{"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":" Vi\u1ebft t\u1ec9 s\u1ed1 c\u1ee7a c\u1eb7p \u0111o\u1ea1n th\u1eb3ng sau: $AB$ = $90cm$; $CD$ = $80cm$ ","select":[" A. $ \\dfrac{AB}{CD}=\\dfrac{90}{80}=\\dfrac{9}{8}$ "," B. $\\dfrac{AB}{CD}=\\dfrac{80}{90}=\\dfrac{8}{9}$"],"explain":" <span class='basic_left'>T\u1ec9 s\u1ed1 c\u1ee7a hai \u0111o\u1ea1n th\u1eb3ng $AB$ v\u00e0 $CD$ l\u00e0:<br\/>$\\dfrac{AB}{CD}=\\dfrac{90}{80}=\\dfrac{9}{8}$<br\/>V\u1eady ta ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'> A. $ \\dfrac{AB}{CD}=\\dfrac{90}{80}=\\dfrac{9}{8}$<\/span><\/span>","column":2}]}],"id_ques":1770},{"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":" Hai \u0111o\u1ea1n th\u1eb3ng $AB = 18cm$, $CD = 40cm$ t\u1ec9 l\u1ec7 v\u1edbi hai \u0111o\u1ea1n th\u1eb3ng $A\u2019B\u2019 = 36cm$ v\u00e0 $C\u2019D\u2019$. \u0110o\u1ea1n th\u1eb3ng $C\u2019D\u2019$ c\u00f3 \u0111\u1ed9 d\u00e0i (theo \u0111\u01a1n v\u1ecb $cm$) l\u00e0: ","select":[" A. $16,2$ "," B. $60$","C. $80$","D. $100$"],"explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>S\u1eed d\u1ee5ng \u0111\u1ecbnh ngh\u0129a \u0111o\u1ea1n th\u1eb3ng t\u1ec9 l\u1ec7<\/span> <br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Hai \u0111o\u1ea1n th\u1eb3ng $AB$, $CD$ t\u1ec9 l\u1ec7 v\u1edbi hai \u0111o\u1ea1n th\u1eb3ng $A\u2019B\u2019$ v\u00e0 $C\u2019D\u2019$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{AB}{CD}=\\dfrac{A'B'}{C'D'}$ hay $\\dfrac{18}{40}=\\dfrac{36}{C'D'}$<br\/>$\\Rightarrow C'D'=\\dfrac{40.36}{18}=80 \\text{(cm)}$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: <span class='basic_pink'>C. $80$<\/span>","column":2}]}],"id_ques":1771},{"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 bi\u1ebft \u0111\u1ed9 d\u00e0i c\u1ee7a $AB$ g\u1ea5p $7$ l\u1ea7n \u0111\u1ed9 d\u00e0i c\u1ea1nh $CD$ v\u00e0 \u0111\u1ed9 d\u00e0i c\u1ee7a $A\u2019B\u2019$ g\u1ea5p $9$ l\u1ea7n \u0111\u1ed9 d\u00e0i c\u1ee7a $CD$. T\u00ednh t\u1ec9 s\u1ed1 c\u1ee7a hai \u0111o\u1ea1n th\u1eb3ng $AB$ v\u00e0 $A\u2019B\u2019$. ","select":[" A. $\\dfrac{7}{9}$ "," B. $\\dfrac{9}{7}$","C. $\\dfrac{7}{16}$","D. $\\dfrac{16}{7}$"],"explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>S\u1eed d\u1ee5ng \u0111\u1ecbnh ngh\u0129a t\u1ec9 s\u1ed1 c\u1ee7a hai \u0111o\u1ea1n th\u1eb3ng<\/span> <br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Theo \u0111\u1ec1 b\u00e0i ta c\u00f3:<br\/>$AB = 7.CD$<br\/>$A\u2019B\u2019 = 9.CD$<br\/>T\u1ec9 s\u1ed1 c\u1ee7a hai \u0111o\u1ea1n th\u1eb3ng $AB$ v\u00e0 $A\u2019B\u2019$ l\u00e0:<br\/>$\\dfrac{AB}{A'B'}=\\dfrac{7.CD}{9.CD}=\\dfrac{7}{9}$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: <span class='basic_pink'>A. $\\dfrac{7}{9}$<\/span>","column":2}]}],"id_ques":1772},{"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 $\\triangle ABC$, tr\u00ean c\u1ea1nh $AC$ l\u1ea5y \u0111i\u1ec3m $D$ sao cho $AD = 6cm$, $DC = 2cm$. Qua $D$ k\u1ebb $DE \/\/ AB$ ($E \\in BC$). Bi\u1ebft $CB = 12cm$. T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ee7a $CE$.","select":[" A. $2,5cm$ "," B. $3cm$","C. $4cm$","D. $6cm$"],"hint":" T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh AC sau \u0111\u00f3 s\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00fd Ta-l\u00e9t \u0111\u1ec3 t\u00ecm $CE$","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> T\u00ednh $AC$<br\/><b>B\u01b0\u1edbc 2:<\/b> \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Ta-l\u00e9t \u0111\u1ec3 \u0111\u01b0a ra h\u1ec7 th\u1ee9c: $\\dfrac{CD}{CA} = \\dfrac{CE}{CB}$<br\/><b>B\u01b0\u1edbc 3:<\/b> T\u1eeb h\u1ec7 th\u1ee9c \u1edf b\u01b0\u1edbc 2 t\u00ednh $CE$.<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/bai18/lv1/img\/H8C3B5_D101.png' \/><\/center><br\/>Ta c\u00f3: $D \\in AC$ (gi\u1ea3 thi\u1ebft)<br\/> $\\Rightarrow AC = AD + DC = 6 + 2 = 8 \\text{(cm)}$<br\/>V\u00ec $DE \/\/ AB$ (gi\u1ea3 thi\u1ebft), theo \u0111\u1ecbnh l\u00ed Ta-l\u00e9t ta c\u00f3:<br\/>$\\dfrac{CD}{CA} = \\dfrac{CE}{CB}$ hay $\\dfrac{2}{8} = \\dfrac{CE}{12}$<br\/>$\\Rightarrow CE = \\dfrac{2.12}{8} = 3 \\text{(cm)}$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: <span class='basic_pink'>B. $3cm$<\/span>","column":2}]}],"id_ques":1773},{"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 h\u00ecnh v\u1ebd sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai18/lv1/img\/H8C3B5_D102.png' \/><\/center><br\/>Bi\u1ebft $\\dfrac{ME}{MN} = \\dfrac{3}{5}$. T\u00ednh $NP$.","select":[" A. $NP = 7cm$ "," B. $NP = 5cm$","C. $NP = 9cm$","D. $NP = 12cm$"],"hint":" S\u1eed d\u1ee5ng h\u1ec7 qu\u1ea3 c\u1ee7a \u0111\u1ecbnh l\u00fd Ta-l\u00e9t","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai18/lv1/img\/H8C3B5_D102.png' \/><\/center><br\/> $\\triangle MNP$ c\u00f3:<br\/>$\\left.\\begin{array}{l} EF \/\/ NP \\text{(gi\u1ea3 thi\u1ebft)}\\\\ E \\in MN; F \\in MP \\text{(gi\u1ea3 thi\u1ebft)} \\end{array} \\right\\}$ <br\/> $\\Rightarrow \\dfrac{ME}{MN} = \\dfrac{EF}{NP}$ (h\u1ec7 qu\u1ea3 c\u1ee7a \u0111\u1ecbnh l\u00ed Ta-l\u00e9t)<br\/> $\\Rightarrow \\dfrac{3}{5} = \\dfrac{4,2}{NP}$<br\/>$\\Rightarrow NP = \\dfrac{5.4,2}{3} = 7 \\text{(cm)}$<br\/><br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>A. $NP = 7cm$<\/span><\/span>","column":2}]}],"id_ques":1774},{"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":" T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ee7a $x$ trong h\u00ecnh sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai18/lv1/img\/H8C3B5_D103.png' \/><\/center>","select":[" A. $8$ "," B. $8,6$","C. $10$","D. $12$"],"hint":"S\u1eed d\u1ee5ng h\u1ec7 qu\u1ea3 c\u1ee7a \u0111\u1ecbnh l\u00ed Ta-l\u00e9t.","explain":"<span class='basic_left'>X\u00e9t $\\triangle EFG$ c\u00f3:<br\/>$\\left.\\begin{array}{l} AB \/\/ FG \\text{(gi\u1ea3 thi\u1ebft)}\\\\ A \\in EG; B \\in EF \\end{array} \\right\\}$ $\\Rightarrow \\dfrac{AE}{EG} = \\dfrac{BE}{EF}$ (h\u1ec7 qu\u1ea3 c\u1ee7a \u0111\u1ecbnh l\u00fd Ta-l\u00e9t)<br\/> $\\Rightarrow \\dfrac{4}{x} = \\dfrac{3}{9}$<br\/>$\\Rightarrow x = \\dfrac{4.9}{3} = 12 $<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>D. $12$<\/span><\/span> ","column":2}]}],"id_ques":1775},{"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'>T\u00ednh $x$ trong h\u00ecnh v\u1ebd sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai18/lv1/img\/H8C3B5_D104.png' \/><\/center><br\/><\/span>","select":[" A. $x = 6$"," B. $x = 4,75$","C. $x = 5,25$","D. $x = 5,75$"],"explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai18/lv1/img\/H8C3B5_D104.png' \/><\/center><br\/> $\\triangle MNP$ c\u00f3:<br\/> $NH$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{MNP}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{NM}{NP} = \\dfrac{HM}{HP}$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c)<br\/>$\\Rightarrow \\dfrac{4}{7} = \\dfrac{3}{x}$<br\/> $\\Rightarrow x = \\dfrac{3.7}{4} = 5,25$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'> C. $x = 5,25$<\/span>","column":2}]}],"id_ques":1776},{"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'>T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh $AB$ v\u00e0 $AC$ trong h\u00ecnh v\u1ebd sau: <br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai18/lv1/img\/H8C3B5_D105.png' \/><\/center><\/span>","select":[" A. $AC = 15cm; AB = 20cm$"," B. $AC = 20cm; AB = 25cm$","C. $AC = 25cm; AB = 21cm$","D. $AC = 28cm; AB = 21cm$"],"explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai18/lv1/img\/H8C3B5_D105.png' \/><\/center><br\/>$\\triangle ABC$ vu\u00f4ng t\u1ea1i $A$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow AB^2 + AC^2 = BC^2$ ( \u0111\u1ecbnh l\u00ed Py-ta-go)<br\/> $\\Rightarrow AB^2 + AC^2 = (DB + DC)^2 = (15 + 20)^2 = 35^2 = 1225$<br\/> $\\triangle ABC$ c\u00f3:<br\/> $AD$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{BAC}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{AB}{AC} = \\dfrac{DB}{DC}$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c)<br\/>$\\Rightarrow \\dfrac{AB}{AC} = \\dfrac{15}{20} = \\dfrac{3}{4}$<br\/> $\\Rightarrow \\dfrac{AB}{3} = \\dfrac{AC}{4 }$<br\/> $\\Rightarrow \\dfrac{AB^2}{9} = \\dfrac{AC^2}{16}$<br\/>\u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ta c\u00f3:<br\/>$\\dfrac{AB^2}{9} = \\dfrac{AC^2}{16} = \\dfrac{AB^2 + AC^2}{9 + 16} = \\dfrac{1225}{25} = 49$ <br\/>$\\Rightarrow$ $\\begin{cases}AC^2 = 16.49 = 784\\\\ AB^2 = 9. 49 = 441\\end{cases}$<br\/>$\\Rightarrow$ $\\begin{cases}AC = 28 \\text{(cm)} \\\\ AB = 21 \\text{(cm)} \\end{cases}$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'> D. $AC = 28cm; AB = 21cm$<\/span>","column":2}]}],"id_ques":1777},{"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"],["18"],["27"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"<span class='basic_left'>Bi\u1ebft $\\triangle{ABC} \\backsim \\triangle{A'B'C'}$ v\u00e0 \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh $\\triangle{ABC}$ l\u00e0 $AB = 5cm$; $AC = 6cm$; $BC = 9cm$. T\u00ednh \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh $\\triangle{A'B'C'}$ bi\u1ebft chu vi tam gi\u00e1c $A'B'C'$ b\u1eb1ng $60cm$. <br\/><b>\u0110\u00e1p \u00e1n:<\/b> $A'B'$ = _input_ ($cm$); $A'C'$ = _input_ ($cm$); $B'C'$ = _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> T\u1eeb $\\triangle{ABC} \\backsim \\triangle{A'B'C'} $ t\u00ecm t\u1ec9 s\u1ed1 \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh c\u1ee7a hai tam gi\u00e1c<br\/><b>B\u01b0\u1edbc 2:<\/b> T\u1eeb b\u01b0\u1edbc 1 \u00e1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau c\u1ee7a tam gi\u00e1c \u0111\u1ec3 t\u00ecm $A'B', A'C', B'C'$<\/span><br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>$\\triangle{ABC} \\backsim \\triangle{A'B'C'} $ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{A'B'}{AB} = \\dfrac{B'C'}{BC} = \\dfrac{A'C'}{AC}$ hay $\\dfrac{A'B'}{5} = \\dfrac{B'C'}{9} = \\dfrac{A'C'}{6}$<br\/>\u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3:<br\/> $\\dfrac{A'B'}{5} = \\dfrac{B'C'}{9} = \\dfrac{A'C'}{6} = \\dfrac{A'B' + B'C' + A'C'}{5 + 6 + 9} = \\dfrac{60}{20} = 3$<br\/>Do \u0111\u00f3<br\/>$A'B' = 3.5 = 15$ ($cm$)<br\/>$A'C' = 3.6 = 18$ ($cm$)<br\/>$B'C' = 3.9 = 27$ ($cm$)<br\/>V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0: <span class='basic_pink'>15; 18; 27<\/span>"}]}],"id_ques":1778},{"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 tam gi\u00e1c $ABC$ c\u00f3 $AB = 8cm, AC = 16cm$. \u0110i\u1ec3m $D$ thu\u1ed9c c\u1ea1nh $AC$ sao cho $\\widehat{ABD} = \\widehat{C}$. T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh $AD$.<br\/><\/span>","select":[" A. $AD = 4cm$"," B. $AD = 4,5cm$","C. $AD = 5cm$","D. $AD = 5,5cm$"],"hint":"","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 $\\triangle{ABD} \\backsim \\triangle{ACB}$<br\/><b>B\u01b0\u1edbc 2:<\/b> T\u1eeb b\u01b0\u1edbc 1 suy ra c\u00e1c c\u1eb7p c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng t\u1ec9 l\u1ec7<br\/><b>B\u01b0\u1edbc 3:<\/b> T\u00ednh $AD$<\/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/bai18/lv1/img\/H8C3B5_D106.png' \/><\/center><br\/>X\u00e9t $\\triangle{ABD}$ v\u00e0 $\\triangle{ACB}$ c\u00f3:<br\/>$\\widehat{ABD} = \\widehat{C}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\widehat{A}$ chung<br\/>$\\Rightarrow$ $\\triangle{ABD} \\backsim \\triangle{ACB}$ (g-g)<br\/>$\\Rightarrow \\dfrac{AD}{AB} = \\dfrac{AB}{AC}$ (c\u1eb7p c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng t\u1ec9 l\u1ec7) <br\/>$\\Rightarrow \\dfrac{AD}{8} = \\dfrac{8}{16}$<br\/>$\\Rightarrow AD = \\dfrac{8.8}{16} = 4 \\text{(cm)}$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>A. $AD = 4cm$<\/span><\/span> <br\/><\/span><br\/>","column":2}]}],"id_ques":1779},{"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":[[["6"]]],"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/bai18/lv1/img\/H8C3B5_D107.png' \/><\/center><br\/>T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh $DE$<br\/><b>\u0110\u00e1p \u00e1n:<\/b> $DE =$ _input_ ($cm$)<\/span>","hint":"S\u1eed d\u1ee5ng tr\u01b0\u1eddng h\u1ee3p \u0111\u1ed3ng d\u1ea1ng th\u1ee9 hai: c\u1ea1nh-g\u00f3c-c\u1ea1nh. ","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 $\\triangle{ADE} \\backsim \\triangle{ACB}$ t\u1eeb \u0111\u00f3 suy ra c\u00e1c c\u1eb7p c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng t\u1ec9 l\u1ec7<br\/><b>B\u01b0\u1edbc 2:<\/b> T\u1eeb b\u01b0\u1edbc 1 suy ra \u0111\u1ed9 d\u00e0i c\u1ea1nh $DE$<\/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/bai18/lv1/img\/H8C3B5_D107.png' \/><\/center><br\/>X\u00e9t $\\triangle{ADE}$ v\u00e0 $\\triangle{ACB}$ c\u00f3:<br\/>$\\widehat{A}$ chung<br\/>$\\dfrac{AE}{EB} = \\dfrac{AD}{AC}$ (v\u00ec $\\dfrac{5}{10} = \\dfrac{4}{8}$)<br\/> $\\Rightarrow$ $\\triangle{ADE} \\backsim \\triangle{ACB}$ (c\u1ea1nh-g\u00f3c-c\u1ea1nh)<br\/>$\\Rightarrow \\dfrac{AD}{AC} = \\dfrac{DE}{BC}$ (c\u1eb7p c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng t\u1ec9 l\u1ec7) <br\/>$\\Rightarrow DE = \\dfrac{AD.BC}{AC} = \\dfrac{4.12}{8} = 6 \\text{(cm)}$ <br\/>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 <span class='basic_pink'>6<\/span>"}]}],"id_ques":1780},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"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/bai18/lv1/img\/H8C3B5_D108.png' \/><\/center><br\/>T\u00ednh $BN, MN$.<\/span>","select":["A. $BN = 5$; $MN = 3$","B. $BN = 3$; $MN = 5$","C. $BN = 4$; $MN = 3$","D. $BN = 5$; $MN = 4$"],"hint":"Ch\u1ee9ng minh $MN \/\/ AC$. T\u1eeb \u0111\u00f3 \u00e1p d\u1ee5ng h\u1ec7 qu\u1ea3 c\u1ee7a \u0111\u1ecbnh l\u00ed Ta-l\u00e9t \u0111\u1ec3 t\u00ednh $BN$ v\u00e0 $MN$.","explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai18/lv1/img\/H8C3B5_D108.png' \/><\/center><br\/>Ta c\u00f3:<br\/>$\\left.\\begin{array}{l} MN \\perp AB \\text{(gi\u1ea3 thi\u1ebft)}\\\\ AC \\perp AB \\text{(gi\u1ea3 thi\u1ebft)} \\end{array} \\right\\}$ $\\Rightarrow MN \/\/ AC$ (t\u00ednh ch\u1ea5t t\u1eeb vu\u00f4ng g\u00f3c \u0111\u1ebfn song song) <br\/>X\u00e9t $\\triangle ABC$ c\u00f3: $MN \/\/ AC$ (ch\u1ee9ng minh tr\u00ean)<br\/> $\\Rightarrow \\dfrac{BM}{BA}=\\dfrac{BN}{BC} = \\dfrac{MN}{AC}$ (h\u1ec7 qu\u1ea3 c\u1ee7a \u0111\u1ecbnh l\u00ed Ta-l\u00e9t)<br\/>$\\Rightarrow \\dfrac{4}{12}=\\dfrac{BN}{15} = \\dfrac{MN}{9}$<br\/> $\\Rightarrow$ $\\begin{cases}BN = \\dfrac{4.15}{12} = 5 \\\\ MN = \\dfrac{4.9}{12} = 3\\end{cases}$ <br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: <span class='basic_pink'>A. $BN = 5$ v\u00e0 $MN = 3$<\/span><\/span> <br\/><\/span> ","column":2}]}],"id_ques":1781},{"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":[[["6"]]],"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/bai18/lv1/img\/H8C3B5_D109.png' \/><\/center><br\/>T\u00ednh $S_{\\triangle{MBN}}$, bi\u1ebft $S_{\\triangle{ABC}} = 54 \\text{cm}^2$<br\/><b>\u0110\u00e1p \u00e1n:<\/b> $S_{\\triangle{MBN}}$ _input_ ($cm^2$)<\/span>","hint":"Hai tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng c\u00f3 t\u1ec9 s\u1ed1 di\u1ec7n t\u00edch b\u1eb1ng b\u00ecnh ph\u01b0\u01a1ng 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 $\\triangle{MBN} \\backsim \\triangle{ABC}$<br\/><b>B\u01b0\u1edbc 2:<\/b> T\u00ednh $S_{\\triangle{MBN}}$<\/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/bai18/lv1/img\/H8C3B5_D109.png' \/><\/center><br\/>Ta c\u00f3: <br\/>$\\left.\\begin{array}{l} MN \\perp AB \\text{(gi\u1ea3 thi\u1ebft)}\\\\ AC \\perp AB \\text{(gi\u1ea3 thi\u1ebft)} \\end{array} \\right\\}$ $\\Rightarrow MN \/\/ AC$ (t\u00ednh ch\u1ea5t t\u1eeb vu\u00f4ng g\u00f3c \u0111\u1ebfn song song) <br\/> X\u00e9t $\\triangle ABC$ c\u00f3: $MN \/\/ AC$ (ch\u1ee9ng minh tr\u00ean) <br\/>$\\Rightarrow \\triangle{MBN} \\backsim \\triangle{ABC}$<br\/>$\\Rightarrow \\dfrac{S_{\\triangle{MBN}}}{S_{\\triangle{ABC}}} = \\left(\\dfrac{MB}{AB}\\right)^2 = \\left(\\dfrac{4}{12}\\right)^2 = \\dfrac{1}{9}$<br\/>$\\Rightarrow S_{\\triangle{MBN}} = \\dfrac{1}{9}.S_{\\triangle{ABC}} = \\dfrac{1}{9}.54 = 6 (\\text{cm}^2)$ <br\/>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 <span class='basic_pink'>6<\/span>"}]}],"id_ques":1782},{"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'>T\u00ednh $x$, $y$ trong h\u00ecnh v\u1ebd sau, bi\u1ebft $HK \/\/ BC$: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai18/lv1/img\/H8C3B5_D110.png' \/><\/center><br\/><\/span>","select":[" A. $x = 7,5cm; y = 15cm$"," B. $x = 15cm; y = 7,5cm$","C. $x = 8cm; y = 10cm$","D. $x = 9cm; y = 12cm$"],"hint":"S\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00ed Ta-l\u00e9t t\u00ecm $y$, s\u1eed d\u1ee5ng t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u1ea7n gi\u00e1c c\u1ee7a tam gi\u00e1c t\u00ecm $x$.","explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai18/lv1/img\/H8C3B5_D110.png' \/><\/center><br\/> $\\triangle ABC$ c\u00f3: $HK \/\/ BC$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{AK}{KB} = \\dfrac{HA}{HC}$ (\u0111\u1ecbnh l\u00ed Ta-l\u00e9t) <br\/>$\\Rightarrow \\dfrac{4}{6} = \\dfrac{5}{y}$ $\\Rightarrow y = \\dfrac{5.6}{4} = 7,5 \\text{(cm)}$ <br\/>$\\triangle ABC$ c\u00f3: $BH$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{ABC}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{BA}{BC} = \\dfrac{HA}{HC}$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c)<br\/>$\\Rightarrow \\dfrac{4 + 6}{x} = \\dfrac{5}{7,5}$ $\\Rightarrow \\dfrac{10}{x} = \\dfrac{5}{7,5}$ $\\Rightarrow x = \\dfrac{10.7,5}{5} = 15 \\text{(cm)}$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'> B. $x = 15cm; y = 7,5cm$<\/span>","column":2}]}],"id_ques":1783},{"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: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai18/lv1/img\/H8C3B5_D111.png' \/><\/center><br\/>T\u00ednh $BN, MN$.<\/span>","select":["A. $BN = 3,75cm$; $MN = 2,25cm$","B. $BN = 4,25cm$; $MN = 3,75cm$","C. $BN = 5cm$; $MN = 6cm$","D. $BN = 6,25cm$; $MN = 3,75cm$"],"hint":"Ch\u1ee9ng minh $MN \/\/ AC$. T\u1eeb \u0111\u00f3 \u00e1p d\u1ee5ng h\u1ec7 qu\u1ea3 c\u1ee7a \u0111\u1ecbnh l\u00ed Ta-l\u00e9t \u0111\u1ec3 t\u00ednh $BN$ v\u00e0 $MN$.","explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai18/lv1/img\/H8C3B5_D111.png' \/><\/center><br\/>Ta c\u00f3:<br\/>$\\left.\\begin{array}{l} MN \\perp AB \\text{(gi\u1ea3 thi\u1ebft)}\\\\ AC \\perp AB \\text{(gi\u1ea3 thi\u1ebft)} \\end{array} \\right\\}$ $\\Rightarrow MN \/\/ AC$ (t\u00ednh ch\u1ea5t t\u1eeb vu\u00f4ng g\u00f3c \u0111\u1ebfn song song) <br\/>X\u00e9t $\\triangle ABC$ c\u00f3: $MN \/\/ AC$ (ch\u1ee9ng minh tr\u00ean)<br\/> $\\Rightarrow \\dfrac{BM}{BA}=\\dfrac{BN}{BC} = \\dfrac{MN}{AC}$ (h\u1ec7 qu\u1ea3 c\u1ee7a \u0111\u1ecbnh l\u00ed Ta-l\u00e9t)<br\/>$\\Rightarrow \\dfrac{5}{12}=\\dfrac{BN}{15} = \\dfrac{MN}{9}$<br\/> $\\Rightarrow$ $\\begin{cases}BN = \\dfrac{5.15}{12} = 6,25 \\text{(cm)} \\\\ MN = \\dfrac{5.9}{12} = 3,75 \\text{(cm)} \\end{cases}$ <br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: <span class='basic_pink'>D. $BN = 6,25cm$ v\u00e0 $MN = 3,75cm$<\/span><\/span> <br\/><\/span> ","column":2}]}],"id_ques":1784},{"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"]],"list":[{"point":5,"img":"","ques":"Cho c\u00e1c c\u1eb7p tam gi\u00e1c c\u00f3 c\u00e1c c\u1ea1nh c\u00f3 \u0111\u1ed9 d\u00e0i sau \u0111\u00e2y<br\/><b> H\u00e3y ch\u1ecdn nh\u1eefng c\u1eb7p tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng.<\/b>","hint":"","column":2,"number_true":2,"select":["A. 1,5cm; 2cm; 3cm v\u00e0 3cm; 4cm; 6cm","B. 2cm; 5cm; 6cm v\u00e0 4cm; 10cm; 12cm ","C. 3cm; 5cm; 7cm v\u00e0 6cm; 10cm; 12cm","D. 4cm; 9cm; 10cm v\u00e0 8cm; 15cm; 20cm"],"explain":"\u0110\u00e1p \u00e1n $A$ \u0111\u00fang v\u00ec: $\\dfrac{1,5}{3} = \\dfrac{2}{4} = \\dfrac{3}{6}$ <br\/>\u0110\u00e1p \u00e1n $B$ \u0111\u00fang v\u00ec: $\\dfrac{2}{4} = \\dfrac{5}{10} = \\dfrac{6}{12}$<br\/>\u0110\u00e1p \u00e1n $C$ sai v\u00ec: $\\dfrac{3}{6} = \\dfrac{5}{10} \\neq \\dfrac{5}{7} $<br\/>\u0110\u00e1p \u00e1n $D$ sai v\u00ec: $\\dfrac{4}{8} \\neq \\dfrac{9}{15} $"}]}],"id_ques":1785},{"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":[[["20"]]],"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/bai18/lv1/img\/H8C3B5_D112.png' \/><\/center><br\/> T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh $AC$.<br\/><b>\u0110\u00e1p \u00e1n:<\/b> $AC = $ _input_ ($cm$)<\/span>","hint":"Ch\u1ee9ng minh $\\triangle$ vu\u00f4ng $ABH$ $\\backsim$ $\\triangle$ vu\u00f4ng $CAH$ $\\Rightarrow$ $AH$ $\\Rightarrow$ $AC$. ","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai18/lv1/img\/H8C3B5_D112.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 b\u1eb1ng $90^o$)<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 t\u1ec9 l\u1ec7)<br\/>$\\Rightarrow$ $AH^2 = BH.CH = 9.16 = 144 \\Rightarrow AH = 12 \\text{(cm)}$<br\/>+) $\\triangle{ACH}$ vu\u00f4ng t\u1ea1i $H$ (gi\u1ea3 thi\u1ebft)<br\/> $\\Rightarrow AH^2 + CH^2 = AC^2$ (\u0111\u1ecbnh l\u00ed py-ta-go)<br\/> $\\Rightarrow AC^2 = 16^2 + 12^2 = 400 \\Rightarrow AC = 20 \\text{(cm)}$<br\/>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 <span class='basic_pink'>$20$<\/span> "}]}],"id_ques":1786},{"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":"<span class='basic_left'>Cho tam gi\u00e1c $ABC$ c\u00f3 ba \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c $AD$, $BE$, $CF$<br\/>So s\u00e1nh $\\dfrac{FA}{FB}. \\dfrac{DB}{DC}. \\dfrac{EC}{EA}$ v\u1edbi $1$ <br\/><b>\u0110\u00e1p \u00e1n:<\/b> $\\dfrac{FA}{FB}. \\dfrac{DB}{DC}. \\dfrac{EC}{EA}$ _input_ $1$<\/span>","hint":"\u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai18/lv1/img\/H8C3B5_D113.png' \/><\/center><br\/>\u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c trong tam gi\u00e1c $ABC$ c\u00f3:<br\/>$\\dfrac{FA}{FB} = \\dfrac{CA}{CB}$; $\\dfrac{DB}{DC} = \\dfrac{AB}{AC}$; $\\dfrac{EC}{EA} = \\dfrac{BC}{AB}$<br\/>$\\Rightarrow$ $\\dfrac{FA}{FB}. \\dfrac{DB}{DC}. \\dfrac{EC}{EA} = \\dfrac{CA}{CB}. \\dfrac{AB}{AC}. \\dfrac{BC}{AB} = 1$ <br\/>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 <span class='basic_pink'>\"=\"<\/span> "}]}],"id_ques":1787},{"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":"<span class='basic_left'>Cho h\u00ecnh thoi $ABCD$ c\u00f3 \u0111i\u1ec3m $M$ n\u1eb1m tr\u00ean c\u1ea1nh $AB$. C\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng $DM$ v\u00e0 $BC$ c\u1eaft nhau t\u1ea1i $N$. So s\u00e1nh: $AB^2$ v\u00e0 $AM.CN$ <br\/><b>\u0110\u00e1p \u00e1n:<\/b> $AB^2$ _input_ $AM.CN$<\/span>","hint":"\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Ta-l\u00e9t.","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai18/lv1/img\/H8C3B5_D114.png' \/><\/center><br\/>$\\blacktriangleright$ $ABCD$ l\u00e0 h\u00ecnh thoi (gi\u1ea3 thi\u1ebft)<br\/> $\\Rightarrow \\begin{cases}AB = BC = CD = AD \\\\AB \/\/ CD; AD \/\/ BC\\end{cases}$ (t\u00ednh ch\u1ea5t h\u00ecnh thoi)<br\/>$\\blacktriangleright$ $AB \/\/ CD$ (ch\u1ee9ng minh tr\u00ean); $N \\in BC$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow BN \/\/ AD$<br\/>$\\Rightarrow \\dfrac{AD}{BN} = \\dfrac{AM}{BM}$ (h\u1ec7 qu\u1ea3 c\u1ee7a \u0111\u1ecbnh l\u00ed Ta-l\u00e9t)<br\/>$\\Rightarrow \\dfrac{AD}{AD + BN} = \\dfrac{AM}{AM + BM}$<br\/> $\\Rightarrow \\dfrac{AB}{BC + BN} = \\dfrac{AM}{AB}$ (v\u00ec $AD = BC = AB$)<br\/>$\\Rightarrow \\dfrac{AB}{CN} = \\dfrac{AM}{AB}$<br\/> $\\Rightarrow AB^2 = AM.CN$ <br\/>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 <span class='basic_pink'>\"=\"<\/span> <br\/><span class='basic_left'><span class='basic_green'>Nh\u1eadn x\u00e9t:<\/span><br\/>$ \\dfrac{a}{b} = \\dfrac{c}{d}$ $\\Rightarrow \\dfrac{a}{a + b} = \\dfrac{c}{c + d}$<\/span> <br\/><br\/>"}]}],"id_ques":1788},{"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'>Tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A$, \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c $BD$ chia c\u1ea1nh $AC$ th\u00e0nh c\u00e1c \u0111o\u1ea1n th\u1eb3ng $DA = 3cm, DC = 5cm$. T\u00ednh c\u00e1c \u0111\u1ed9 d\u00e0i $AB, BC$.<br\/><\/span>","select":[" A. $AB = 5cm; BC = 10cm$"," B. $AB = 6cm; BC = 10cm$","C. $AB = 4cm; BC = 8cm$","D. $AB = 6cm; BC = 12cm$"],"hint":"K\u1ebft h\u1ee3p t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c v\u00e0 \u0111\u1ecbnh l\u00ed Py-ta-go \u0111\u1ec3 t\u00ednh $AB, BC$.","explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai18/lv1/img\/H8C3B5_D115.png' \/><\/center><br\/>$\\blacktriangleright$ $BD$ l\u00e0 ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{ABC}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow$ $\\dfrac{AB}{BC} = \\dfrac{AD}{DC} = \\dfrac{3}{5}$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c) <br\/>$\\blacktriangleright$ \u0110\u1eb7t $AB = 3k$, $BC = 5k$ ($k > 0$).<br\/>$\\blacktriangleright$ Tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow$ $AB^2 + AC^2 = BC^2$ (\u0111\u1ecbnh l\u00ed Py-ta-go)<br\/>$\\Rightarrow BC^2 - AB^2 = AC^2 \\\\ \\Rightarrow 25k^2 - 9k^2 = (3 + 5)^2 \\\\ \\Rightarrow 16k^2 = 64 \\Rightarrow k^2 = 4 \\Rightarrow k = 2$<br\/>V\u1eady $AB = 3.2 = 6 \\text{(cm)}; BC = 5.2 = 10 \\text{(cm)}$ <br\/>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'> B. $AB = 6cm; BC = 10cm$<\/span>","column":2}]}],"id_ques":1789}],"lesson":{"save":0,"level":1}}