{"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 tam gi\u00e1c, \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a m\u1ed9t g\u00f3c chia c\u1ea1nh \u0111\u1ed1i di\u1ec7n th\u00e0nh hai \u0111o\u1ea1n th\u1eb3ng t\u1ec9 l\u1ec7 v\u1edbi hai c\u1ea1nh k\u1ec1 hai \u0111o\u1ea1n \u1ea5y. <b>\u0110\u00fang<\/b> hay <b>Sai<\/b>? ","select":[" A. \u0110\u00fang"," B. Sai"],"explain":" \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0: <span class='basic_pink'>A. \u0110\u00fang<\/span>","column":2}]}],"id_ques":1681},{"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/bai15/lv1/img\/H8C3B2_D101.png' \/><\/center><br\/><b>H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t<\/b><\/span>","select":[" A. $\\dfrac{DB}{DC} = \\dfrac{AB}{AC}$"," B. $\\dfrac{DB}{DC} = \\dfrac{AC}{AB}$","C. $\\dfrac{DB}{BC} = \\dfrac{AB}{AC}$","D. $\\dfrac{DC}{BC} = \\dfrac{AB}{AC}$"],"explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D101.png' \/><\/center><br\/> $\\triangle ABC$ c\u00f3: $AD$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{BAC}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{DB}{DC} = \\dfrac{AB}{AC}$ (\u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c)<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'> A. $\\dfrac{DB}{DC} = \\dfrac{AB}{AC}$<\/span>","column":2}]}],"id_ques":1682},{"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 v\u1ebd nh\u01b0 sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D102.png' \/><\/center><br\/>T\u00ednh $\\dfrac{x}{y}$<\/span>","select":[" A. $\\dfrac{x}{y} = \\dfrac{7}{5}$"," B. $\\dfrac{x}{y} = \\dfrac{5}{7}$","C. $\\dfrac{x}{y} = \\dfrac{5}{12}$","D. $\\dfrac{x}{y} = \\dfrac{7}{12}$"],"explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D102.png' \/><\/center><br\/> $\\triangle ABC$ c\u00f3:<br\/> $AD$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{BAC}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{DB}{DC} = \\dfrac{AB}{AC}$ (\u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c)<br\/>$\\Rightarrow \\dfrac{x}{y} = \\dfrac{5}{7}$ <br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'> B. $\\dfrac{x}{y} = \\dfrac{5}{7}$<\/span>","column":2}]}],"id_ques":1683},{"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 $x$ trong h\u00ecnh v\u1ebd sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D103.png' \/><\/center><br\/><\/span>","select":[" A. $x = 1,67$"," B. $x = 3,6$","C. $x = 4,5$","D. $x = 5,4$"],"explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D103.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\/>$\\Rightarrow \\dfrac{NM}{NP} = \\dfrac{HM}{HP}$ (\u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c)<br\/>$\\Rightarrow \\dfrac{5}{9} = \\dfrac{3}{x}$<br\/> $\\Rightarrow x = \\dfrac{3.9}{5} = 5,4$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'> D. $x = 5,4$<\/span>","column":2}]}],"id_ques":1684},{"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":[[["12"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"T\u00ednh $x$ trong h\u00ecnh v\u1ebd sau, bi\u1ebft $DH$ l\u00e0 \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a $\\triangle DEF$ ($H \\in EF$). <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D104.png' \/><\/center><br\/><b>\u0110\u00e1p \u00e1n:<\/b> $x$ = _input_ ($cm$)","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c \u0111\u1ec3 t\u00ednh $EH$<br\/><b>B\u01b0\u1edbc 2:<\/b> T\u00ednh $x$<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D104.png' \/><\/center><br\/> $\\triangle DEF$ c\u00f3:<br\/> $DH$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{EDF}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{DE}{DF} = \\dfrac{HE}{HF}$ (\u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c)<br\/>$\\Rightarrow \\dfrac{6}{9} = \\dfrac{HE}{7,2}$<br\/>$\\Rightarrow HE = \\dfrac{6.7,2}{9} = 4,8 \\text{(cm)}$<br\/>L\u1ea1i c\u00f3: $EF = HE + HF = 4,8 + 7,2 = 12 \\text{(cm)}$<br\/>Hay $x = 12cm$<br\/>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 <span class='basic_pink'>12<\/span>"}]}],"id_ques":1685},{"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/bai15/lv1/img\/H8C3B2_D102.png' \/><\/center><br\/>T\u00ednh $\\dfrac{x}{y}$<\/span>","select":[" A. $\\dfrac{x}{y} = \\dfrac{2}{5}$"," B. $\\dfrac{x}{y} = \\dfrac{5}{2}$","C. $\\dfrac{x}{y} = \\dfrac{5}{7}$","D. $\\dfrac{x}{y} = \\dfrac{2}{7}$"],"explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D102.png' \/><\/center><br\/> $\\triangle ABC$ c\u00f3:<br\/> $AD$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{BAC}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{DB}{DC} = \\dfrac{AB}{AC}$ (\u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c)<br\/>$\\Rightarrow \\dfrac{x}{y} = \\dfrac{5}{7}$ <br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'> C. $\\dfrac{x}{y} = \\dfrac{5}{7}$<\/span>","column":2}]}],"id_ques":1686},{"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'>Tam gi\u00e1c $ABC$ c\u00f3 $AB = 15cm, AC = 25cm, BC = 32cm$. \u0110\u01b0\u1eddng ph\u00e2n gi\u00e1c g\u00f3c $BAC$ c\u1eaft c\u1ea1nh $BC$ t\u1ea1i $D$. T\u00ednh \u0111\u1ed9 d\u00e0i c\u00e1c \u0111o\u1ea1n th\u1eb3ng $DB$ v\u00e0 $DC$<\/span>","select":[" A. $DB = 19,2cm; DC = 12,8cm$"," B. $DB = 12,8cm; DC = 19,2cm$","C. $DB = 12cm; DC = 20cm$","D. $DB = 20cm; DC = 12cm$"],"explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D106.png' \/><\/center><br\/> $\\triangle ABC$ c\u00f3:<br\/> $AD$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{BAC}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{DB}{DC} = \\dfrac{AB}{AC}$ (\u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c)<br\/>$\\Rightarrow \\dfrac{DB}{DC} = \\dfrac{15}{25} = \\dfrac{3}{5}$<br\/> $\\Rightarrow \\dfrac{DB}{DB + DC} = \\dfrac{3}{3 + 5} = \\dfrac{3}{8}$ hay $\\dfrac{DB}{BC} = \\dfrac{3}{8}$<br\/> $\\Rightarrow DB = \\dfrac{3. BC}{8} = \\dfrac{3. 32}{8} = 12 \\text{(cm)}$<br\/>L\u1ea1i c\u00f3: $DB + DC = BC$<br\/>$\\Rightarrow DC = BC - DB = 32 - 12 = 20 \\text{(cm)}$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'> C. $DB = 12cm; DC = 20cm$<\/span>","column":2}]}],"id_ques":1687},{"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'>Tam gi\u00e1c $MNP$ c\u00f3 $MN = 16cm, MP = 20cm, NP = 27cm$. \u0110\u01b0\u1eddng ph\u00e2n gi\u00e1c g\u00f3c $NMP$ c\u1eaft c\u1ea1nh $NP$ t\u1ea1i $H$. T\u00ednh \u0111\u1ed9 d\u00e0i c\u00e1c \u0111o\u1ea1n th\u1eb3ng $HN$ v\u00e0 $HP$<\/span>","select":[" A. $HN = 12cm; HP = 15cm$"," B. $HN = 15cm; HP = 12cm$","C. $HN = 10cm; HP = 17cm$","D. $HN = 13cm; HP = 14cm$"],"explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D107.png' \/><\/center><br\/> $\\triangle MNP$ c\u00f3:<br\/> $MH$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{NMP}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{HN}{HP} = \\dfrac{MN}{MP}$ (\u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c)<br\/>$\\Rightarrow \\dfrac{HN}{HP} = \\dfrac{16}{20} = \\dfrac{4}{5}$<br\/> $\\Rightarrow \\dfrac{HN}{HN + HP} = \\dfrac{4}{4 + 5} = \\dfrac{4}{9}$ hay $\\dfrac{HN}{NP} = \\dfrac{4}{9}$<br\/> $\\Rightarrow HN = \\dfrac{4. NP}{9} = \\dfrac{4.27}{9} = 12 \\text{(cm)}$<br\/>L\u1ea1i c\u00f3: $HN + HP = NP$<br\/>$\\Rightarrow HP = NP - HN = 27 - 12 = 15 \\text{(cm)}$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'> A. $HN = 12cm; HP = 15cm$<\/span>","column":2}]}],"id_ques":1688},{"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/bai15/lv1/img\/H8C3B2_D108.png' \/><\/center><\/span>","select":[" A. $AC = 18cm, AB = 24cm$"," B. $AC = 33cm, AB = 25cm$","C. $AC = 25,2cm, AB = 33,6cm$","D. $AC = 33,6cm, AB = 25,2cm$"],"explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D108.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\/> $\\Rightarrow AB^2 + AC^2 = (DB + DC)^2 = (18 + 24)^2 = 42^2 = 1764$<br\/> $\\triangle ABC$ c\u00f3:<br\/> $AD$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{BAC}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{AB}{AC} = \\dfrac{DB}{DC}$ (\u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c)<br\/>$\\Rightarrow \\dfrac{AB}{AC} = \\dfrac{18}{24} = \\dfrac{3}{4}$<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\/>$\\dfrac{AB^2}{9} = \\dfrac{AC^2}{16} = \\dfrac{AB^2 + AC^2}{9 + 16} = \\dfrac{1764}{25} = 70,56$ <br\/>$\\Rightarrow$ $\\begin{cases}AC^2 = 16.70,56 = 1128,96\\\\ AB^2 = 9. 70,56 = 635,04\\end{cases}$<br\/>$\\Rightarrow$ $\\begin{cases}AC = 33,6 \\text{(cm)} \\\\ AB = 25,2 \\text{(cm)} \\end{cases}$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'> D. $AC = 33,6cm, AB = 25,2cm$<\/span>","column":2}]}],"id_ques":1689},{"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 tam gi\u00e1c $ABC$ vu\u00f4ng c\u00e2n t\u1ea1i $A$, \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c $BD$. T\u00ednh \u0111\u1ed9 d\u00e0i $AD, DC$ bi\u1ebft $AB = 10cm$.<\/span>","select":[" A. $AD = \\dfrac{10}{2 + \\sqrt{2}} \\text{(cm)}, DC = \\dfrac{10 \\sqrt{2}}{2 + \\sqrt{2}} \\text{cm}$"," B. $AD = \\dfrac{1}{1 + \\sqrt{2}} \\text{(cm)}, DC = \\dfrac{\\sqrt{2}}{1 + \\sqrt{2}} \\text{cm}$","C. $AD = \\dfrac{1}{1 + \\sqrt{2}} \\text{(cm)}, DC = \\dfrac{10 \\sqrt{2}}{1 + \\sqrt{2}} \\text{cm}$","D. $AD = \\dfrac{10}{1 + \\sqrt{2}} \\text{(cm)}, DC = \\dfrac{10 \\sqrt{2}}{1 + \\sqrt{2}} \\text{cm}$"],"hint":"S\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c","explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D109.png' \/><\/center><br\/>$\\triangle ABC$ vu\u00f4ng c\u00e2n t\u1ea1i $A$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow$ $\\begin{cases}AB^2 + AC^2 = BC^2 \\text{(\u0111\u1ecbnh l\u00ed py-ta-go)}\\\\ AB = AC = 10 \\text{cm} \\text{(t\u00ednh ch\u1ea5t tam gi\u00e1c c\u00e2n)}\\end{cases}$<br\/>$\\Rightarrow BC^2 = 10^2 + 10^2 = 200$<br\/>$\\Rightarrow BC = 10 \\sqrt{2}$ <br\/> $\\triangle ABC$ c\u00f3:<br\/> $BD$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{ABC}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{AD}{DC} = \\dfrac{AB}{BC}$ (\u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c)<br\/>$\\Rightarrow \\dfrac{AD}{DC} = \\dfrac{10}{10 \\sqrt{2}} = \\dfrac{1}{\\sqrt{2}}$<br\/>$\\Rightarrow \\dfrac{AD}{1} = \\dfrac{DC}{\\sqrt{2}} = \\dfrac{AD + DC}{1 + \\sqrt{2}} = \\dfrac{AC}{1 + \\sqrt{2}} = \\dfrac{10}{1 + \\sqrt{2}}$ (t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau)<br\/> $\\Rightarrow \\begin{cases}AD = \\dfrac{10}{1 + \\sqrt{2}}\\text{(cm)}\\\\ DC = \\dfrac{10 \\sqrt{2}}{1 + \\sqrt{2}} \\text{cm}\\end{cases}$ <br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'> D. $AD = \\dfrac{10}{1 + \\sqrt{2}} \\text{(cm)}, DC = \\dfrac{10 \\sqrt{2}}{1 + \\sqrt{2}} \\text{cm}$<\/span>","column":2}]}],"id_ques":1690},{"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","3"]],"list":[{"point":5,"img":"","ques":"<span class='basic_left'>Cho tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A$, \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c $AD$. Bi\u1ebft $DB = 12cm, DC = 18cm$.<br\/><b>H\u00e3y ch\u1ecdn nh\u1eefng \u0111\u00e1p \u00e1n \u0111\u00fang<\/b><\/span>","hint":"","column":2,"number_true":2,"select":["A. $AC \\approx 25 cm$","B. $AB = 16,6 cm$","C. $\\dfrac{AB}{AC} = \\dfrac{2}{3}$","D. $\\dfrac{AC}{AB} = \\dfrac{DB}{DC}$"],"explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D110.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\/> $\\Rightarrow AB^2 + AC^2 = (DB + DC)^2 = (12 + 18)^2 = 30^2 = 900$<br\/> $\\triangle ABC$ c\u00f3:<br\/> $AD$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{BAC}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{AB}{AC} = \\dfrac{DB}{DC}$ (\u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c)<br\/>$\\Rightarrow \\dfrac{AB}{AC} = \\dfrac{12}{18} = \\dfrac{2}{3}$<br\/> $\\Rightarrow \\dfrac{AB}{2} = \\dfrac{AC}{3 }$<br\/> $\\Rightarrow \\dfrac{AB^2}{4} = \\dfrac{AC^2}{9}$<br\/>\u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ta c\u00f3:<br\/>$\\dfrac{AB^2}{4} = \\dfrac{AC^2}{9} = \\dfrac{AB^2 + AC^2}{4 + 9} = \\dfrac{900}{13} $ <br\/>$\\Rightarrow$ $\\begin{cases}AC^2 = \\dfrac{900. 9}{13} = \\dfrac{8100}{13}\\\\ AB^2 = \\dfrac{900. 4}{13} = \\dfrac{3600}{13}\\end{cases}$<br\/>$\\Rightarrow$ $\\begin{cases}AC \\approx 25 \\text{(cm)} \\\\ AB = 16,6 \\text{(cm)} \\end{cases}$<br\/>V\u1eady nh\u1eefng \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'> A, B v\u00e0 C<\/span><br\/><span class='basic_left'><span class='basic_green'>Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i:<\/span><br\/>+ \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Py-ta-go \u0111\u1ec3 \u0111\u01b0\u1ee3c: $AB^2 + AC^2 = m^2$ ($m$ l\u00e0 h\u1eb1ng s\u1ed1)<br\/>+ S\u1eed d\u1ee5ng t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c trong tam gi\u00e1c l\u00e0m xu\u1ea5t hi\u1ec7n t\u1ec9 l\u1ec7 th\u1ee9c $\\dfrac{AB}{AC} = \\dfrac{a}{b}$ ($a + b = m$, $a, b$ l\u00e0 c\u00e1c h\u1eb1ng s\u1ed1) t\u1eeb \u0111\u00f3 bi\u1ec3n \u0111\u1ed5i \u0111\u1ec3 xu\u1ea5t hi\u1ec7n t\u1ec9 l\u1ec7 th\u1ee9c c\u00f3 d\u1ea1ng $\\dfrac{AB^2}{a^2} = \\dfrac{AC^2}{b^2}$<br\/>+ \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau \u0111\u1ec3 t\u00ednh $AB^2, AC^2$ t\u1eeb \u0111\u00f3 suy ra $AB, AC$.<\/span> <br\/><br\/> "}]}],"id_ques":1691},{"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":[[["3"],["4"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"<span class='basic_left'>Cho h\u00ecnh v\u1ebd sau, bi\u1ebft $AD$ l\u00e0 ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{BAC}$<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D111.png' \/><\/center><br\/><b>T\u1ec9 s\u1ed1 di\u1ec7n t\u00edch $\\triangle ABD$ v\u00e0 $\\triangle ACD$ l\u00e0:<\/b> $\\dfrac{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}$<\/span>","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c \u0111\u1ec3 t\u00ednh t\u1ec9 s\u1ed1 $DB$ v\u00e0 $DC$ <br\/><b>B\u01b0\u1edbc 2:<\/b> T\u1eeb t\u1ec9 s\u1ed1 $DB$ v\u00e0 $DC$ t\u00ecm \u0111\u01b0\u1ee3c t\u1ec9 s\u1ed1 di\u1ec7n t\u00edch $\\triangle{ABD}$ v\u00e0 $\\triangle{ACD}$<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D111.png' \/><\/center><br\/> $\\triangle{ABC}$ c\u00f3:<br\/> $AD$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{BAC}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{DB}{DC} = \\dfrac{AB}{AC}$ (\u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c)<br\/>$\\Rightarrow \\dfrac{DB}{DC} = \\dfrac{3}{4}$<br\/>L\u1ea1i c\u00f3: $\\dfrac{ S_{ \\triangle{ABD}}}{S_{ \\triangle{ACD}}} = \\dfrac{\\dfrac{AH.BD}{2}}{\\dfrac{AH.CD}{2}} = \\dfrac{BD}{CD} = \\dfrac{3}{4}$<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'>3; 4<\/span><br\/><span class='basic_left'><span class='basic_green'>Nh\u1eadn x\u00e9t:<\/span> Hai tam gi\u00e1c c\u00f3 chung \u0111\u01b0\u1eddng cao th\u00ec t\u1ec9 l\u1ec7 hai tam gi\u00e1c \u0111\u00f3 b\u1eb1ng t\u1ec9 l\u1ec7 hai c\u1ea1nh \u0111\u00e1y t\u01b0\u01a1ng \u1ee9ng.<\/span>"}]}],"id_ques":1692},{"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"],["7"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"<span class='basic_left'>Cho h\u00ecnh v\u1ebd sau, bi\u1ebft $DH$ l\u00e0 ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{EDF}$<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D112.png' \/><\/center><br\/>T\u1ec9 s\u1ed1 di\u1ec7n t\u00edch $\\triangle{DEH}$ v\u00e0 $\\triangle{DFH}$ l\u00e0: $\\dfrac{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}$<\/span>","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c \u0111\u1ec3 t\u00ednh t\u1ec9 s\u1ed1 $HE$ v\u00e0 $HF$ <br\/><b>B\u01b0\u1edbc 2:<\/b> T\u1eeb t\u1ec9 s\u1ed1 $HE$ v\u00e0 $HF$ t\u00ecm \u0111\u01b0\u1ee3c t\u1ec9 s\u1ed1 di\u1ec7n t\u00edch $\\triangle{DEH}$ v\u00e0 $\\triangle{DFH}$<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D112.png' \/><\/center><br\/> $\\triangle{DEF}$ c\u00f3:<br\/> $DH$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{EDF}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{HE}{HF} = \\dfrac{DE}{DF}$ (\u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c)<br\/>$\\Rightarrow \\dfrac{HE}{HF} = \\dfrac{4}{7}$<br\/>L\u1ea1i c\u00f3: $\\dfrac{ S_{ \\triangle{DEH}}}{S_{ \\triangle{DHF}}} = \\dfrac{\\dfrac{DK.HE}{2}}{\\dfrac{DK.HF}{2}} = \\dfrac{HE}{HF} = \\dfrac{4}{7}$<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'>4; 7<\/span><br\/><span class='basic_left'><span class='basic_green'>Nh\u1eadn x\u00e9t:<\/span> Hai tam gi\u00e1c c\u00f3 chung \u0111\u01b0\u1eddng cao th\u00ec t\u1ec9 l\u1ec7 di\u1ec7n t\u00edch hai tam gi\u00e1c \u0111\u00f3 b\u1eb1ng t\u1ec9 l\u1ec7 hai c\u1ea1nh \u0111\u00e1y t\u01b0\u01a1ng \u1ee9ng.<\/span>"}]}],"id_ques":1693},{"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 \u0111\u1ed9 d\u00e0i c\u1ea1nh $DM$ trong h\u00ecnh v\u1ebd sau: <br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D113.png' \/><\/center><\/span>","select":[" A. $DM = 8cm$"," B. $DM = 10cm$","$DM = 12cm$","D. $DM = 15cm$"],"explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t d\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c t\u00ecm $\\dfrac{DM}{DP}$<br\/><b>B\u01b0\u1edbc 2:<\/b> Bi\u1ebfn \u0111\u1ed5i $\\dfrac{DM}{DP}$ v\u1ec1 d\u1ea1ng ph\u00e2n s\u1ed1 ch\u1ec9 ch\u1ee9a \u1ea9n l\u00e0 $DM$<br\/><b>B\u01b0\u1edbc 3:<\/b> T\u00ecm $DM$<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D113.png' \/><\/center><br\/>$\\triangle{MNP}$ c\u00f3:<br\/> $ND$ l\u00e0 ph\u00e2n gi\u00e1c ngo\u00e0i c\u1ee7a $\\widehat{MNP}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{NM}{NP} = \\dfrac{DM}{DP}$ (\u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c)<br\/>$\\Rightarrow \\dfrac{DM}{DP} = \\dfrac{6}{9} = \\dfrac{2}{3}$<br\/> $\\Rightarrow \\dfrac{DM}{DM + MP} = \\dfrac{2}{3}$ hay $\\dfrac{DM}{DM + 5} = \\dfrac{2}{3}$<br\/>$\\Rightarrow 3.DM = 2.DM + 10$ $\\Rightarrow DM = 10 \\text{(cm)}$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>$DM = 10cm$<\/span>","column":2}]}],"id_ques":1694},{"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'>T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh $GD$ trong h\u00ecnh v\u1ebd sau: <br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D114.png' \/><\/center><\/span>","select":[" A. $GD=10cm$"," B. $GD= 3cm$","C. $GD \\approx 2,8cm$","D. $GD \\approx 3,5cm$"],"explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t d\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c t\u00ecm $\\dfrac{GD}{GE}$<br\/><b>B\u01b0\u1edbc 2:<\/b> Bi\u1ebfn \u0111\u1ed5i $\\dfrac{GD}{GE}$ v\u1ec1 d\u1ea1ng ph\u00e2n s\u1ed1 ch\u1ec9 ch\u1ee9a \u1ea9n l\u00e0 $GD$<br\/><b>B\u01b0\u1edbc 3:<\/b> T\u00ecm $GD$<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D114.png' \/><\/center><br\/>$\\triangle{DEF}$ c\u00f3:<br\/> $FG$ l\u00e0 ph\u00e2n gi\u00e1c ngo\u00e0i c\u1ee7a $\\widehat{EFD}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{FD}{FE} = \\dfrac{GD}{GE}$ (\u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c)<br\/>$\\Rightarrow \\dfrac{GD}{GE} = \\dfrac{5}{7} $<br\/> $\\Rightarrow \\dfrac{GD}{GD + DE} = \\dfrac{5}{7}$ hay $\\dfrac{GD}{GD + 4} = \\dfrac{5}{7}$<br\/>$\\Rightarrow 7.GD = 5.GD + 20$ $\\Rightarrow 2.GD = 20 \\Rightarrow GD =10\\, cm$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>A. $GD=10cm$<\/span>","column":2}]}],"id_ques":1695},{"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, bi\u1ebft $BD$ l\u00e0 ph\u00e2n gi\u00e1c $\\widehat{ABC}$. T\u1eeb $B$ k\u1ebb $BH \\perp AC$ t\u1ea1i $H$.<br\/>So s\u00e1nh: $\\dfrac{S_{\\triangle{ABD}}}{S_{\\triangle{CBD}}}$ v\u00e0 $\\dfrac{AD}{DC}$<br\/> <b>\u0110\u00e1p \u00e1n:<\/b> $\\dfrac{S_{\\triangle{ABD}}}{S_{\\triangle{CBD}}}$ _input_ $\\dfrac{AD}{DC}$<\/span>","hint":"","explain":"<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/bai15/lv1/img\/H8C3B2_D115.png' \/><\/center><br\/> Ta c\u00f3:<br\/> $\\dfrac{ S_{ \\triangle{ABD}}}{S_{ \\triangle{CBD}}} = \\dfrac{\\dfrac{BH.AD}{2}}{\\dfrac{BH.DC}{2}} = \\dfrac{AD}{DC} $<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> Hai tam gi\u00e1c c\u00f3 chung \u0111\u01b0\u1eddng cao th\u00ec t\u1ec9 l\u1ec7 hai tam gi\u00e1c \u0111\u00f3 b\u1eb1ng t\u1ec9 l\u1ec7 hai c\u1ea1nh \u0111\u00e1y t\u01b0\u01a1ng \u1ee9ng.<\/span>"}]}],"id_ques":1696},{"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/bai15/lv1/img\/H8C3B2_D116.png' \/><\/center><br\/>T\u00ednh $\\dfrac{NM}{NP}$<\/span>","select":[" A. $\\dfrac{NM}{NP} = \\dfrac{4}{3}$"," B. $\\dfrac{NM}{NP} = \\dfrac{4}{7}$","C. $\\dfrac{NM}{NP} = \\dfrac{3}{7}$","D. $\\dfrac{NM}{NP} = \\dfrac{3}{4}$"],"hint":"S\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u1ea7n gi\u00e1c c\u1ee7a tam gi\u00e1c.","explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D116.png' \/><\/center><br\/> $\\triangle MNP$ c\u00f3:<br\/> $NK$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{MNP}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{NM}{NP} = \\dfrac{KM}{KP}$ (\u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c)<br\/>$\\Rightarrow \\dfrac{NM}{NP} = \\dfrac{3}{4}$ <br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'> D. $\\dfrac{NM}{NP} = \\dfrac{3}{4}$<\/span>","column":2}]}],"id_ques":1697},{"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 $x$, $y$ trong h\u00ecnh v\u1ebd sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D118_1.jpg' \/><\/center><br\/><\/span>","select":[" A. $x = 6; y = 9cm$"," B. $x = 5cm; y = 10cm$","C. $x = 5,625cm; y = 9,375cm$","D. $x = 5,65cm; y = 9,35cm$"],"hint":"S\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u1ea7n gi\u00e1c c\u1ee7a tam gi\u00e1c.","explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D118.png' \/><\/center><br\/> $\\triangle ABC$ c\u00f3:<br\/> $AD$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{BAC}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{AB}{AC} = \\dfrac{DB}{DC}$ (\u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c)<br\/>$\\Rightarrow \\dfrac{6}{10} = \\dfrac{x}{y}$<br\/> $\\Rightarrow \\dfrac{x}{6} = \\dfrac{y}{10}$<br\/>\u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ta c\u00f3:<br\/>$\\dfrac{x}{6} = \\dfrac{y}{10} = \\dfrac{x + y}{6 + 10} = \\dfrac{15}{16}$<br\/>$\\Rightarrow \\begin{cases} x = \\dfrac{6.15}{16} = 5,625 \\text{(cm)} \\\\ y = \\dfrac{10.15}{16} = 9,375 \\text{(cm)} \\end{cases}$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'> C. $x = 5,625cm; y = 9,375cm$<\/span>","column":2}]}],"id_ques":1698},{"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'>T\u00ednh $x$, $y$ trong h\u00ecnh v\u1ebd sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D119.png' \/><\/center><br\/><\/span>","select":[" A. $x = 8cm; y = 12cm$"," B. $x = 12cm; y = 8cm$","C. $x = 6cm; y = 14cm$","D. $x = 9cm; y = 11cm$"],"hint":"S\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u1ea7n gi\u00e1c c\u1ee7a tam gi\u00e1c.","explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv1/img\/H8C3B2_D119.png' \/><\/center><br\/> $\\triangle DEF$ c\u00f3:<br\/> $DH$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{EDF}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{DE}{DF} = \\dfrac{HE}{HF}$ (\u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c)<br\/>$\\Rightarrow \\dfrac{12}{18} = \\dfrac{x}{y}$<br\/> $\\Rightarrow \\dfrac{x}{12} = \\dfrac{y}{18}$<br\/>\u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ta c\u00f3:<br\/>$\\dfrac{x}{12} = \\dfrac{y}{18} = \\dfrac{x + y}{12 + 18} = \\dfrac{20}{30}$<br\/>$\\Rightarrow \\begin{cases} x = \\dfrac{12.20}{30} = 8 \\text{(cm)} \\\\ y = \\dfrac{18.20}{30} = 12 \\text{(cm)} \\end{cases}$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'> A. $x = 8cm; y = 12cm$<\/span>","column":2}]}],"id_ques":1699}],"lesson":{"save":0,"level":1}}