{"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":10,"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/lv3/img\/H8C3B2_K101.png' \/><\/center><br\/><\/span>","select":[" A. $x \\approx 13,3cm; y = 7,5cm$"," B. $x = 7cm; y = 13cm$","C. $x = 6cm; y = 10cm$","D. $x = 8cm; y = 12cm$"],"hint":"S\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00ed Te-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/bai15/lv3/img\/H8C3B2_K101.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\/>$\\Rightarrow \\dfrac{3}{5} = \\dfrac{4,5}{y}$ $\\Rightarrow y = \\dfrac{4,5.5}{3} = 7,5 \\text{(cm)}$ <br\/>$\\triangle ABC$ c\u00f3: $BH$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{ABC}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{BA}{BC} = \\dfrac{HA}{HC}$ (\u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c)<br\/>$\\Rightarrow \\dfrac{3 + 5}{x} = \\dfrac{4,5}{7,5}$ $\\Rightarrow \\dfrac{8}{x} = \\dfrac{4,5}{7,5}$ $\\Rightarrow x = \\dfrac{8.7,5}{4,5} \\approx 13,3 \\text{(cm)}$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'> A. $x \\approx 13,3cm; y = 7,5cm$<\/span>","column":2}]}],"id_ques":1700},{"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":[[["13,3"]]],"list":[{"point":10,"width":50,"content":"","type_input":"","ques":"<span class='basic_left'>Cho tam gi\u00e1c $ABC$ c\u00f3 $AB = 20cm$, $AC = 40cm$, $BC = 54cm$. \u0110\u01b0\u1eddng ph\u00e2n gi\u00e1c g\u00f3c $A$ c\u1eaft $BC$ t\u1ea1i $D$. Qua $D$ k\u1ebb $DE \/\/ AB$ ($E \\in AC$). T\u00ednh \u0111\u1ed9 d\u00e0i $DE$ (l\u00e0m tr\u00f2n \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 nh\u1ea5t)<br\/> <b>\u0110\u00e1p \u00e1n:<\/b> $DE$ = _input_<\/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 t\u00ednh $DB, DC$<br\/><b>B\u01b0\u1edbc 2:<\/b> \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Ta-l\u00e9t \u0111\u1ec3 t\u00ednh $DE$.<\/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/bai15/lv3/img\/H8C3B2_K102.png' \/><\/center><br\/>$\\triangle ABC$ c\u00f3: $AD$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{BAC}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{AB}{AC} = \\dfrac{DB}{DC}$ (\u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c)<br\/>$\\Rightarrow \\dfrac{20}{40} = \\dfrac{DB}{DC}$ $\\Rightarrow \\dfrac{DB}{20} = \\dfrac{DC}{40}$<br\/>\u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3:<br\/> $\\dfrac{DB}{20} = \\dfrac{DC}{40} = \\dfrac{DB + DC}{20 + 40} = \\dfrac{54}{60} = \\dfrac{9}{10}$<br\/> $\\Rightarrow \\begin{cases} DB = \\dfrac{20.9}{10} = 18 \\text{(cm)} \\\\ DC = \\dfrac{40.9}{10} = 36 \\text{(cm)} \\end{cases}$<br\/>X\u00e9t $\\triangle ABC$ c\u00f3: $DE \/\/ AB$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{DE}{AB} = \\dfrac{DC}{BC}$ (\u0111\u1ecbnh l\u00ed Ta-l\u00e9t)<br\/> Hay $\\dfrac{DE}{20} = \\dfrac{36}{54}$ $\\Rightarrow DE = \\dfrac{36 . 20}{54} = 13,3 \\text{(cm)}$<br\/>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 <span class='basic_pink'>13,3<\/span> <\/span>"}]}],"id_ques":1701},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":" <span class='basic_left'>Cho tam gi\u00e1c $ABC$ c\u00e2n t\u1ea1i $A$, bi\u1ebft $AB = AC = b$, $BC = a$. \u0110\u01b0\u1eddng ph\u00e2n gi\u00e1c g\u00f3c $B$ c\u1eaft $AN$ t\u1ea1i $N$, \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $C$ c\u1eaft $AB$ t\u1ea1i $M$. \u0110\u1ed9 d\u00e0i $MN$ \u0111\u01b0\u1ee3c t\u00ednh theo c\u00f4ng th\u1ee9c n\u00e0o d\u01b0\u1edbi \u0111\u00e2y?<\/span>","select":[" A. $MN = \\dfrac{a + b}{a.b}$"," B. $MN = \\dfrac{b - a}{a.b}$","C. $MN = \\dfrac{a.b}{a + b}$","D. $MN = \\dfrac{a.b}{b - a}$"],"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 $\\dfrac{AM}{BM} = \\dfrac{AN}{CN}$<br\/><b>B\u01b0\u1edbc 2:<\/b> Ch\u1ee9ng minh $MN \/\/ BC$<br\/><b>B\u01b0\u1edbc 3:<\/b> T\u1eeb b\u01b0\u1edbc 2 \u00e1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Ta-l\u00e9t t\u00ecm c\u00f4ng th\u1ee9c li\u00ean h\u1ec7 $MN$ v\u00e0 $AN$<br\/><b>B\u01b0\u1edbc 4:<\/b> T\u00ednh $AN$<br\/><b>B\u01b0\u1edbc 5:<\/b> T\u00ednh $MN$.<\/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/bai15/lv3/img\/H8C3B2_K103.png' \/><\/center><br\/>$\\triangle ABC$ c\u00f3: $BN, CM$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{ABC}$ v\u00e0 $\\widehat{ACB}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\begin{cases} \\dfrac{AM}{BM} = \\dfrac{AC}{BC} = \\dfrac{b}{a} \\\\ \\dfrac{AN}{CN} = \\dfrac{AB}{BC} = \\dfrac{b}{a} \\end{cases}$ (\u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c trong tam gi\u00e1c)<br\/>$\\Rightarrow \\dfrac{AM}{BM} = \\dfrac{AN}{CN}$<br\/>$\\Rightarrow MN \/\/ BC$ (\u0111\u1ecbnh l\u00ed Ta-l\u00e9t \u0111\u1ea3o)<br\/>X\u00e9t $\\triangle ABC$ c\u00f3: $MN \/\/ BC$ (ch\u1ee9ng minh tr\u00ean) <br\/>$\\Rightarrow \\dfrac{MN}{BC} = \\dfrac{AN}{AC}$ (\u0111\u1ecbnh l\u00ed Ta-l\u00e9t)<br\/>Hay $\\dfrac{MN}{a} = \\dfrac{AN}{b}$ <b>(1)<\/b><br\/>L\u1ea1i c\u00f3: $\\dfrac{AN}{CN} = \\dfrac{b}{a}$ (ch\u1ee9ng minh tr\u00ean)<br\/>$\\Rightarrow \\dfrac{AN}{AN + CN} = \\dfrac{b}{b + a}$ hay $\\dfrac{AN}{b} = \\dfrac{AN + CN}{b + a} = \\dfrac{AC}{b + a} = \\dfrac{b}{b + a}$<br\/>$\\Rightarrow AN = \\dfrac{b^2}{b + a}$<br\/>Thay $AN$ v\u00e0o (1) ta \u0111\u01b0\u1ee3c:<br\/>$\\dfrac{MN}{a} = \\dfrac{\\dfrac{b^2}{b + a}}{b}$ $\\Rightarrow MN = \\dfrac{a.b}{a + b}$ <br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'> C. $MN = \\dfrac{a.b}{a + b}$<\/span>","column":2}]}],"id_ques":1702},{"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":[[["16"],["20"],["24"]]],"list":[{"point":10,"width":50,"content":"","type_input":"","ques":"<span class='basic_left'>Cho tam gi\u00e1c $ABC$, c\u00e1c \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c $BD$, $CE$. Bi\u1ebft $\\dfrac{AD}{DC} = \\dfrac{2}{3}$, $\\dfrac{AE}{EB} = \\dfrac{5}{6}$. T\u00ednh \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh $AB$, $AC$, $BC$, bi\u1ebft chu vi tam gi\u00e1c $ABC$ b\u1eb1ng $60cm$.<br\/> <b>\u0110\u00e1p \u00e1n:<\/b> $AB$ = _input_ ($cm$); $AC$ = _input_ ($cm$); $BC$ = _input_ ($cm$)<\/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/lv3/img\/H8C3B2_K104.png' \/><\/center><br\/>$\\triangle ABC$ c\u00f3: $BD$ v\u00e0 $CE$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{ABC}$ v\u00e0 $\\widehat{ACB}$(gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\begin{cases}\\dfrac{AC}{BC} = \\dfrac{AE}{EB} = \\dfrac{5}{6} \\\\ \\dfrac{AB}{BC} = \\dfrac{AD}{DC} = \\dfrac{2}{3} \\end{cases}$ (\u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c)<br\/>$\\Rightarrow \\begin{cases}\\dfrac{AC}{5} = \\dfrac{BC}{6} \\\\ \\dfrac{AB}{2} = \\dfrac{BC}{3} \\Rightarrow \\dfrac{AB}{4} = \\dfrac{BC}{6} \\end{cases}$ <br\/>$\\Rightarrow \\dfrac{AB}{4} = \\dfrac{AC}{5} = \\dfrac{BC}{6}$<br\/>\u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3:<br\/>$\\dfrac{AB}{4} = \\dfrac{AC}{5} = \\dfrac{BC}{6} = \\dfrac{AB + AC + BC}{4 + 5 + 6} = \\dfrac{60}{15} = 4$<br\/>Do \u0111\u00f3<br\/>$AC = 4.5 = 20 \\text{cm}$ <br\/>$AB = 4.4 = 16 \\text{cm}$<br\/>$BC = 4.6 = 24 \\text{cm}$<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'>16; 20; 24<\/span> <br\/> <span class='basic_left'><span class='basic_green'>Nh\u1eadn x\u00e9t:<\/span> \u0110\u1ed1i v\u1edbi d\u1ea1ng b\u00e0i cho bi\u1ebft c\u00e1c \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c v\u00e0 c\u00e1c t\u1ec9 s\u1ed1 \u0111\u1ed9 d\u00e0i hai \u0111o\u1ea1n th\u1eb3ng ta \u0111i l\u1eadp c\u00e1c \u0111o\u1ea1n th\u1eb3ng t\u1ec9 l\u1ec7 t\u1eeb t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c \u0111\u1ec3 gi\u1ea3i.<\/span>"}]}],"id_ques":1703},{"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":[[["21"],["28"]]],"list":[{"point":10,"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. T\u00ecm $x$, $y$.<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv3/img\/H8C3B2_K105.png' \/><\/center><br\/> <b>\u0110\u00e1p \u00e1n:<\/b> $x$ = _input_ ($cm$); $y$ = _input_ ($cm$)<\/span> ","hint":"","explain":"<span class='basic_left'><span class='basic_green'>T\u00ecm h\u01b0\u1edbng gi\u1ea3i<\/span><br\/>Ph\u00e2n t\u00edch \u0111\u1ec1 b\u00e0i ta th\u1ea5y:<br\/>+ \u0110\u1ec1 b\u00e0i cho tam gi\u00e1c vu\u00f4ng v\u00e0 y\u00eau c\u1ea7u t\u00ednh \u0111\u1ed9 d\u00e0i n\u00ean ta ngh\u0129 ngay \u0111\u1ebfn vi\u1ec7c s\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00ed Py-ta-go<br\/>+ \u0110\u1ec1 b\u00e0i cho \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c v\u00e0 y\u00eau c\u1ea7u t\u00ednh \u0111\u1ed9 d\u00e0i n\u00ean ta s\u1eed d\u1ee5ng ki\u1ebfn th\u1ee9c t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c<br\/>T\u1eeb \u0111\u00f3 ta v\u1eadn d\u1ee5ng linh ho\u1ea1t 2 ki\u1ebfn th\u1ee9c tr\u00ean \u0111\u1ec3 gi\u1ea3i b\u00e0i to\u00e1n<\/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/bai15/lv3/img\/H8C3B2_K105.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\/>Hay $x^2 + y^2 = (15 + 20)^2 = 1225$<br\/>$\\triangle DEF$ c\u00f3: $DH$ 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\/>$\\Rightarrow \\dfrac{x}{y} = \\dfrac{15}{20} = \\dfrac{3}{4}$ <br\/>$\\Rightarrow \\dfrac{x}{3} = \\dfrac{y}{4} \\Rightarrow \\dfrac{x^2}{9} = \\dfrac{y^2}{16}$<br\/>\u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3:<br\/>$\\dfrac{x^2}{9} = \\dfrac{y^2}{16} = \\dfrac{x^2 + y^2}{9 + 16} = \\dfrac{1225}{25} = 49$<br\/>Do \u0111\u00f3<br\/>$x^2 = 49. 9 = 441 \\Rightarrow x = 21 \\text{(cm)}$ <br\/>$y^2 = 49. 16 = 784 \\Rightarrow y = 28 \\text{(cm)} $<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'>21; 28<\/span> "}]}],"id_ques":1704},{"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":[[["18"],["29,25"]]],"list":[{"point":10,"width":50,"content":"","type_input":"","ques":"<span class='basic_left'>Cho h\u00ecnh v\u1ebd sau, bi\u1ebft $BD$ l\u00e0 ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{ABC}$ v\u00e0 $DE \/\/ BC$. T\u00ecm $x$, $y$ (l\u00e0m trong \u0111\u1ebfn s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 hai).<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv3/img\/H8C3B2_K107.png' \/><\/center><br\/> <b>\u0110\u00e1p \u00e1n:<\/b> $x$ = _input_ ($cm$); $y$ = _input_ ($cm$)<\/span> ","hint":"","explain":"<span class='basic_left'><span class='basic_green'>T\u00ecm h\u01b0\u1edbng gi\u1ea3i<\/span><br\/>Ph\u00e2n t\u00edch \u0111\u1ec1 b\u00e0i ta th\u1ea5y:<br\/>+ \u0110\u1ec1 b\u00e0i cho $DE \/\/ BC$ v\u00e0 y\u00eau c\u1ea7u t\u00ednh \u0111\u1ed9 d\u00e0i n\u00ean ta ngh\u0129 ngay \u0111\u1ebfn vi\u1ec7c s\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00ed Ta-l\u00e9t<br\/>+ \u0110\u1ec1 b\u00e0i cho \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c v\u00e0 y\u00eau c\u1ea7u t\u00ednh \u0111\u1ed9 d\u00e0i n\u00ean ta s\u1eed d\u1ee5ng ki\u1ebfn th\u1ee9c t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c<br\/>T\u1eeb \u0111\u00f3 ta v\u1eadn d\u1ee5ng linh ho\u1ea1t 2 ki\u1ebfn th\u1ee9c tr\u00ean \u0111\u1ec3 gi\u1ea3i b\u00e0i to\u00e1n<\/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/bai15/lv3/img\/H8C3B2_K107.png' \/><\/center><br\/>$\\triangle ABC$ c\u00f3: $DE \/\/ BC$ (gi\u1ea3 thi\u1ebft)<br\/> $\\Rightarrow \\dfrac{EA}{EB} = \\dfrac{DA}{DC}$ (\u0111\u1ecbnh l\u00ed Ta-l\u00e9t)<br\/>$\\Rightarrow \\dfrac{4}{9} = \\dfrac{8}{x}$ $\\Rightarrow x = \\dfrac{8.9}{4} = 18 \\text{(cm)}$ <br\/>$\\triangle ABC$ c\u00f3: $BD$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{ABC}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{BA}{BC} = \\dfrac{DA}{DC}$ (\u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c)<br\/>$\\Rightarrow \\dfrac{4 + 9}{y} = \\dfrac{8}{18} =$ hay $\\dfrac{13}{y} = \\dfrac{8}{18}$<br\/>$ \\Rightarrow y = \\dfrac{13.18}{8} = 29,25 \\text{(cm)}$ <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'>18; 29,25<\/span> "}]}],"id_ques":1705},{"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"],["15"]]],"list":[{"point":10,"width":50,"content":"","type_input":"","ques":"<span class='basic_left'>Cho h\u00ecnh v\u1ebd sau, bi\u1ebft $NK$ l\u00e0 ph\u00e2n gi\u00e1c $\\widehat{MNP}$. T\u00ecm $x$, $y$.<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv3/img\/H8C3B2_K106.png' \/><\/center><br\/> <b>\u0110\u00e1p \u00e1n:<\/b> $x$ = _input_ ($cm$); $y$ = _input_ ($cm$)<\/span> ","hint":"","explain":"<span class='basic_left'><span class='basic_green'>T\u00ecm h\u01b0\u1edbng gi\u1ea3i<\/span><br\/>Ph\u00e2n t\u00edch \u0111\u1ec1 b\u00e0i ta th\u1ea5y:<br\/>+ \u0110\u1ec1 b\u00e0i cho tam gi\u00e1c vu\u00f4ng v\u00e0 y\u00eau c\u1ea7u t\u00ednh \u0111\u1ed9 d\u00e0i n\u00ean ta ngh\u0129 ngay \u0111\u1ebfn vi\u1ec7c s\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00ed Py-ta-go<br\/>+ \u0110\u1ec1 b\u00e0i cho \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c v\u00e0 y\u00eau c\u1ea7u t\u00ednh \u0111\u1ed9 d\u00e0i n\u00ean ta s\u1eed d\u1ee5ng ki\u1ebfn th\u1ee9c t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c<br\/>T\u1eeb \u0111\u00f3 ta v\u1eadn d\u1ee5ng linh ho\u1ea1t 2 ki\u1ebfn th\u1ee9c tr\u00ean \u0111\u1ec3 gi\u1ea3i b\u00e0i to\u00e1n<\/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/bai15/lv3/img\/H8C3B2_K106.png' \/><\/center><br\/>$\\triangle MNP$ vu\u00f4ng t\u1ea1i $M$ (gi\u1ea3 thi\u1ebft)<br\/> $\\Rightarrow MN^2 + MP^2 = NP^2$ (\u0111\u1ecbnh l\u00ed Py-ta-go)<br\/>$\\Rightarrow NP^2 - MN^2 = MP^2$ hay $y^2 - x^2 = (4 + 5)^2 = 81$<br\/>$\\triangle MNP$ c\u00f3: $NK$ 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{x}{y} = \\dfrac{4}{5} $ <br\/>$\\Rightarrow \\dfrac{x}{4} = \\dfrac{y}{5}$<br\/>$ \\Rightarrow \\dfrac{x^2}{16} = \\dfrac{y^2}{25}$<br\/>\u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3:<br\/>$\\dfrac{x^2}{16} = \\dfrac{y^2}{25} = \\dfrac{y^2 - x^2}{25 - 16} = \\dfrac{81}{9} = 9$<br\/>$\\Rightarrow \\dfrac{x}{4} = \\dfrac{y}{5} = 3$<br\/>$\\Rightarrow$ $x = 3.4 = 12cm$; $y = 3.5 = 15cm$<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'>12; 15<\/span> "}]}],"id_ques":1706},{"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":10,"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/lv3/img\/H8C3B2_K108.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 Py-ta-go t\u00ednh $AC$<br\/><b>B\u01b0\u1edbc 2:<\/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 3:<\/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/lv3/img\/H8C3B2_K108.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\/>$\\Rightarrow AC^2 = BC^2 - AB^2 = 5^2 - 3^2 = 16$<br\/>$\\Rightarrow AC = 4 \\text{(cm)}$ <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":1707},{"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","3","4"]],"list":[{"point":10,"img":"","ques":"<span class='basic_left'>Cho tam gi\u00e1c $ABC$ c\u00e2n t\u1ea1i $A$, K\u1ebb c\u00e1c \u0111\u01b0\u1eddng cao $BD$, $CE$. Qua $C$ k\u1ebb \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi c\u1ea1nh $AC$, \u0111\u01b0\u1eddng n\u00e0y c\u1eaft \u0111\u01b0\u1eddng th\u1eb3ng $AB$ t\u1ea1i \u0111i\u1ec3m $F$.<br\/><b>H\u00e3y ch\u1ecdn nh\u1eefng \u0111\u00e1p \u00e1n \u0111\u00fang<\/b><\/span>","hint":"K\u1ebft h\u1ee3p s\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00ed Ta-l\u00e9t v\u00e0 \u0111\u1ecbnh l\u00ed t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c \u0111\u1ec3 gi\u1ea3i.","column":2,"number_true":2,"select":["A. $AB^2 = AE.AF$","B. $AC^2 < AE.AF$","C. $\\dfrac{AD}{AC} = \\dfrac{AB}{AF}$","D. $\\dfrac{CE}{CF} = \\dfrac{BE}{BF}$"],"explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv3/img\/H8C3B2_K109.png' \/><\/center><br\/> Ta c\u00f3:<br\/>$\\left.\\begin{array}{l} BD \\bot AC \\text{(gi\u1ea3 thi\u1ebft)}\\\\ CF \\bot AC \\text{(gi\u1ea3 thi\u1ebft)} \\end{array} \\right\\}$ $\\Rightarrow BD \/\/ CF$ (t\u1eeb vu\u00f4ng g\u00f3c \u0111\u1ebfn song song)<br\/>$\\Rightarrow \\widehat{B_1} = \\widehat{C_2}$ (c\u1eb7p g\u00f3c so le trong) <br\/> $\\triangle ACF$ c\u00f3: $BD \/\/ CF$ (ch\u1ee9ng minh tr\u00ean)<br\/> $\\Rightarrow \\dfrac{AD}{AC} = \\dfrac{AB}{AF}$ (\u0111\u1ecbnh l\u00ed Ta-l\u00e9t) <b>(1)<\/b><br\/>L\u1ea1i c\u00f3: <br\/>$\\triangle ABC$ c\u00e2n t\u1ea1i $A$ (gi\u1ea3 thi\u1ebft)<br\/> $\\Rightarrow \\begin{cases}AB = AC \\text{(t\u00ednh ch\u1ea5t tam gi\u00e1c c\u00e2n)} \\\\ \\widehat{ABC} = \\widehat{ACB} \\text{(\u0111\u1ecbnh ngh\u0129a tam gi\u00e1c c\u00e2n)} \\end{cases}$ <b>(2)<\/b><br\/> X\u00e9t tam gi\u00e1c vu\u00f4ng $ABD$ v\u00e0 tam gi\u00e1c vu\u00f4ng $ACE$ c\u00f3:<br\/>+ $\\widehat{A}$ chung<br\/>+ $AB = AC$ (ch\u1ee9ng minh tr\u00ean)<br\/>$\\Rightarrow \\triangle ABD = \\triangle ACE$ (c\u1ea1nh huy\u1ec1n - g\u00f3c nh\u1ecdn)<br\/>$\\Rightarrow AD = AE$ (c\u1eb7p c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) <b>(3)<\/b><br\/>T\u1eeb (1),(2) v\u00e0 (3) $\\Rightarrow AB^2 = AE.AF$ <br\/> X\u00e9t X\u00e9t tam gi\u00e1c vu\u00f4ng $BEC$ v\u00e0 tam gi\u00e1c vu\u00f4ng $BDC$ c\u00f3:<br\/>+ $\\widehat{ABC} = \\widehat{ACB}$ (ch\u1ee9ng minh tr\u00ean)<br\/>+ $BC$ chung<br\/>$\\Rightarrow \\triangle BEC = \\triangle BDC$ (c\u1ea1nh huy\u1ec1n-g\u00f3c nh\u1ecdn)<br\/>$\\Rightarrow \\widehat{B_1} = \\widehat{C_1} $ (c\u1eb7p g\u00f3c t\u01b0\u01a1ng \u1ee9ng)<br\/>L\u1ea1i c\u00f3: $\\widehat{B_1} = \\widehat{C_2}$ (ch\u1ee9ng minh tr\u00ean)<br\/>$\\Rightarrow \\widehat{C_1} = \\widehat{C_2} $<br\/>$\\Rightarrow$ $CB$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{CEF}$ <br\/>$\\Rightarrow \\dfrac{CE}{CF} = \\dfrac{BE}{BF}$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c) <br\/>V\u1eady nh\u1eefng \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'> A, C v\u00e0 D<\/span> "}]}],"id_ques":1708},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":" <span class='basic_left'>Tam gi\u00e1c $ABC$ c\u00f3 $AB = 6cm, AC = 15cm, BC = 14cm$. \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. $DB = 2cm; DC = 12cm$"," B. $DB = 3cm; DC = 11cm$","C. $DB = 4cm; DC = 10cm$","D. $DB = 5cm; DC = 9cm$"],"explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai15/lv3/img\/H8C3B2_K110.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\/>$\\Rightarrow \\dfrac{DB}{DC} = \\dfrac{6}{15} = \\dfrac{2}{5}$<br\/> $\\Rightarrow \\dfrac{DB}{2} = \\dfrac{DC}{5}$ <br\/>Apd d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3:<br\/>$\\dfrac{DB}{2} = \\dfrac{DC}{5} = \\dfrac{DB + DC}{2 + 5} = \\dfrac{14}{7} = 2$ <br\/> $\\Rightarrow \\begin{cases}DB = 2.2 = 4 \\text{(cm)} \\\\ DC = 2.5 = 10 \\text{(cm)} \\end{cases}<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'> C. $DB = 4cm; DC = 10cm$<\/span>","column":2}]}],"id_ques":1709}],"lesson":{"save":0,"level":3}}