau)<br\/> $\\Rightarrow \\widehat{E} = 90^o - \\widehat{F} = 90^o - 30^o = 60^o$<br\/>X\u00e9t $\\triangle{ABC}$ v\u00e0 $\\triangle{DEF}$ c\u00f3:<br\/>$\\widehat{B} = \\widehat{E}$ (v\u00ec c\u00f9ng $= 60^o$)<br\/>$\\Rightarrow$ $\\triangle$ vu\u00f4ng $ABC$ $\\backsim$ $\\triangle$ vu\u00f4ng $DEF$ (g\u00f3c - g\u00f3c) <br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: <span class='basic_pink'>A. C\u00f3 \u0111\u1ed3ng d\u1ea1ng<\/span><\/span><\/span>","column":2}]}],"id_ques":1742},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["4"],["5"],["15"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"<span class='basic_left'> Cho h\u00ecnh v\u1ebd nh\u01b0 sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai17/lv1/img\/H8C3B4_D102.png' \/><\/center><br\/>T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh $AC, BC, EF$ <br\/><b>\u0110\u00e1p \u00e1n:<\/b> $AC =$ _input_ ($cm$), $BC =$ _input_ ($cm$), $EF =$ _input_ ($cm$)<\/span>","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> S\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00ed Py-ta-go t\u00ednh $EF$<br\/><b>B\u01b0\u1edbc 2:<\/b> Ch\u1ee9ng minh $\\triangle{ABC} \\backsim \\triangle{DEF}$ t\u1eeb \u0111\u00f3 suy ra c\u00e1c c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng t\u1ec9 l\u1ec7<br\/><b>B\u01b0\u1edbc 3:<\/b> T\u1eeb b\u01b0\u1edbc 1 suy ra \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh $AC, BC$.<\/span><br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai17/lv1/img\/H8C3B4_D102.png' \/><\/center><br\/>$\\triangle{DEF}$ vu\u00f4ng t\u1ea1i $D$ (gi\u1ea3 thi\u1ebft) <br\/>$\\Rightarrow DE^2 + DF^2 = EF^2$ (\u0111\u1ecbnh l\u00ed Py-ta-go)<br\/> $\\Rightarrow EF^2 = 9^2 + 12^2 = 225 \\Rightarrow EF = 15 \\text{(cm)}$<br\/>X\u00e9t $\\triangle{ABC}$ v\u00e0 $\\triangle{DEF}$ c\u00f3:<br\/>$\\widehat{A} = \\widehat{D}$ (c\u00f9ng $=90^o$)<br\/>$\\widehat{C} = \\widehat{F}$ (gi\u1ea3 thi\u1ebft)<br\/> $\\Rightarrow$ $\\triangle{ABC} \\backsim \\triangle{DEF}$ (g\u00f3c - g\u00f3c)<br\/>$\\Rightarrow \\dfrac{AB}{DE} = \\dfrac{AC}{DF} = \\dfrac{BC}{EF}$ (c\u1eb7p c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng t\u1ec9 l\u1ec7)<br\/>$\\Rightarrow \\dfrac{3}{9} = \\dfrac{AC}{12} = \\dfrac{BC}{15}$<br\/>$\\Rightarrow \\begin{cases} AC = \\dfrac{3.12}{9} = 4 \\text{(cm)} \\\\ BC = \\dfrac{3.15}{9} = 5 \\text{(cm)} \\end{cases}$ <br\/>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 <span class='basic_pink'>4; 5; 15<\/span>"}]}],"id_ques":1743},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["1"],["2"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"<span class='basic_left'> Cho h\u00ecnh v\u1ebd nh\u01b0 sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai17/lv1/img\/H8C3B4_D103.png' \/><\/center><br\/>T\u00ednh $\\dfrac{MA}{DO}$ <br\/><b>\u0110\u00e1p \u00e1n:<\/b> $\\dfrac{MA}{DO} = \\dfrac{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}$<\/span>","hint":"T\u1ec9 s\u1ed1 hai \u0111\u01b0\u1eddng cao t\u01b0\u01a1ng \u1ee9ng c\u1ee7a hai tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng b\u1eb1ng t\u1ec9 s\u1ed1 \u0111\u1ed3ng d\u1ea1ng.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> Ch\u1ee9ng minh $\\triangle{MNP} \\backsim \\triangle{IHK}$ t\u1eeb \u0111\u00f3 suy ra c\u00e1c \u0111o\u1ea1n th\u1eb3ng t\u1ec9 l\u1ec7<br\/><b>B\u01b0\u1edbc 2:<\/b> T\u1eeb b\u01b0\u1edbc 1 suy ra $\\dfrac{MA}{DO}$.<\/span><br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai17/lv1/img\/H8C3B4_D103.png' \/><\/center><br\/>X\u00e9t $\\triangle{MNP}$ v\u00e0 $\\triangle{DEF}$ c\u00f3:<br\/>$\\widehat{NMP} = \\widehat{EDF}$ (c\u00f9ng $=90^o$)<br\/>$\\dfrac{MN}{DE} = \\dfrac{MP}{DF}$ (v\u00ec $\\dfrac{4}{8} = \\dfrac{5}{10}$)<br\/> $\\Rightarrow$ $\\triangle{MNP} \\backsim \\triangle{DEF}$ (c\u1ea1nh-g\u00f3c-c\u1ea1nh)<br\/>$\\Rightarrow \\dfrac{MA}{DO} = \\dfrac{MN}{DE} = \\dfrac{4}{8} = \\dfrac{1}{2}$ <br\/>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 <span class='basic_pink'>1; 2<\/span>"}]}],"id_ques":1744},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["1"],["4"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"<span class='basic_left'> Cho h\u00ecnh v\u1ebd nh\u01b0 sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai17/lv1/img\/H8C3B4_D103.png' \/><\/center><br\/>T\u00ednh $\\dfrac{S_{\\triangle{MNP}}}{S_{\\triangle{IHK}}}$ <br\/><b>\u0110\u00e1p \u00e1n:<\/b> $\\dfrac{S_{\\triangle{MNP}}}{S_{\\triangle{DEF}}} = \\dfrac{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}$<\/span>","hint":"T\u1ec9 s\u1ed1 di\u1ec7n t\u00edch c\u1ee7a hai tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng b\u1eb1ng b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a t\u1ec9 s\u1ed1 \u0111\u1ed3ng d\u1ea1ng.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> Ch\u1ee9ng minh $\\triangle{MNP} \\backsim \\triangle{DEF}$ t\u1eeb \u0111\u00f3 suy ra t\u1ec9 s\u1ed1 \u0111\u1ed3ng d\u1ea1ng<br\/><b>B\u01b0\u1edbc 2:<\/b> T\u1eeb b\u01b0\u1edbc 1 suy ra $\\dfrac{S_{\\triangle{MNP}}}{S_{\\triangle{DEF}}}$.<\/span><br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai17/lv1/img\/H8C3B4_D103.png' \/><\/center><br\/>X\u00e9t $\\triangle{MNP}$ v\u00e0 $\\triangle{DEF}$ c\u00f3:<br\/>$\\widehat{NMP} = \\widehat{EDF}$ (c\u00f9ng $=90^o$)<br\/>$\\dfrac{MN}{DE} = \\dfrac{MP}{DF}$ (v\u00ec $\\dfrac{4}{8} = \\dfrac{5}{10}$)<br\/> $\\Rightarrow$ $\\triangle{MNP} \\backsim \\triangle{DEF}$ (c\u1ea1nh-g\u00f3c-c\u1ea1nh)<br\/>$\\Rightarrow \\dfrac{S_{\\triangle{MNP}}}{S_{\\triangle{DEF}}} = \\left(\\dfrac{MN}{DE}\\right)^2 = \\left(\\dfrac{4}{8}\\right)^2 = \\dfrac{1}{4}$ <br\/>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 <span class='basic_pink'>1; 4<\/span>"}]}],"id_ques":1745},{"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":" <span class='basic_left'> Cho h\u00ecnh v\u1ebd nh\u01b0 sau:<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai17/lv1/img\/H8C3B4_D104.png' \/><\/center><br\/>T\u00ednh $\\dfrac{AO}{AH} $.<\/span>","select":[" A. $\\dfrac{AO}{AH} = \\dfrac{2}{3}$"," B. $\\dfrac{AO}{AH} = \\dfrac{3}{4}$","C. $\\dfrac{AO}{AH} = \\dfrac{2}{5}$","D. $\\dfrac{AO}{AH} = \\dfrac{3}{2}$"],"hint":"$\\dfrac{AO}{AH} $ l\u00e0 t\u1ec9 s\u1ed1 hai \u0111\u01b0\u1eddng cao c\u1ee7a hai tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> Ch\u1ee9ng minh $AO \\bot IK$<br\/><b>B\u01b0\u1edbc 2:<\/b> Ch\u1ee9ng minh $\\triangle{AOI} \\backsim \\triangle{AHC}$<br\/><b>B\u01b0\u1edbc 3:<\/b> T\u00ednh $\\dfrac{AO}{AH} $<\/span> <br\/><br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3: <br\/>$\\left.\\begin{array}{l} IK \/\/ BC \\text{(gi\u1ea3 thi\u1ebft)}\\\\ AH \\bot BC \\text{(gi\u1ea3 thi\u1ebft)} \\end{array} \\right\\}$<br\/>$\\Rightarrow AH \\bot IK $ (\u0111\u1ecbnh l\u00ed t\u1eeb vu\u00f4ng g\u00f3c \u0111\u1ebfn song song)<br\/>$\\Rightarrow \\widehat{AOI} = 90^o $ <br\/>X\u00e9t $\\triangle{AOI}$ v\u00e0 $\\triangle{AHC}$ c\u00f3:<br\/>$\\widehat{AOI} = \\widehat{AHC}$ (v\u00ec c\u00f9ng $ = 90^o$)<br\/>$\\widehat{A} $ chung<br\/>$\\Rightarrow$ $\\triangle$ $AOI$ $\\backsim$ $\\triangle$ $AHC$ (g\u00f3c - g\u00f3c) <br\/>$\\Rightarrow \\dfrac{AO}{AH} = \\dfrac{AI}{AC} = \\dfrac{4}{4 + 6} = \\dfrac{2}{5}$ (c\u1eb7p c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng t\u1ec9 l\u1ec7) <br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>C. $\\dfrac{AO}{AH} = \\dfrac{2}{5}$<\/span><\/span><\/span><br\/><span class='basic_left'><span class='basic_green'>Nh\u1eadn x\u00e9t:<\/span><br\/>T\u1ec9 s\u1ed1 hai \u0111\u01b0\u1eddng cao t\u01b0\u01a1ng \u1ee9ng c\u1ee7a hai tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng b\u1eb1ng t\u1ec9 s\u1ed1 \u0111\u1ed3ng d\u1ea1ng.<\/span> <br\/><\/span> <br\/>","column":2}]}],"id_ques":1746},{"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":" <span class='basic_left'> Cho $\\triangle{ABC}$ vu\u00f4ng t\u1ea1i $A$. Tr\u00ean $AB$ l\u1ea5y \u0111i\u1ec3m $M$ sao cho $MB = 6cm$, $MA = 5cm$. T\u1eeb $M$ k\u1ebb \u0111\u01b0\u1eddng th\u1eb3ng song song v\u1edbi $AC$ c\u1eaft $BC$ t\u1ea1i $N$. T\u00ednh $AC$, bi\u1ebft $MN = 9cm$.<\/span>","select":[" A. $AC = 16,5cm$"," B. $AC = 10,8cm$","C. $AC = 4,9cm$","D. $AC = 7,5cm$"],"hint":"Ch\u1ee9ng minh $\\triangle{BMN} \\backsim \\triangle{BAC}$ theo tr\u01b0\u1eddng h\u1ee3p: g\u00f3c - g\u00f3c.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> Ch\u1ee9ng minh $MN \\bot AB$<br\/><b>B\u01b0\u1edbc 2:<\/b> Ch\u1ee9ng minh $\\triangle{BMN} \\backsim \\triangle{BAC}$ t\u1eeb \u0111\u00f3 suy ra c\u00e1c c\u1eb7p \u0111o\u1ea1n th\u1eb3ng t\u1ec9 l\u1ec7<br\/><b>B\u01b0\u1edbc 3:<\/b> T\u00ednh $AC$<\/span> <br\/><br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai17/lv1/img\/H8C3B4_D105.png' \/><\/center><br\/>Ta c\u00f3: <br\/>$\\left.\\begin{array}{l} MN \/\/ AC \\text{(gi\u1ea3 thi\u1ebft)}\\\\ AB \\bot AC \\text{(gi\u1ea3 thi\u1ebft)} \\end{array} \\right\\}$<br\/>$\\Rightarrow MN \\bot AB $ (\u0111\u1ecbnh l\u00ed t\u1eeb vu\u00f4ng g\u00f3c \u0111\u1ebfn song song)<br\/>$\\Rightarrow \\widehat{BMN} = 90^o $ <br\/>X\u00e9t $\\triangle{BMN}$ v\u00e0 $\\triangle{BAC}$ c\u00f3:<br\/>$\\widehat{BMN} = \\widehat{BAC}$ (v\u00ec c\u00f9ng $ = 90^o$)<br\/>$\\widehat{B} $ chung<br\/>$\\Rightarrow$ $\\triangle$ $BMN$ $\\backsim$ $\\triangle$ $BAC$ (g\u00f3c - g\u00f3c) <br\/>$\\Rightarrow \\dfrac{BM}{BA} = \\dfrac{MN}{AC} $ (c\u1eb7p c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng t\u1ec9 l\u1ec7)<br\/> Hay $ \\dfrac{6}{6 + 5} = \\dfrac{9}{AC} $ <br\/>$\\Rightarrow AC = 16,5 \\text{(cm)}$ <br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>A. $AC = 16,5cm$<\/span><br\/><\/span> <br\/>","column":2}]}],"id_ques":1747},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["36"],["121"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"<span class='basic_left'> Cho h\u00ecnh v\u1ebd nh\u01b0 sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai17/lv1/img\/H8C3B4_D105.png' \/><\/center><br\/>Bi\u1ebft $MN \/\/ AC$. T\u00ednh $\\dfrac{S_{\\triangle{MBN}}}{S_{\\triangle{ABC}}}$ <br\/><b>\u0110\u00e1p \u00e1n:<\/b> $\\dfrac{S_{\\triangle{MBN}}}{S_{\\triangle{ABC}}} = \\dfrac{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}$<\/span>","hint":"T\u1ec9 s\u1ed1 di\u1ec7n t\u00edch c\u1ee7a hai tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng b\u1eb1ng b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a t\u1ec9 s\u1ed1 \u0111\u1ed3ng d\u1ea1ng.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> Ch\u1ee9ng minh $MN \\bot AB$<br\/><b>B\u01b0\u1edbc 2:<\/b> Ch\u1ee9ng minh $\\triangle{BMN} \\backsim \\triangle{BAC}$ t\u1eeb \u0111\u00f3 suy ra c\u00e1c c\u1eb7p \u0111o\u1ea1n th\u1eb3ng t\u1ec9 l\u1ec7<br\/><b>B\u01b0\u1edbc 3:<\/b> T\u00ednh $\\dfrac{S_{\\triangle{MBN}}}{S_{\\triangle{ABC}}}$<\/span> <br\/><br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai17/lv1/img\/H8C3B4_D105.png' \/><\/center><br\/>Ta c\u00f3: <br\/>$\\left.\\begin{array}{l} MN \/\/ AC \\text{(gi\u1ea3 thi\u1ebft)}\\\\ AB \\bot AC \\text{(gi\u1ea3 thi\u1ebft)} \\end{array} \\right\\}$<br\/>$\\Rightarrow MN \\bot AB $ (\u0111\u1ecbnh l\u00ed t\u1eeb vu\u00f4ng g\u00f3c \u0111\u1ebfn song song)<br\/>$\\Rightarrow \\widehat{BMN} = 90^o $ <br\/>X\u00e9t $\\triangle{BMN}$ v\u00e0 $\\triangle{BAC}$ c\u00f3:<br\/>$\\widehat{BMN} = \\widehat{BAC}$ (v\u00ec c\u00f9ng $ = 90^o$)<br\/>$\\widehat{B} $ chung<br\/>$\\Rightarrow$ $\\triangle$ $BMN$ $\\backsim$ $\\triangle$ $BAC$ (g\u00f3c - g\u00f3c) <br\/>$\\Rightarrow \\left(\\dfrac{BM}{BA}\\right)^2 = \\dfrac{S_{\\triangle{MBN}}}{S_{\\triangle{ABC}}} $ hay $ \\dfrac{S_{\\triangle{MBN}}}{S_{\\triangle{ABC}}} = \\left(\\dfrac{6}{6 + 5}\\right)^2 = \\dfrac{36}{121}$ <br\/>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 <span class='basic_pink'>36; 121<\/span><br\/>"}]}],"id_ques":1748},{"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":" <span class='basic_left'> Cho h\u00ecnh v\u1ebd nh\u01b0 sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai17/lv1/img\/H8C3B4_D106.png' \/><\/center><br\/>$\\triangle$ $ABC$ $\\backsim$ $\\triangle$ $DEF$. <b>\u0110\u00fang<\/b> hay <b>Sai<\/b>?<\/span>","select":[" A. \u0110\u00fang"," B. Sai"],"hint":"","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai17/lv1/img\/H8C3B4_D106.png' \/><\/center><br\/>$\\triangle$ $ABC$ v\u00e0 $\\triangle$ $DEF$ c\u00f3:<br\/>$\\widehat{A} = \\widehat{D}$ (c\u00f9ng $ = 90^o$)<br\/>$\\dfrac{AB}{DE} = \\dfrac{BC}{EF}$ (v\u00ec $\\dfrac{3}{9} = \\dfrac{5}{15}$)<br\/>$\\Rightarrow$ $\\triangle$ vu\u00f4ng $ABC$ $\\backsim$ $\\triangle$ vu\u00f4ng $DEF$ (c\u1ea1nh huy\u1ec1n-c\u1ea1nh g\u00f3c vu\u00f4ng) <br\/>V\u1eady ta ch\u1ecdn \u0111\u00e1p \u00e1n <span class='basic_pink'>A. \u0110\u00fang<\/span>","column":2}]}],"id_ques":1749},{"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":" <span class='basic_left'> Cho $\\triangle{DEF}$, c\u00e1c \u0111\u01b0\u1eddng cao $EH$ l\u00e0 $FK$. So s\u00e1nh $DK.DE$ v\u00e0 $DH.DF$<\/span>","select":[" A. $DK.DE$ = $DH.DF$"," B. $DK.DE$ > $DH.DF$","C. $DK.DE$ < $DH.DF$"],"hint":"","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai17/lv1/img\/H8C3B4_D107.png' \/><\/center><br\/>X\u00e9t $\\triangle$ vu\u00f4ng $DKF$ v\u00e0 $\\triangle$ vu\u00f4ng $DHE$ c\u00f3:<br\/>$\\widehat{DKF} = \\widehat{DHE}$ (c\u00f9ng $ = 90^o$)<br\/>$\\widehat{D}$ chung<br\/>$\\Rightarrow$ $\\triangle$ $DKF$ $\\backsim$ $\\triangle$ $DHE$ (g\u00f3c - g\u00f3c)<br\/>$\\Rightarrow$ $\\dfrac{DK}{DH} = \\dfrac{DF}{DE}$<br\/>$\\Rightarrow$ $DK.DE = DH.DF$ <br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>A. $DK.DE$ = $DH.DF$<\/span><br\/><span class='basic_left'><span class='basic_green'>Nh\u1eadn x\u00e9t:<\/span><br\/> \u0110\u1ec3 ch\u1ee9ng minh \u0111\u1eb3ng th\u1ee9c t\u00edch, th\u00f4ng th\u01b0\u1eddng ch\u00fang ta bi\u1ebfn \u0111\u1ed5i ch\u00fang d\u01b0\u1edbi d\u1ea1ng t\u1ec9 l\u1ec7 th\u1ee9c v\u00e0 ch\u1ee9ng minh t\u1ec9 l\u1ec7 th\u1ee9c \u1ea5y.<\/span> <br\/><br\/>","column":3}]}],"id_ques":1750},{"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":" <span class='basic_left'> Cho $\\triangle{ABC}$ vu\u00f4ng t\u1ea1i $A$. Tr\u00ean c\u1ea1nh $BC$ l\u1ea5y \u0111i\u1ec3m $K$, t\u1eeb $K$ k\u1ebb \u0111\u01b0\u1eddng th\u1eb3ng song song v\u1edbi $AC$ c\u1eaft $AB$ t\u1ea1i $I$. Bi\u1ebft $BI = 3cm, AB = 9cm$ v\u00e0 $S_{\\triangle{ABC}} = 54m^2$. T\u00ednh $S_{\\triangle{IBK}}$<\/span>","select":[" A. $S_{\\triangle{IBK}} = 4cm^2$"," B. $S_{\\triangle{IBK}} = 5cm^2$","C. $S_{\\triangle{IBK}} = 6cm^2$","D. $S_{\\triangle{IBK}} = 7cm^2$"],"hint":"Ch\u1ee9ng minh $\\triangle{BIK} \\backsim \\triangle{BAC}$, t\u1eeb \u0111\u00f3 suy ra $\\dfrac{S_{\\triangle{BIK}}}{S_{\\triangle{BAC}}}$","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai17/lv1/img\/H8C3B4_D108.png' \/><\/center><br\/>Ta c\u00f3:<br\/>$IK \/\/ AC$ (gi\u1ea3 thi\u1ebft)<br\/>$AB \\bot AC$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow$ $IK \\bot AB$ (\u0111\u1ecbnh l\u00ed t\u1eeb vu\u00f4ng g\u00f3c \u0111\u1ebfn song song)<br\/>Hay $\\widehat{BIK} = 90^o$<br\/>X\u00e9t $\\triangle$ vu\u00f4ng $BIK$ v\u00e0 $\\triangle$ vu\u00f4ng $BAC$ c\u00f3:<br\/>$\\widehat{B}$ chung<br\/>$\\Rightarrow$ $\\triangle$ vu\u00f4ng $BIK$ $\\backsim$ $\\triangle$ vu\u00f4ng $BAC$ (g\u00f3c - g\u00f3c)<br\/>$\\Rightarrow \\left(\\dfrac{BI}{BA}\\right)^2 = \\dfrac{S_{\\triangle{BIK}}}{S_{\\triangle{BAC}}} $ hay $ \\dfrac{S_{\\triangle{BIK}}}{S_{\\triangle{BAC}}} = \\left(\\dfrac{3}{9}\\right)^2 = \\dfrac{1}{9}$ <br\/>$\\Rightarrow S_{\\triangle{BIK}} = \\dfrac{S_{\\triangle{BAC}}}{9} = \\dfrac{54}{9} = 6 (\\text{cm}^2)$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>C. $S_{\\triangle{IBK}} = 6 (\\text{cm}^2)$<\/span><br\/><span class='basic_left'><span class='basic_green'>Nh\u1eadn x\u00e9t:<\/span><br\/>T\u1ec9 s\u1ed1 di\u1ec7n t\u00edch c\u1ee7a hai tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng b\u1eb1ng b\u00ecnh ph\u01b0\u01a1ng t\u1ec9 s\u1ed1 \u0111\u1ed3ng d\u1ea1ng<\/span> <br\/><br\/>","column":2}]}],"id_ques":1751},{"time":24,"part":[{"title":"Ch\u1ecdn <u>nh\u1eefng<\/u> \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"Ch\u1ecdn \u0111\u01b0\u1ee3c nhi\u1ec1u \u0111\u00e1p \u00e1n","temp":"checkbox","correct":[["1","2","4"]],"list":[{"point":5,"img":"","ques":"<span class='basic_left'> Cho h\u00ecnh v\u1ebd nh\u01b0 sau:<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai17/lv1/img\/H8C3B4_D109.png' \/><\/center><br\/><b>H\u00e3y ch\u1ecdn nh\u1eefng \u0111\u00e1p \u00e1n \u0111\u00fang<\/b><\/span><br\/>","hint":"","column":2,"number_true":2,"select":["A. $\\triangle{IBK} \\backsim \\triangle{ABC} $","B. $IK \/\/ AC$","C. $\\dfrac{S_{\\triangle{IBK}}}{S_{\\triangle{ABC}}} = \\dfrac{1}{3}$","D. $ \\dfrac{IK}{AC} = \\dfrac{1}{3}$"],"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai17/lv1/img\/H8C3B4_D109.png' \/><\/center><br\/>Ta c\u00f3:<br\/>$\\dfrac{BI}{IA} = \\dfrac{3}{6} = \\dfrac{1}{2}$<br\/>$\\dfrac{KB}{KC} = \\dfrac{4}{8} = \\dfrac{1}{2}$<br\/>$\\Rightarrow$ $\\dfrac{BI}{IA} = \\dfrac{KB}{KC}$<br\/> $\\Rightarrow IK \/\/ AC$ (\u0111\u1ecbnh l\u00ed Ta-l\u00e9t \u0111\u1ea3o) <b>(\u0111\u00e1p \u00e1n B \u0111\u00fang)<\/b><br\/>$\\Rightarrow \\widehat{BIK} = \\widehat{BAC}$ (c\u1eb7p g\u00f3c \u0111\u1ed3ng v\u1ecb) <br\/> X\u00e9t $\\triangle{IBK}$ v\u00e0 $\\triangle{ABC}$ c\u00f3:<br\/>$\\widehat{BIK} = \\widehat{BAC}$ (ch\u1ee9ng minh tr\u00ean)<br\/>$\\widehat{B} $ chung<br\/>$\\Rightarrow$ $\\triangle{BIK}$ $\\backsim$ $\\triangle{BAC}$ (g\u00f3c - g\u00f3c) <b>(\u0111\u00e1p \u00e1n A \u0111\u00fang)<\/b><br\/>$\\Rightarrow \\begin{cases} \\dfrac{S_{\\triangle{IBK}}}{S_{\\triangle{ABC}}} = \\left(\\dfrac{BI}{BA}\\right)^2 = \\left(\\dfrac{3}{3 + 6}\\right)^2 = \\dfrac{1}{9} \\\\ \\dfrac{IK}{AC} = \\dfrac{BI}{AB} = \\dfrac{3}{3 + 6} = \\dfrac{1}{3} \\end{cases} $ <br\/>V\u1eady nh\u1eefng \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>A, B, D<\/span> "}]}],"id_ques":1752},{"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":" <span class='basic_left'> Cho hai tam gi\u00e1c vu\u00f4ng c\u00f3 \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh g\u00f3c vu\u00f4ng l\u1ea7n l\u01b0\u1ee3t l\u00e0: 5cm; 6cm v\u00e0 10cm; 14cm. Hai tam gi\u00e1c vu\u00f4ng \u0111\u00f3 c\u00f3 \u0111\u1ed3ng d\u1ea1ng hay kh\u00f4ng?<br\/><\/span>","select":[" A. C\u00f3 \u0111\u1ed3ng d\u1ea1ng"," B. Kh\u00f4ng \u0111\u1ed3ng d\u1ea1ng"],"hint":"","explain":"<span class='basic_left'>Ta c\u00f3:<br\/> $\\dfrac{5}{10} \\ne \\dfrac{6}{14}$ <br\/>N\u00ean hai tam gi\u00e1c vu\u00f4ng \u0111\u00f3 kh\u00f4ng \u0111\u1ed3ng d\u1ea1ng v\u1edbi nhau<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: <span class='basic_pink'>B. Kh\u00f4ng \u0111\u1ed3ng d\u1ea1ng<\/span><\/span><\/span>","column":2}]}],"id_ques":1753},{"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":" <span class='basic_left'> Cho $\\triangle{ABC}$ vu\u00f4ng t\u1ea1i $A$ v\u00e0 \u0111\u01b0\u1eddng cao $AH$. So s\u00e1nh $CA^2$ v\u00e0 $CH.CB$<\/span>","select":[" A. $CA^2 > CH.CB$"," B. $CA^2 = CH.CB$","C. $CA^2 < CH.CB$"],"hint":"","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai17/lv1/img\/H8C3B4_D110.png' \/><\/center><br\/>X\u00e9t $\\triangle$ vu\u00f4ng $ABC$ v\u00e0 $\\triangle$ vu\u00f4ng $HAC$ c\u00f3:<br\/>$\\widehat{BAC} = \\widehat{AHC}$ (c\u00f9ng $ = 90^o$)<br\/>$\\widehat{C}$ chung<br\/>$\\Rightarrow$ $\\triangle$ vu\u00f4ng $ABC$ $\\backsim$ $\\triangle$ vu\u00f4ng $HAC$ (g\u00f3c - g\u00f3c)<br\/>$\\Rightarrow$ $\\dfrac{CA}{CH} = \\dfrac{CB}{CA}$ (c\u1eb7p c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng t\u1ec9 l\u1ec7)<br\/>$\\Rightarrow$ $CA^2 = CH.CB$ <br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>B. $CA^2 = CH.CB$<\/span><br\/><span class='basic_left'><span class='basic_green'>Nh\u1eadn x\u00e9t:<\/span><br\/> \u0110\u1ec3 ch\u1ee9ng minh \u0111\u1eb3ng th\u1ee9c t\u00edch, th\u00f4ng th\u01b0\u1eddng ch\u00fang ta bi\u1ebfn \u0111\u1ed5i ch\u00fang d\u01b0\u1edbi d\u1ea1ng t\u1ec9 l\u1ec7 th\u1ee9c v\u00e0 ch\u1ee9ng minh t\u1ec9 l\u1ec7 th\u1ee9c \u1ea5y.<\/span> <br\/><br\/>","column":3}]}],"id_ques":1754},{"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":" <span class='basic_left'>Cho h\u00ecnh ch\u1eef nh\u1eadt $ABCD$ c\u00f3 $AB > AD$ v\u00e0 $AD = 5cm$. Tr\u00ean $DC$ l\u1ea5y \u0111i\u1ec3m $M$ sao cho $DM = 2cm$. Bi\u1ebft $\\widehat{AMB} = 90^o$. T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh $MC$.<\/span>","select":[" A. $MC = 10cm$"," B. $MC = 12,5cm$","C. $MC = 15cm$","D. $MC = 18cm$"],"hint":"","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai17/lv1/img\/H8C3B4_D111.png' \/><\/center><br\/>$ABCD$ l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt (gi\u1ea3 thi\u1ebft)<br\/> $\\Rightarrow \\begin{cases} \\widehat{BAD} = \\widehat{ABC} = \\widehat{C} = \\widehat{D} = 90^o \\\\ AD = BC = 5 \\text{(cm)}\\end{cases}$ (t\u00ednh ch\u1ea5t h\u00ecnh ch\u1eef nh\u1eadt)<br\/>$\\triangle{ADM}$ vu\u00f4ng t\u1ea1i $D$ <br\/>$\\Rightarrow \\widehat{DAM} + \\widehat{AMD} = 90^o$ (hai g\u00f3c ph\u1ee5 nhau)<br\/>L\u1ea1i c\u00f3: $\\widehat{BMC} + \\widehat{AMD} = 90^o$<br\/>$\\Rightarrow \\widehat{DAM} = \\widehat{BMC}$ <br\/> X\u00e9t $\\triangle$ vu\u00f4ng $ADM$ v\u00e0 $\\triangle$ vu\u00f4ng $MCB$ c\u00f3:<br\/>$\\widehat{DAM} = \\widehat{BMC}$ (ch\u1ee9ng minh tr\u00ean)<br\/>$\\Rightarrow$ $\\triangle$ vu\u00f4ng $ADM$ $\\backsim$ $\\triangle$ vu\u00f4ng $MCB$ (g\u00f3c - g\u00f3c)<br\/>$\\Rightarrow$ $\\dfrac{AD}{MC} = \\dfrac{DM}{CB}$ (c\u1eb7p c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng t\u1ec9 l\u1ec7)<br\/>$\\Rightarrow$ $MC = \\dfrac{AD.CB}{DM} = \\dfrac{5.5}{2} = 12,5 \\text{(cm)}$ <br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>B. $MC = 12,5cm$<\/span>","column":2}]}],"id_ques":1755},{"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":" <span class='basic_left'> Cho h\u00ecnh v\u1ebd nh\u01b0 sau: <br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai17/lv1/img\/H8C3B4_D112.png' \/><\/center><br\/> T\u00ednh $S_{\\triangle{DEF}}$<\/span>","select":[" A. $S_{\\triangle{DEF}} = 100cm^2$"," B. $S_{\\triangle{DEF}} = 120cm^2$","C. $S_{\\triangle{DEF}} = 125cm^2$","D. $S_{\\triangle{DEF}} = 150cm^2$"],"hint":"Ch\u1ee9ng minh $\\triangle{EDF} \\backsim \\triangle{EHD}$, $\\triangle{EDF} \\backsim \\triangle{DHF}$","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai17/lv1/img\/H8C3B4_D112.png' \/><\/center><br\/>+) $\\triangle$ vu\u00f4ng $EDF$ $\\backsim$ $\\triangle$ vu\u00f4ng $EHD$ (v\u00ec c\u00f3 chung $\\widehat{E}$)<br\/>$\\Rightarrow \\dfrac{ED}{EH} = \\dfrac{EF}{ED} $ (c\u1eb7p c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng t\u1ec9 l\u1ec7) <br\/>Hay $ \\dfrac{ED}{9} = \\dfrac{9 + 16}{ED}$ <br\/>$\\Rightarrow ED^2 = 9.25 = 225 \\Rightarrow ED = 15 \\text{(cm)}$<br\/>+) $\\triangle$ vu\u00f4ng $EDF$ $\\backsim$ $\\triangle$ vu\u00f4ng $DHF$ (v\u00ec c\u00f3 chung $\\widehat{F}$)<br\/>$\\Rightarrow \\dfrac{DF}{HF} = \\dfrac{EF}{DF} $ (c\u1eb7p c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng t\u1ec9 l\u1ec7)<br\/> Hay $ \\dfrac{DF}{16} = \\dfrac{9 + 16}{DF}$ <br\/>$\\Rightarrow DF^2 = 16.25 = 400 \\Rightarrow DF = 20 \\text{(cm)}$<br\/>$S_{\\triangle{DEF}} = \\dfrac{DE.DF}{2} = \\dfrac{15.20}{2} = 150 (\\text{cm}^2)$ <br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>D. $S_{\\triangle{DEF}} = 150 (\\text{cm}^2)$<\/span>","column":2}]}],"id_ques":1756},{"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":" <span class='basic_left'>Cho h\u00ecnh v\u1ebd nh\u01b0 sau: <br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai17/lv1/img\/H8C3B4_D113.png' \/><\/center><br\/> T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh $AH$.<\/span>","select":[" A. $AH = 3cm$"," B. $AH = 4,5cm$","C. $AH = 5cm$","D. $AH = 6cm$"],"hint":"Ch\u1ee9ng minh $\\triangle$ vu\u00f4ng $ABH$ $\\backsim$ $\\triangle$ vu\u00f4ng $CAH$.","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai17/lv1/img\/H8C3B4_D113.png' \/><\/center><br\/>+) $\\triangle{ABH}$ vu\u00f4ng t\u1ea1i $H$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow$ $\\widehat{B} + \\widehat{BAH} = 90^o$ (hai g\u00f3c ph\u1ee5 nhau)<br\/>L\u1ea1i c\u00f3: $\\widehat{CAH} + \\widehat{BAH} = \\widehat{BAC} = 90^o$ <br\/>$\\Rightarrow \\widehat{B} = \\widehat{CAH}$<br\/>+) X\u00e9t $\\triangle{ABH}$ v\u00e0 $\\triangle{CAH}$ c\u00f3:<br\/>$\\widehat{B} = \\widehat{CAH}$ (ch\u1ee9ng minh tr\u00ean)<br\/>$\\widehat{AHC} = \\widehat{BHA}$ (c\u00f9ng = $90^o$)<br\/>$\\Rightarrow$ $\\triangle{ABH}$ $\\backsim$ $\\triangle{CAH}$ (g\u00f3c - g\u00f3c)<br\/>$\\Rightarrow$ $\\dfrac{AH}{CH} = \\dfrac{BH}{AH}$ (c\u1eb7p c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng)<br\/>$\\Rightarrow$ $AH^2 = BH.CH = 4.9 = 36 \\Rightarrow AH = 6 \\text{(cm)}$ <br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>D. $AH = 6cm$<\/span>","column":2}]}],"id_ques":1757},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["15"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"<span class='basic_left'>Cho h\u00ecnh v\u1ebd nh\u01b0 sau: <br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai17/lv1/img\/H8C3B4_D113.png' \/><\/center><br\/> T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh $AB$.<br\/><b>\u0110\u00e1p \u00e1n:<\/b> $AB = $ _input_ ($cm$)<\/span>","hint":"Ch\u1ee9ng minh $\\triangle$ vu\u00f4ng $ABH$ $\\backsim$ $\\triangle$ vu\u00f4ng $CAH$ $\\Rightarrow$ $AH$ $\\Rightarrow$ $AB$. ","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai17/lv1/img\/H8C3B4_D114.png' \/><\/center><br\/>+) $\\triangle{ABH}$ vu\u00f4ng t\u1ea1i $H$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow$ $\\widehat{B} + \\widehat{BAH} = 90^o$ (hai g\u00f3c ph\u1ee5 nhau)<br\/>L\u1ea1i c\u00f3: $\\widehat{CAH} + \\widehat{BAH} = \\widehat{BAC} = 90^o$ <br\/>$\\Rightarrow \\widehat{B} = \\widehat{CAH}$<br\/>+) X\u00e9t $\\triangle{ABH}$ v\u00e0 $\\triangle{CAH}$ c\u00f3:<br\/>$\\widehat{B} = \\widehat{CAH}$ (ch\u1ee9ng minh tr\u00ean)<br\/>$\\widehat{AHC} = \\widehat{BHA}$ (c\u00f9ng = $90^o$)<br\/>$\\Rightarrow$ $\\triangle{ABH}$ $\\backsim$ $\\triangle{CAH}$ (g\u00f3c - g\u00f3c)<br\/>$\\Rightarrow$ $\\dfrac{AH}{CH} = \\dfrac{BH}{AH}$<br\/>$\\Rightarrow$ $AH^2 = BH.CH = 9.16 = 144 \\Rightarrow AH = 12 \\text{(cm)}$<br\/>+) $\\triangle{ABH}$ vu\u00f4ng t\u1ea1i $H$ (gi\u1ea3 thi\u1ebft)<br\/> $\\Rightarrow AH^2 + BH^2 = AB^2$ (\u0111\u1ecbnh l\u00ed py-ta-go)<br\/> $\\Rightarrow AB^2 = 9^2 + 12^2 = 225 \\Rightarrow AB = 15 \\text{(cm)}$<br\/>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 <span class='basic_pink'>$15$<\/span> "}]}],"id_ques":1758},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t \u0111\u1ec3 v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" <span class='basic_left'>N\u1ebfu c\u1ea1nh huy\u1ec1n v\u00e0 m\u1ed9t c\u1ea1nh g\u00f3c vu\u00f4ng c\u1ee7a tam gi\u00e1c vu\u00f4ng n\u00e0y t\u1ec9 l\u1ec7 v\u1edbi c\u1ea1nh huy\u1ec1n v\u00e0 c\u1ea1nh g\u00f3c vu\u00f4ng c\u1ee7a tam gi\u00e1c vu\u00f4ng kia th\u00ec hai tam gi\u00e1c vu\u00f4ng \u0111\u00f3 ..................<\/span>","select":[" A. \u0110\u1ed3ng d\u1ea1ng"," B. B\u1eb1ng nhau"],"hint":"","explain":"\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0: <span class='basic_pink'>A. \u0110\u1ed3ng d\u1ea1ng<\/span>","column":2}]}],"id_ques":1759}],"lesson":{"save":0,"level":1}}