Bài tập cơ bản bài Các trường hợp đồng dạng của hai tam giác

Home Lớp 8 Toán lớp 8 Các trường hợp đồng dạng của hai tam giác Bài tập cơ bản

{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t \u0111i\u1ec1n v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" N\u1ebfu m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft hai c\u1ea1nh c\u1ee7a tam gi\u00e1c v\u00e0 song song v\u1edbi c\u1ea1nh c\u00f2n l\u1ea1i th\u00ec n\u00f3 t\u1ea1o th\u00e0nh m\u1ed9t tam gi\u00e1c m\u1edbi ............... v\u1edbi tam gi\u00e1c \u0111\u00e3 cho.<\/span>","select":[" A. \u0110\u1ed3ng d\u1ea1ng"," B. B\u1eb1ng"],"hint":"","explain":"\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0: A. \u0110\u1ed3ng d\u1ea1ng<\/span><\/span>","column":2}]}],"id_ques":1710},{"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":" N\u1ebfu ba c\u1ea1nh c\u1ee7a tam gi\u00e1c n\u00e0y l\u1ea7n l\u01b0\u1ee3t t\u1ec9 l\u1ec7 v\u1edbi ba c\u1ea1nh c\u1ee7a tam gi\u00e1c kia th\u00ec hai tam gi\u00e1c \u0111\u00f3 \u0111\u1ed3ng d\u1ea1ng. \u0110\u00fang<\/b> hay Sai<\/b>?<\/span>","select":[" A. \u0110\u00fang"," B. Sai"],"hint":"","explain":"\u0110\u00e1p \u00e1n l\u00e0: A. \u0110\u00fang<\/span><\/span>","column":2}]}],"id_ques":1711},{"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 hai tam gi\u00e1c c\u00f3 \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh l\u1ea7n l\u01b0\u1ee3t l\u00e0: 4cm; 6cm; 8cm v\u00e0 8cm; 12cm; 16cm. Hai tam gi\u00e1c \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":"Ta c\u00f3:<br\/> $\\dfrac{4}{8} = \\dfrac{6}{12} = \\dfrac{8}{16} = \\dfrac{1}{2}$<br\/>N\u00ean hai tam gi\u00e1c \u0111\u00f3 c\u00f3 \u0111\u1ed3ng d\u1ea1ng v\u1edbi nhau<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: A. C\u00f3 \u0111\u1ed3ng d\u1ea1ng<\/span><\/span><\/span>","column":2}]}],"id_ques":1712},{"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 hai tam gi\u00e1c c\u00f3 \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh l\u1ea7n l\u01b0\u1ee3t l\u00e0: 3cm; 5cm; 7cm v\u00e0 6cm; 10cm; 21cm. Hai tam gi\u00e1c \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":"Ta c\u00f3:<br\/> $\\dfrac{3}{6} = \\dfrac{5}{10} = \\dfrac{1}{2} $<br\/>$ \\dfrac{7}{21} = \\dfrac{1}{3}$<br\/>V\u00ec $\\dfrac{1}{2} \\neq \\dfrac{1}{3}$ $\\Rightarrow \\dfrac{3}{6} = \\dfrac{5}{10} \\neq \\dfrac{7}{21}$<br\/>N\u00ean hai tam gi\u00e1c \u0111\u00f3 kh\u00f4ng \u0111\u1ed3ng d\u1ea1ng v\u1edbi nhau<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: B. Kh\u00f4ng \u0111\u1ed3ng d\u1ea1ng<\/span><\/span><\/span>","column":2}]}],"id_ques":1713},{"time":24,"part":[{"title":"Ch\u1ecdn 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":" Cho tam gi\u00e1c $ABC$ v\u00e0 \u0111i\u1ec3m $O$ n\u1eb1m trong tam gi\u00e1c $ABC$. G\u1ecdi $M, N, P$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $OA, OB, OC$. Bi\u1ebft chu vi tam gi\u00e1c $ABC$ b\u1eb1ng $15cm$. <br\/>H\u00e3y ch\u1ecdn nh\u1eefng \u0111\u00e1p \u00e1n \u0111\u00fang<\/b><\/span><br\/>","hint":"","column":1,"number_true":2,"select":["A. $\\triangle{ABC} \\backsim \\triangle{MNP} $","B. Chu vi $\\triangle{MNP}$ $= 7,5 cm$","C. T\u1ec9 s\u1ed1 \u0111\u1ed3ng d\u1ea1ng c\u1ee7a $\\triangle{ABC}$ v\u00e0 $\\triangle{MNP}$ l\u00e0 2","D. $ \\dfrac{MN}{AB} = \\dfrac{NP}{BC} = \\dfrac{MP}{AC}$"],"explain":"B\u00e0i gi\u1ea3i:<\/span><br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai16/lv1/img\/H8C3B3_D101.png' \/><\/center><br\/> $\\triangle{OAB}$ c\u00f3:<br\/> $M, N$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $OA,OB$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow MN$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a $\\triangle{OAB}$<br\/>$\\Rightarrow MN = \\dfrac{1}{2}AB$ hay $\\dfrac{MN}{AB} = \\dfrac{1}{2}$<br\/>T\u01b0\u01a1ng t\u1ef1 ta ch\u1ee9ng minh \u0111\u01b0\u1ee3c: $\\dfrac{NP}{BC} = \\dfrac{1}{2}$ ; $\\dfrac{MP}{AC} = \\dfrac{1}{2}$<br\/>$\\Rightarrow \\dfrac{MN}{AB} = \\dfrac{NP}{BC} = \\dfrac{MP}{AC} = \\dfrac{1}{2}$<br\/>$\\Rightarrow $ $\\triangle{ABC} \\backsim \\triangle{MNP} $ v\u00e0 h\u1ec7 s\u1ed1 t\u1ec9 l\u1ec7 l\u00e0 $\\dfrac{1}{2}$<br\/>L\u1ea1i c\u00f3: $ \\dfrac{MN}{AB} = \\dfrac{NP}{BC} = \\dfrac{MP}{AC} = \\dfrac{1}{2} = \\dfrac{MN + NP + MP }{AB + BC + AC} = \\dfrac{ C_{\\triangle_{MNP}}}{C_{\\triangle_{ABC}}}$<br\/>$\\Rightarrow C_{\\triangle_{MNP}} = \\dfrac{ C_{\\triangle_{ABC}}}{2} = \\dfrac{15}{2} = 7,5 \\text{(cm)}$<br\/>V\u1eady nh\u1eefng \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A, B, D<\/span> "}]}],"id_ques":1714},{"time":24,"part":[{"title":"Ch\u1ecdn 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":5,"img":"","ques":" Cho tam gi\u00e1c $ABC$ v\u00e0 \u0111i\u1ec3m $O$ n\u1eb1m trong tam gi\u00e1c $ABC$. G\u1ecdi $M, N, P$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $OA, OB, OC$. Bi\u1ebft chu vi tam gi\u00e1c $ABC$ b\u1eb1ng $20cm$. <br\/>H\u00e3y ch\u1ecdn nh\u1eefng \u0111\u00e1p \u00e1n \u0111\u00fang<\/b><\/span><br\/>","hint":"","column":2,"number_true":2,"select":["A. $\\triangle{ABC} \\backsim \\triangle{MNP} $","B. $C_{\\triangle{MNP}}$ $= 40cm$","C. $C_{\\triangle{MNP}} = \\dfrac{ C_{\\triangle{ABC}}}{2}$","D. $ \\dfrac{MN}{AB} = \\dfrac{NP}{BC} = \\dfrac{MP}{AC}$"],"explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai16/lv1/img\/H8C3B3_D101.png' \/><\/center><br\/> X\u00e9t $\\triangle{OAB}$ c\u00f3:<br\/> $M, N$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $OA,OB$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow MN$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a $\\triangle{OAB}$<br\/>$\\Rightarrow MN = \\dfrac{1}{2}AB$ hay $\\dfrac{MN}{AB} = \\dfrac{1}{2}$<br\/>T\u01b0\u01a1ng t\u1ef1 ta ch\u1ee9ng minh \u0111\u01b0\u1ee3c: $\\dfrac{NP}{BC} = \\dfrac{1}{2}$ ; $\\dfrac{MP}{AC} = \\dfrac{1}{2}$<br\/>$\\Rightarrow \\dfrac{MN}{AB} = \\dfrac{NP}{BC} = \\dfrac{MP}{AC} = \\dfrac{1}{2}$<br\/>$\\Rightarrow $ $\\triangle{ABC} \\backsim \\triangle{MNP} $ (c\u1ea1nh - c\u1ea1nh -c\u1ea1nh) v\u00e0 h\u1ec7 s\u1ed1 t\u1ec9 l\u1ec7 l\u00e0 $\\dfrac{1}{2}$<br\/>L\u1ea1i c\u00f3: $ \\dfrac{MN}{AB} = \\dfrac{NP}{BC} = \\dfrac{MP}{AC} = \\dfrac{1}{2} = \\dfrac{MN + NP + MP }{AB + BC + AC} = \\dfrac{ C_{\\triangle_{MNP}}}{C_{\\triangle_{ABC}}}$ (t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau)<br\/>$\\Rightarrow C_{\\triangle{MNP}} = \\dfrac{ C_{\\triangle{ABC}}}{2} = \\dfrac{20}{2} = 10 \\text{(cm)}$<br\/>V\u1eady nh\u1eefng \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A, C, D<\/span><br\/> "}]}],"id_ques":1715},{"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"],["18"],["24"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"Bi\u1ebft $\\triangle{ABC} \\backsim \\triangle{A'B'C'}$ v\u00e0 \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh $\\triangle{ABC}$ l\u00e0 $AB = 4cm$; $AC = 6cm$; $BC = 8cm$. 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 $54cm$. <br\/>\u0110\u00e1p \u00e1n:<\/b> $A'B'$ = _input_ ($cm$); $A'C'$ = _input_ ($cm$); $B'C'$ = _input_ ($cm$)<\/span>","hint":"","explain":"H\u01b0\u1edbng d\u1eabn:<\/span><br\/>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\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\/>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 $\\dfrac{A'B'}{4} = \\dfrac{B'C'}{8} = \\dfrac{A'C'}{6}$<br\/>\u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3:<br\/> $\\dfrac{A'B'}{4} = \\dfrac{B'C'}{8} = \\dfrac{A'C'}{6} = \\dfrac{A'B' + B'C' + A'C'}{4 + 8 + 6} = \\dfrac{54}{18} = 3$<br\/>Do \u0111\u00f3<br\/>$A'B' = 3.4 = 12$ ($cm$)<br\/>$A'C' = 3.6 = 18$ ($cm$)<br\/>$B'C' = 3.8 = 24$ ($cm$)<br\/>V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0: 12; 18; 24<\/span>"}]}],"id_ques":1716},{"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":[[["32"],["28"],["20"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"Bi\u1ebft $\\triangle{ABC} \\backsim \\triangle{MNP}$ v\u00e0 \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh $\\triangle{MNP}$ l\u00e0 $MN = 8cm$; $MP = 7cm$; $NP = 5cm$. T\u00ednh \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh $\\triangle{ABC}$ bi\u1ebft chu vi tam gi\u00e1c $ABC$ b\u1eb1ng $80cm$. <br\/>\u0110\u00e1p \u00e1n:<\/b> $AB$ = _input_ ($cm$); $AC$ = _input_ ($cm$); $BC$ = _input_ ($cm$)<\/span>","hint":"","explain":"H\u01b0\u1edbng d\u1eabn:<\/span><br\/>B\u01b0\u1edbc 1:<\/b> T\u1eeb $\\triangle{ABC} \\backsim \\triangle{MNP} $ t\u00ecm t\u1ec9 s\u1ed1 \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh c\u1ee7a hai tam gi\u00e1c<br\/>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 $AB, AC, BC$<\/span><br\/>B\u00e0i gi\u1ea3i:<\/span><br\/>$\\triangle{ABC} \\backsim \\triangle{MNP} $ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow \\dfrac{AB}{MN} = \\dfrac{AC}{MP} = \\dfrac{BC}{NP}$ hay $\\dfrac{AB}{8} = \\dfrac{AC}{7} = \\dfrac{BC}{5}$<br\/>\u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3:<br\/> $\\dfrac{AB}{8} = \\dfrac{AC}{7} = \\dfrac{BC}{5} = \\dfrac{AB + AC + BC}{8 + 7 + 5} = \\dfrac{80}{20} = 4$<br\/>Do \u0111\u00f3<br\/>$AB = 4.8 = 32$ ($cm$)<br\/>$AC = 4.7 = 28$ ($cm$)<br\/>$BC = 4.5 = 20$ ($cm$)<br\/>V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0: 32; 28; 20<\/span>"}]}],"id_ques":1717},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":" Cho tam gi\u00e1c $ABC$ c\u00f3 $AB = 6cm, AC = 12cm$. \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. $AD = 2cm$"," B. $AD = 2,5cm$","C. $AD = 3cm$","D. $AD = 4cm$"],"hint":"","explain":"H\u01b0\u1edbng d\u1eabn:<\/span><br\/>B\u01b0\u1edbc 1:<\/b> Ch\u1ee9ng minh $\\triangle{ABD} \\backsim \\triangle{ACB}$<br\/>B\u01b0\u1edbc 2:<\/b> T\u1eeb b\u01b0\u1edbc 2 suy ra c\u00e1c c\u1eb7p \u0111o\u1ea1n th\u1eb3ng t\u1ec9 l\u1ec7<br\/>B\u01b0\u1edbc 3:<\/b> T\u00ednh $AD$<\/span> <br\/>B\u00e0i gi\u1ea3i:<\/span><br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai16/lv1/img\/H8C3B3_D102.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\/>$\\Rightarrow \\dfrac{AD}{6} = \\dfrac{6}{12}$<br\/>$\\Rightarrow AD = \\dfrac{6.6}{12} = 3 \\text{(cm)}$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C. $AD = 3cm$<\/span><\/span> <br\/><\/span><br\/>","column":2}]}],"id_ques":1718},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["="]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":" Cho h\u00ecnh ch\u1eef nh\u1eadt $ABCD$, tr\u00ean c\u1ea1nh $AB$ l\u1ea5y \u0111i\u1ec3m $E$. Tia $DE$ c\u1eaft tia $CB$ \u1edf $G$, c\u1eaft $AC$ \u1edf $F$. So s\u00e1nh $FD^2$ v\u00e0 $FE.FG$<br\/>\u0110\u00e1p \u00e1n:<\/b> $FD^2$ _input_ $FE.FG$<\/span>","hint":"","explain":"H\u01b0\u1edbng d\u1eabn:<\/span><br\/>B\u01b0\u1edbc 1:<\/b> Ch\u1ee9ng minh $\\triangle{AEF} \\backsim \\triangle{CDF}$ t\u1eeb \u0111\u00f3 suy ra c\u00e1c \u0111o\u1ea1n th\u1eb3ng t\u1ec9 l\u1ec7<br\/>B\u01b0\u1edbc 2:<\/b> Ch\u1ee9ng minh $\\triangle{AFD} \\backsim \\triangle{CFG}$ t\u1eeb \u0111\u00f3 suy ra c\u00e1c \u0111o\u1ea1n th\u1eb3ng t\u1ec9 l\u1ec7<br\/>B\u01b0\u1edbc 3:<\/b> K\u1ebft h\u1ee3p b\u01b0\u1edbc 1 v\u00e0 b\u01b0\u1edbc 2 \u0111\u1ec3 t\u00ecm ra k\u1ebft qu\u1ea3<\/span><br\/>B\u00e0i gi\u1ea3i:<\/span><br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai16/lv1/img\/H8C3B3_D103.png' \/><\/center><br\/>$ABCD$ l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow AB \/\/ DC; AD \/\/ BC$ (t\u00ednh ch\u1ea5t h\u00ecnh ch\u1eef nh\u1eadt)<br\/>V\u00ec $AB \/\/ DC$ (ch\u1ee9ng minh tr\u00ean)<br\/>$\\Rightarrow$ $\\widehat{DCA} = \\widehat{CAB} $ (c\u1eb7p g\u00f3c so le trong)<br\/>V\u00ec $AD \/\/ BC$ (ch\u1ee9ng minh tr\u00ean)<br\/> $\\Rightarrow \\widehat{ADF} = \\widehat{FGC}$ (c\u1eb7p g\u00f3c so le trong)<br\/>X\u00e9t $\\triangle{AEF}$ v\u00e0 $\\triangle{CDF}$ c\u00f3:<br\/>$\\widehat{DCA} = \\widehat{CAB}$ (ch\u1ee9ng minh tr\u00ean)<br\/>$\\widehat{DFC} = \\widehat{AFE}$ (c\u1eb7p g\u00f3c \u0111\u1ed1i \u0111\u1ec9nh)<br\/> $\\Rightarrow$ $\\triangle{AEF} \\backsim \\triangle{CDF}$ (g-g)<br\/>$\\Rightarrow \\dfrac{FE}{FD} = \\dfrac{AF}{CF}$ (1)<\/b><br\/>X\u00e9t $\\triangle{AFD}$ v\u00e0 $\\triangle{CFG}$ c\u00f3:<br\/>$\\widehat{ADF} = \\widehat{FGC}$ (ch\u1ee9ng minh tr\u00ean)<br\/>$\\widehat{DFA} = \\widehat{CFG}$ (c\u1eb7p g\u00f3c \u0111\u1ed1i \u0111\u1ec9nh)<br\/>$\\Rightarrow \\triangle{AFD} \\backsim \\triangle{CFG}$ (g-g)<br\/>$\\Rightarrow \\dfrac{FD}{FG} = \\dfrac{AF}{CF}$ (2)<\/b><br\/>T\u1eeb (1) v\u00e0 (2) $\\Rightarrow \\dfrac{FE}{FD} = \\dfrac{FD}{FG}$<br\/>$\\Rightarrow FD^2 = FE.FG$ <br\/>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 \"=\"<\/span>"}]}],"id_ques":1719},{"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"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":" Cho h\u00ecnh v\u1ebd nh\u01b0 sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai16/lv1/img\/H8C3B3_D104.png' \/><\/center><br\/>T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh $DE$ <br\/>\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":"H\u01b0\u1edbng d\u1eabn:<\/span><br\/>B\u01b0\u1edbc 1:<\/b> Ch\u1ee9ng minh $\\triangle{ADE} \\backsim \\triangle{ACB}$ t\u1eeb \u0111\u00f3 suy ra c\u00e1c \u0111o\u1ea1n th\u1eb3ng t\u1ec9 l\u1ec7<br\/>B\u01b0\u1edbc 2:<\/b> T\u1eeb b\u01b0\u1edbc 1 suy ra \u0111\u1ed9 d\u00e0i c\u1ea1nh $DE$<\/span><br\/>B\u00e0i gi\u1ea3i:<\/span><br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai16/lv1/img\/H8C3B3_D104.png' \/><\/center><br\/>X\u00e9t $\\triangle{ADE}$ v\u00e0 $\\triangle{ACB}$ c\u00f3:<br\/>$\\widehat{A}$ chung<br\/>$\\dfrac{AE}{AB} = \\dfrac{AD}{AC}$ (v\u00ec $\\dfrac{5}{10} = \\dfrac{6}{12}$)<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) <br\/>$\\Rightarrow DE = \\dfrac{AD.BC}{AC} = \\dfrac{6.8}{12} = 4 \\text{(cm)}$ <br\/>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 4<\/span>"}]}],"id_ques":1720},{"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":[[["6,6"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":" Cho h\u00ecnh v\u1ebd nh\u01b0 sau: <center><img src=\"https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai16/lv1/img\/H8C3B3_D105_.png\" \/><\/center><br\/>T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh $BC$ (k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 nh\u1ea5t)<br\/>\u0110\u00e1p \u00e1n:<\/b> $BC =$ _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":"H\u01b0\u1edbng d\u1eabn:<\/span><br\/>B\u01b0\u1edbc 1:<\/b> Ch\u1ee9ng minh $\\triangle{OAB} \\backsim \\triangle{OBC}$ t\u1eeb \u0111\u00f3 suy ra c\u00e1c c\u1eb7p c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng t\u1ec9 l\u1ec7<br\/>B\u01b0\u1edbc 2:<\/b> T\u1eeb b\u01b0\u1edbc 1 suy ra \u0111\u1ed9 d\u00e0i c\u1ea1nh $BC$<\/span><br\/>B\u00e0i gi\u1ea3i:<\/span><br\/> <center><img src=\"https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai16/lv1/img\/H8C3B3_D105_.png\" \/><\/center><br\/>X\u00e9t $\\triangle{OAB}$ v\u00e0 $\\triangle{OBC}$ c\u00f3:<br\/>$\\widehat{AOB} = \\widehat{BOC}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\dfrac{OA}{OB} = \\dfrac{OB}{OC}$ (v\u00ec $\\dfrac{6}{9} = \\dfrac{9}{13.5}$)<br\/> $\\Rightarrow$ $\\triangle{OAB} \\backsim \\triangle{OBC}$ (c\u1ea1nh-g\u00f3c-c\u1ea1nh)<br\/>$\\Rightarrow \\dfrac{OA}{OB} = \\dfrac{AB}{BC}$ (c\u1eb7p c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) <br\/>$\\Rightarrow BC = \\dfrac{OB. AB}{OA} = \\dfrac{9.4,4}{6} = 6,6 \\text{(cm)}$ <br\/>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 6,6<\/span>"}]}],"id_ques":1721},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["EFD"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":" Cho h\u00ecnh v\u1ebd nh\u01b0 sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai16/lv1/img\/H8C3B3_D106.png' \/><\/center><br\/>Tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng v\u1edbi tam gi\u00e1c $ABC$ l\u00e0 tam gi\u00e1c n\u00e0o?<br\/>\u0110\u00e1p \u00e1n:<\/b> $\\triangle{ABC} \\backsim $ $\\triangle$ _input_<br\/>(L\u01b0u \u00fd: Vi\u1ebft \u0111\u00fang th\u1ee9 t\u1ef1 c\u00e1c \u0111\u1ec9nh) <\/span>","hint":"","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai16/lv1/img\/H8C3B3_D106.png' \/><\/center><br\/>X\u00e9t $\\triangle{ABC}$ v\u00e0 $\\triangle{EFD}$ c\u00f3:<br\/>$\\widehat{BAC} = \\widehat{FED}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\dfrac{AB}{EF} = \\dfrac{AC}{ED}$ (v\u00ec $\\dfrac{4}{2} = \\dfrac{6}{3}$)<br\/> $\\Rightarrow$ $\\triangle{ABC} \\backsim \\triangle{EFD}$ (c\u1ea1nh-g\u00f3c-c\u1ea1nh)<br\/>V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $EFD$<\/span> "}]}],"id_ques":1722},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["PIK"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":" Cho h\u00ecnh v\u1ebd nh\u01b0 sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai16/lv1/img\/H8C3B3_D107.png' \/><\/center><br\/>Tam gi\u00e1c $DEF$ \u0111\u1ed3ng d\u1ea1ng v\u1edbi tam gi\u00e1c n\u00e0o?<br\/>\u0110\u00e1p \u00e1n:<\/b> $\\triangle{DEF} \\backsim $ $\\triangle$ _input_<br\/>(L\u01b0u \u00fd: Vi\u1ebft \u0111\u00fang th\u1ee9 t\u1ef1 c\u00e1c \u0111\u1ec9nh) <\/span>","hint":"","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai16/lv1/img\/H8C3B3_D107.png' \/><\/center><br\/>X\u00e9t $\\triangle{DEF}$ v\u00e0 $\\triangle{PIK}$ c\u00f3:<br\/>$\\widehat{EDF} = \\widehat{IPK}$ ($=60^o$)<br\/>$\\widehat{DEF} = \\widehat{PIK}$ ($=45^o$)<br\/> $\\Rightarrow$ $\\triangle{DEF} \\backsim \\triangle{PIK}$ (g\u00f3c - g\u00f3c)<br\/>V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $PIK$<\/span> "}]}],"id_ques":1723},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" Cho tam gi\u00e1c $ABC$ c\u00f3 $AB = 8cm, AC = 10cm$. Tr\u00ean c\u1ea1nh $AB$ v\u00e0 $AC$ l\u1ea7n l\u01b0\u1ee3t l\u1ea5y \u0111i\u1ec3m $D$, $E$ sao cho $AD = 5cm$, $AE = 4cm$. Tam gi\u00e1c $ABC$ v\u00e0 tam gi\u00e1c $AED$ c\u00f3 \u0111\u1ed3ng d\u1ea1ng v\u1edbi nhau kh\u00f4ng?<br\/><\/span>","select":[" A. C\u00f3"," B. Kh\u00f4ng"],"hint":"S\u1eed d\u1ee5ng tr\u01b0\u1eddng h\u1ee3p \u0111\u1ed3ng d\u1ea1ng th\u1ee9 hai: C\u1ea1nh - g\u00f3c-c\u1ea1nh.","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai16/lv1/img\/H8C3B3_D108.png' \/><\/center><br\/>X\u00e9t $\\triangle{ABC}$ v\u00e0 $\\triangle{AED}$ c\u00f3:<br\/>$\\widehat{A}$ chung<br\/>$\\dfrac{AB}{AE} = \\dfrac{AC}{AD}$ (v\u00ec $\\dfrac{8}{4} = \\dfrac{10}{5}$) <br\/>$\\Rightarrow$ $\\triangle{ABC} \\backsim \\triangle{AED}$ (c\u1ea1nh-g\u00f3c-c\u1ea1nh)<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. C\u00f3<\/span><\/span><br\/>","column":2}]}],"id_ques":1724},{"time":24,"part":[{"title":"Ch\u1ecdn 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":" T\u1ee9 gi\u00e1c $ABCD$ c\u00f3 $AB = 4cm$, $BC = 12cm, CD = 16cm, AD = 6cm$, \u0111\u01b0\u1eddng ch\u00e9o $BD = 8cm$. <br\/>H\u00e3y ch\u1ecdn nh\u1eefng \u0111\u00e1p \u00e1n \u0111\u00fang<\/b><\/span><br\/>","hint":"","column":1,"number_true":2,"select":["A. $\\triangle{ABD} \\backsim \\triangle{BDC} $","B. $AB \/\/ CD$","C. $ABCD$ l\u00e0 h\u00ecnh thang","D. $ \\dfrac{AB}{BD} = \\dfrac{AD}{DC} = \\dfrac{BD}{BC}$"],"explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai16/lv1/img\/H8C3B3_D109.png' \/><\/center><br\/> X\u00e9t $\\triangle{ABD}$ v\u00e0 $\\triangle{BDC}$ c\u00f3:<br\/> $ \\dfrac{AB}{BD} = \\dfrac{BD}{DC} = \\dfrac{AD}{BC} $ (v\u00ec $ \\dfrac{4}{8} = \\dfrac{8}{16} = \\dfrac{6}{12} $) (\u0111\u00e1p \u00e1n D sai)<\/b><br\/>$\\Rightarrow$ $\\triangle{ABD} \\backsim \\triangle{BDC}$ (c\u1ea1nh-c\u1ea1nh-c\u1ea1nh) (\u0111\u00e1p \u00e1n A \u0111\u00fang)<\/b><br\/>$\\Rightarrow$ $\\widehat{ABD} = \\widehat{BDC}$ (c\u1eb7p g\u00f3c t\u01b0\u01a1ng \u1ee9ng)<br\/>$\\Rightarrow$ $AB \/\/ CD$ (c\u1eb7p g\u00f3c so le trong b\u1eb1ng nhau) (\u0111\u00e1p \u00e1n B \u0111\u00fang)<\/b><br\/>$\\Rightarrow$ $ABCD$ l\u00e0 h\u00ecnh thang (\u0111\u1ecbnh ngh\u0129a) (\u0111\u00e1p \u00e1n C \u0111\u00fang)<\/b><br\/>V\u1eady nh\u1eefng \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A, B, C<\/span> "}]}],"id_ques":1725},{"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 nh\u01b0 sau:<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai16/lv1/img\/H8C3B3_D110.png' \/><\/center> Tam gi\u00e1c $MNP$ v\u00e0 tam gi\u00e1c $FDE$ c\u00f3 \u0111\u1ed3ng d\u1ea1ng v\u1edbi nhau kh\u00f4ng?<br\/><\/span>","select":[" A. C\u00f3"," B. Kh\u00f4ng"],"hint":"T\u00ednh $\\widehat{F}$.","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai16/lv1/img\/H8C3B3_D110.png' \/><\/center><br\/>$\\triangle{DEF}$ c\u00f3: $\\widehat{F} + \\widehat{E} + \\widehat{D} = 180^o$ (\u0111\u1ecbnh l\u00ed t\u1ed5ng ba g\u00f3c trong tam gi\u00e1c)<br\/>$\\Rightarrow$ $\\widehat{F} = 180^o - (\\widehat{E} + \\widehat{D}) = 180^o - (70^o + 50^o) = 60^o$<br\/> X\u00e9t $\\triangle{MNP}$ v\u00e0 $\\triangle{FDE}$ c\u00f3:<br\/>$\\widehat{M} = \\widehat{F}$ ($=60^o$)<br\/>$\\widehat{N} = \\widehat{D}$ ($=50^o$) <br\/>$\\Rightarrow$ $\\triangle{MNP} \\backsim \\triangle{FDE}$ (g\u00f3c - g\u00f3c)<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. C\u00f3<\/span><\/span><br\/>","column":2}]}],"id_ques":1726},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["2,67"],["3,33"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":" Cho h\u00ecnh v\u1ebd nh\u01b0 sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai16/lv1/img\/H8C3B3_D111.png' \/><\/center><br\/>Bi\u1ebft $AB = 4cm; AC = 6cm$, $\\widehat{ABD} = \\widehat{ACB}$. T\u00ednh $AD, DC$ (l\u00e0m tr\u00f2n \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 hai)<br\/>\u0110\u00e1p \u00e1n:<\/b> $AD \\approx$ _input_ ($cm$); $DC \\approx $ _input_ ($cm$)<\/span>","hint":"","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai16/lv1/img\/H8C3B3_D111.png' \/><\/center><br\/>X\u00e9t $\\triangle{ABD}$ v\u00e0 $\\triangle{ACB}$ c\u00f3:<br\/>$\\widehat{ABD} = \\widehat{ACB}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\widehat{A} $ chung<br\/> $\\Rightarrow$ $\\triangle{ABD} \\backsim \\triangle{ACB}$ (g\u00f3c - g\u00f3c)<br\/>$\\Rightarrow \\dfrac{AB}{AC} = \\dfrac{AD}{AB} $ (c\u1eb7p c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng t\u1ec9 l\u1ec7)<br\/>$\\Rightarrow \\dfrac{4}{6} = \\dfrac{AD}{4} $ <br\/>$\\Rightarrow AD = \\dfrac{4.4}{6} \\approx 2,67 \\text{(cm)} $<br\/>L\u1ea1i c\u00f3: $AD + DC = AC$<br\/>$\\Rightarrow DC = AC - AD \\approx 6 - 2,67 \\approx 3,33 \\text{(cm)}$<br\/>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 $2,67; 3,33$<\/span> "}]}],"id_ques":1727},{"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":[[["2,5"],["6"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":" T\u00ednh c\u00e1c \u0111\u1ed9 d\u00e0i $x, y$ c\u1ee7a c\u00e1c \u0111o\u1ea1n th\u1eb3ng trong h\u00ecnh sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai16/lv1/img\/H8C3B3_D112.png' \/><\/center><br\/>\u0110\u00e1p \u00e1n:<\/b> $x =$ _input_ ($cm$); $y = $ _input_ ($cm$)<\/span>","hint":"","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai16/lv1/img\/H8C3B3_D112.png' \/><\/center><br\/>X\u00e9t $\\triangle{ABC}$ v\u00e0 $\\triangle{EDC}$ c\u00f3:<br\/>$\\widehat{ABC} = \\widehat{CDE}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\widehat{ACB} = \\widehat{BCD}$ (c\u1eb7p g\u00f3c \u0111\u1ed1i \u0111\u1ec9nh)<br\/> $\\Rightarrow$ $\\triangle{ABC} \\backsim \\triangle{EDC}$ (g\u00f3c - g\u00f3c)<br\/>$\\Rightarrow \\dfrac{AB}{ED} = \\dfrac{AC}{EC} = \\dfrac{BC}{DC} $ (c\u1eb7p c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng t\u1ec9 l\u1ec7)<br\/>$\\Rightarrow \\dfrac{4}{8} = \\dfrac{3}{y} = \\dfrac{x}{5} $ <br\/>$\\Rightarrow \\begin{cases}x = \\dfrac{4.5}{8} = 2,5 \\text{(cm)} \\\\ y = \\dfrac{3.8}{4} = 6 \\text{(cm)} \\end{cases}$ <br\/>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 $2,5; 6$<\/span> "}]}],"id_ques":1728},{"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 t\u1ee9 gi\u00e1c $ABCD$ c\u00f3 $\\widehat{BAC} = \\widehat{CAD}$, $\\widehat{ABC} = \\widehat{ACD}$. Hai tia $AD$ v\u00e0 $BC$ c\u1eaft nhau t\u1ea1i $H$. So s\u00e1nh $AB.DH$ v\u00e0 $BC.CH$.<br\/><\/span>","select":[" A. $AB.DH > BC.CH$"," B. $AB.DH = BC.CH$","C. $AB.DH < BC.CH$"],"hint":"","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai16/lv1/img\/H8C3B3_D113.png' \/><\/center><br\/>$\\triangle{ABC}$ c\u00f3:<br\/>$\\widehat{BAC} + \\widehat{CBA} = \\widehat{HCA}$ (g\u00f3c ngo\u00e0i tam gi\u00e1c)<br\/>M\u00e0 $\\widehat{ABC} = \\widehat{ACD}$ (gi\u1ea3 thi\u1ebft) ; $ \\widehat{HCA} = \\widehat{ACD} + \\widehat{HCD}$<br\/>$\\Rightarrow$ $\\widehat{HCD} = \\widehat{BAC}$ <br\/>L\u1ea1i c\u00f3: $\\widehat{BAC} = \\widehat{CAD}$<br\/>$\\Rightarrow$ $\\widehat{HCD} = \\widehat{CAD}$ hay $\\widehat{HCD} = \\widehat{CAH}$ <br\/> X\u00e9t $\\triangle{CDH}$ v\u00e0 $\\triangle{ACH}$ c\u00f3:<br\/>$\\widehat{HCD} = \\widehat{CAH}$ (ch\u1ee9ng minh tr\u00ean)<br\/>$\\widehat{H}$ chung <br\/>$\\Rightarrow$ $\\triangle{CDH} \\backsim \\triangle{ACH}$ (g\u00f3c - g\u00f3c)<br\/>$\\Rightarrow$ $\\dfrac{CH}{AH} = \\dfrac{DH}{CH}$ (c\u1eb7p c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng t\u1ec9 l\u1ec7)<br\/>$\\Rightarrow$ $\\dfrac{CH}{DH} = \\dfrac{AH}{CH}$ (1)<\/b><br\/>$\\triangle{ABH}$ c\u00f3: $AC$ l\u00e0 \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow$ $ \\dfrac{AH}{AB} = \\dfrac{CH}{BC}$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c trong tam gi\u00e1c) <br\/>$\\Rightarrow$ $ \\dfrac{AH}{CH} = \\dfrac{AB}{BC}$ (2)<\/b><br\/>T\u1eeb (1) v\u00e0 (2) $\\Rightarrow$ $ \\dfrac{AB}{BC} = \\dfrac{CH}{DH}$ $\\Rightarrow$ $AB.DH = BC.CH$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. $AB.DH = BC.CH$<\/span><br\/>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\/><\/span>","column":1}]}],"id_ques":1729}],"lesson":{"save":0,"level":1}}

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Câu hỏi này theo dạng chọn đáp án đúng, sau khi đọc xong câu hỏi, bạn bấm vào một trong số các đáp án mà chương trình đưa ra bên dưới, sau đó bấm vào nút gửi để kiểm tra đáp án và sẵn sàng chuyển sang câu hỏi kế tiếp

Trả lời đúng trong khoảng thời gian quy định bạn sẽ được + số điểm như sau:
Trong khoảng 1 phút đầu tiên	+ 5 điểm
Trong khoảng 1 phút -> 2 phút	+ 4 điểm
Trong khoảng 2 phút -> 3 phút	+ 3 điểm
Trong khoảng 3 phút -> 4 phút	+ 2 điểm
Trong khoảng 4 phút -> 5 phút	+ 1 điểm

Quá 5 phút: không được cộng điểm

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