Bài tập cơ bản bài Định lí Ta - lét trong tam giác. Định lí đảo và hệ quả của định lí Ta

Home Lớp 8 Toán lớp 8 Định lí Ta - lét trong tam giác. Định lí đảo và hệ quả của định lí Ta - lét Bài tập cơ bản

{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0110\u00fang ho\u1eb7c Sai","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" T\u1ec9 s\u1ed1 c\u1ee7a hai \u0111o\u1ea1n th\u1eb3ng l\u00e0 t\u1ec9 s\u1ed1 \u0111\u1ed9 d\u00e0i c\u1ee7a ch\u00fang theo c\u00f9ng m\u1ed9t \u0111\u01a1n v\u1ecb. \u0110\u00fang<\/b> hay Sai<\/b>? ","select":[" A. \u0110\u00fang"," B. Sai"],"explain":" \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0: A. \u0110\u00fang<\/span>","column":2}]}],"id_ques":1651},{"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 $\\triangle ABC$. Tr\u00ean c\u1ea1nh $AB$, $AC$ l\u1ea7n l\u01b0\u1ee3t l\u1ea5y \u0111i\u1ec3m $D$ v\u00e0 $E$ sao cho $DE \/\/ BC$. Qua $C$ k\u1ebb \u0111\u01b0\u1eddng th\u1eb3ng song song v\u1edbi $EB$, c\u1eaft $AB$ \u1edf $F$. So s\u00e1nh $AB^2$ v\u00e0 $AD.AF$ <br\/> \u0110\u00e1p \u00e1n:<\/b> $AB^2$ _input_ $AD.AF$<\/span>","hint":"S\u1eed d\u1ee5ng h\u1ec7 qu\u1ea3 c\u1ee7a \u0111\u1ecbnh l\u00ed Ta-l\u00e9t \u1ee9ng v\u1edbi $\\triangle ABC$ v\u00e0 $\\triangle AFC$","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai14/lv1/img\/H8C3B1_D115.png' \/><\/center> <br\/> X\u00e9t $\\triangle ABC$ c\u00f3: <br\/> $DE \/\/ BC$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow \\dfrac{AD}{AB} = \\dfrac{AE}{AC}$ (\u0111\u1ecbnh l\u00fd Ta-l\u00e9t) (1)<\/b> <br\/> X\u00e9t $\\triangle AFC$ c\u00f3: <br\/> $EB \/\/ CF$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow \\dfrac{AB}{AF} = \\dfrac{AE}{AC}$ (\u0111\u1ecbnh l\u00fd Ta-l\u00e9t) (2)<\/b> <br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow \\dfrac{AD}{AB} = \\dfrac{AB}{AF}$ <br\/> $\\Rightarrow AB.AB = AD.AF$ hay $AB^2 = AD.AF$ <br\/> V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 \"=\"<\/span><\/span>"}]}],"id_ques":1652},{"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\u00ecm \u0111\u1ed9 d\u00e0i $x$ trong h\u00ecnh sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai14/lv1/img\/H8C3_B101.png' \/><\/center> ","select":[" A. $5cm$ "," B. $2,25cm$","C. $16cm$","D. $4cm$"],"explain":" H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> S\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00fd Ta-l\u00e9t<\/span> <br\/> B\u00e0i gi\u1ea3i:<\/span> <br\/> V\u00ec $EH \/\/ BC$, theo \u0111\u1ecbnh l\u00ed Ta-l\u00e9t ta c\u00f3: <br\/> $\\dfrac{AE}{EB}=\\dfrac{AH}{HC}$ hay $\\dfrac{6}{3}=\\dfrac{8}{x}$ <br\/> $\\Rightarrow x =\\dfrac{3.8}{6}=4 \\text{cm}$ <br\/> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 D. $4cm$<\/span><\/span> <br\/> <br\/> <\/span>","column":2}]}],"id_ques":1653},{"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":" T\u00ecm \u0111\u1ed9 d\u00e0i c\u1ea1nh $BC$ trong h\u00ecnh sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai14/lv1/img\/H8C3_B102.png' \/><\/center> ","select":[" A. $5$ "," B. $8$","C. $12,8$","D. $20$"],"explain":" H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> S\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00fd Ta-l\u00e9t<\/span> <br\/> B\u00e0i gi\u1ea3i:<\/span> <br\/> Ta c\u00f3: <br\/> $MN \\bot AB$ (gt) <br\/> $AC \\bot AB$ (gt) <br\/> $\\Rightarrow MN \/\/ AC$ (\u0111\u1ecbnh l\u00fd t\u1eeb vu\u00f4ng g\u00f3c \u0111\u1ebfn song song) <br\/> V\u00ec $MN \/\/ AC$, theo \u0111\u1ecbnh l\u00fd Ta-l\u00e9t ta c\u00f3: <br\/> $\\dfrac{BM}{BA}=\\dfrac{BN}{BC}$ hay $\\dfrac{5}{5+3}=\\dfrac{8}{BC}$ <br\/> $\\Rightarrow BC=\\dfrac{8.(5+3)}{5}=\\dfrac{64}{5}=12,8$ <br\/> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C. $12,8$<\/span><\/span> <br\/> <br\/> <\/span>","column":2}]}],"id_ques":1654},{"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":" T\u1ec9 s\u1ed1 c\u1ee7a hai \u0111o\u1ea1n th\u1eb3ng ph\u1ee5 thu\u1ed9c v\u00e0o c\u00e1ch ch\u1ecdn \u0111\u01a1n v\u1ecb \u0111o. \u0110\u00fang<\/b> hay sai<\/b>? ","select":[" A. \u0110\u00fang "," B. Sai"],"explain":" Theo ch\u00fa \u00fd t\u1ec9 s\u1ed1 c\u1ee7a hai \u0111o\u1ea1n th\u1eb3ng ta c\u00f3: <br\/> T\u1ec9 s\u1ed1 c\u1ee7a hai \u0111o\u1ea1n th\u1eb3ng kh\u00f4ng<\/b> ph\u1ee5 thu\u1ed9c v\u00e0o c\u00e1ch ch\u1ecdn \u0111\u01a1n v\u1ecb \u0111o <br\/> V\u1eady ta ch\u1ecdn \u0111\u00e1p \u00e1n: B. Sai<\/span>","column":2}]}],"id_ques":1655},{"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: $AB = 120cm$; $CD = 80cm$ ","select":[" A. $ \\dfrac{AB}{CD}=\\dfrac{120}{80}=\\dfrac{3}{2}$ "," B. $\\dfrac{AB}{CD}=\\dfrac{80}{120}=\\dfrac{2}{3}$"],"explain":" T\u1ec9 s\u1ed1 c\u1ee7a hai \u0111o\u1ea1n th\u1eb3ng $AB$ v\u00e0 $CD$ l\u00e0: <br\/> $\\dfrac{AB}{CD}=\\dfrac{120}{80}=\\dfrac{3}{2}$ <br\/> V\u1eady ta ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. $ \\dfrac{AB}{CD}=\\dfrac{120}{80}=\\dfrac{3}{2}$<\/span><\/span>","column":2}]}],"id_ques":1656},{"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":" Vi\u1ebft t\u1ec9 s\u1ed1 c\u1ee7a c\u1eb7p \u0111o\u1ea1n th\u1eb3ng sau: $MN = 18,5cm$; $PQ = 12cm$ ","select":[" A. $ \\dfrac{MN}{PQ}=\\dfrac{12}{18,5}=\\dfrac{24}{37}$ "," B. $\\dfrac{MN}{PQ}=\\dfrac{18,5}{12}=\\dfrac{37}{24}$"],"explain":" T\u1ec9 s\u1ed1 c\u1ee7a hai \u0111o\u1ea1n th\u1eb3ng $MN$ v\u00e0 $PQ$ l\u00e0: <br\/> $\\dfrac{MN}{PQ}=\\dfrac{18,5}{12}=\\dfrac{37}{24}$ <br\/> V\u1eady ta ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. $\\dfrac{MN}{PQ}=\\dfrac{18,5}{12}=\\dfrac{37}{24}$<\/span><\/span>","column":2}]}],"id_ques":1657},{"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 $AB = 15cm$, $CD = 85cm$ t\u1ec9 l\u1ec7 v\u1edbi hai \u0111o\u1ea1n th\u1eb3ng $A\u2019B\u2019 = 24cm$ 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. $84$ "," B. $53,125$","C. $136$","D. $163$"],"explain":" 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\/> 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 $\\dfrac{15}{85}=\\dfrac{24}{C'D'}$ <br\/> $\\Rightarrow C'D'=\\dfrac{85.24}{15}=136 \\text{(cm)}$ <br\/> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: C. $136$<\/span>","column":2}]}],"id_ques":1658},{"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":[[["10"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"Cho bi\u1ebft $\\dfrac{AB}{CD}=\\dfrac{2}{5} $ v\u00e0 $CD = 25cm$. T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh $AB$ <br\/> \u0110\u00e1p \u00e1n: $AB = $_input_ ($cm$)","hint":"","explain":"Ta c\u00f3: <br\/> $\\dfrac{AB}{CD}=\\dfrac{2}{5}$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow AB=\\dfrac{2.CD}{5}=\\dfrac{2.25}{5}=10 \\text{(cm)}$ <br\/> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 10<\/span><\/span>"}]}],"id_ques":1659},{"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":[[["24"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"Cho bi\u1ebft $\\dfrac{MN}{PQ}=\\dfrac{5}{6} $ v\u00e0 $MN = 20cm$. T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh $PQ$ <br\/> \u0110\u00e1p \u00e1n: $PQ =$ _input_ ($cm$)","hint":"","explain":"Ta c\u00f3: <br\/> $\\dfrac{MN}{PQ}=\\dfrac{5}{6} $ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow PQ=\\dfrac{MN.6}{5}=\\dfrac{20.6}{5}= 24 \\text{(cm)}$ <br\/> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 24<\/span><\/span>"}]}],"id_ques":1660},{"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 bi\u1ebft \u0111\u1ed9 d\u00e0i c\u1ee7a $AB$ g\u1ea5p $4$ l\u1ea7n \u0111\u1ed9 d\u00e0i c\u1ea1nh $CD$ v\u00e0 \u0111\u1ed9 d\u00e0i c\u1ee7a $A\u2019B\u2019$ g\u1ea5p $5$ 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. $\\dfrac{5}{4}$ "," B. $\\dfrac{4}{5}$","C. $\\dfrac{7}{8}$","D. $\\dfrac{5}{7}$"],"explain":" 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\/> B\u00e0i gi\u1ea3i:<\/span> <br\/> Theo \u0111\u1ec1 b\u00e0i ta c\u00f3: <br\/> $AB = 4.CD$ <br\/> $A\u2019B\u2019 = 5.CD$ <br\/> T\u1ec9 s\u1ed1 c\u1ee7a hai \u0111o\u1ea1n th\u1eb3ng $AB$ v\u00e0 $A\u2019B\u2019$ l\u00e0: <br\/> $\\dfrac{AB}{A'B'}=\\dfrac{4.CD}{5.CD}=\\dfrac{4}{5}$ <br\/> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: B. <\/span>","column":2}]}],"id_ques":1661},{"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 bi\u1ebft \u0111\u1ed9 d\u00e0i c\u1ee7a $MN$ g\u1ea5p $7$ l\u1ea7n \u0111\u1ed9 d\u00e0i c\u1ea1nh $AB$ v\u00e0 \u0111\u1ed9 d\u00e0i c\u1ee7a $PQ$ g\u1ea5p $12$ l\u1ea7n \u0111\u1ed9 d\u00e0i c\u1ee7a $AB$. T\u00ednh t\u1ec9 s\u1ed1 c\u1ee7a hai \u0111o\u1ea1n th\u1eb3ng $MN$ v\u00e0 $PQ$ ","select":[" A. $\\dfrac{5}{7}$ "," B. $\\dfrac{12}{7}$","C. $\\dfrac{7}{12}$","D. $\\dfrac{19}{12}$"],"explain":" 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\/> B\u00e0i gi\u1ea3i:<\/span> <br\/> Theo \u0111\u1ec1 b\u00e0i ta c\u00f3: <br\/> $MN = 7.AB$ <br\/> $PQ = 12.AB$ <br\/> T\u1ec9 s\u1ed1 c\u1ee7a hai \u0111o\u1ea1n th\u1eb3ng $MN$ v\u00e0 $PQ$ l\u00e0: <br\/> $\\dfrac{MN}{PQ}=\\dfrac{7.AB}{12.AB}=\\dfrac{7}{12}$ <br\/> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: C. $\\dfrac{7}{12}$<\/span>","column":2}]}],"id_ques":1662},{"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":" Cho c\u00e1c \u0111o\u1ea1n th\u1eb3ng $AB = 8cm$; $CD = 6cm$; $MN = 12cm$; $PQ = x$. T\u00ecm gi\u00e1 tr\u1ecb c\u1ee7a $x$ \u0111\u1ec3 $AB$ v\u00e0 $CD$ t\u1ec9 l\u1ec7 v\u1edbi $MN$ v\u00e0 $PQ$.","select":[" A. $4cm$ "," B. $5cm$","C. $16cm$","D. $9cm$"],"hint":"","explain":" 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\/> B\u00e0i gi\u1ea3i:<\/span> <br\/> \u0110\u1ec3 $AB$ v\u00e0 $CD$ t\u1ec9 l\u1ec7 v\u1edbi $MN$ v\u00e0 $PQ$ <br\/> $\\Leftrightarrow \\dfrac{AB}{CD}=\\dfrac{MN}{PQ}$ (\u0111\u1ecbnh ngh\u0129a \u0111o\u1ea1n th\u1eb3ng t\u1ec9 l\u1ec7) <br\/> $\\Leftrightarrow \\dfrac{8}{6}=\\dfrac{12}{x}$ <br\/> $\\Leftrightarrow x=\\dfrac{12.6}{8} = 9 \\text{(cm)} $ <br\/> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D. $9\\,cm$<\/span>","column":2}]}],"id_ques":1663},{"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 c\u00e1c \u0111o\u1ea1n th\u1eb3ng $AB = x\\,cm$; $CD = 9cm$; $MN = 7cm$; $PQ = 12cm$. T\u00ecm gi\u00e1 tr\u1ecb c\u1ee7a $x$ \u0111\u1ec3 $AB$ v\u00e0 $CD$ t\u1ec9 l\u1ec7 v\u1edbi $MN$ v\u00e0 $PQ$.","select":[" A. $4,75cm$ "," B. $15,5cm$","C. $5,25cm$","D. $9,3cm$"],"explain":" 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\/> B\u00e0i gi\u1ea3i:<\/span> <br\/> \u0110\u1ec3 $AB$ v\u00e0 $CD$ t\u1ec9 l\u1ec7 v\u1edbi $MN$ v\u00e0 $PQ$ <br\/> $\\Leftrightarrow \\dfrac{AB}{CD}=\\dfrac{MN}{PQ}$ (\u0111\u1ecbnh ngh\u0129a \u0111o\u1ea1n th\u1eb3ng t\u1ec9 l\u1ec7) <br\/> $\\Leftrightarrow \\dfrac{x}{9}=\\dfrac{7}{12}$ <br\/> $\\Leftrightarrow x=\\dfrac{9.7}{12} = 5,25 \\text{(cm)} $ <br\/> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: C. $5,25cm$<\/span>","column":2}]}],"id_ques":1664},{"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 $\\triangle ABC$, tr\u00ean c\u1ea1nh $AC$ l\u1ea5y \u0111i\u1ec3m $D$ sao cho $AD = 2,4cm$, $DC = 1,6cm$. Qua $D$ k\u1ebb $DE \/\/ AB$ ($E \\in BC$). Bi\u1ebft $CB = 7cm$. T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ee7a $CE$.","select":[" A. $2,8cm$ "," B. $10,5cm$","C. $4,7cm$","D. $5,6cm$"],"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":"H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> B\u01b0\u1edbc 1:<\/b> T\u00ednh $AC$ <br\/> 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\u01b0\u1edbc 3:<\/b> T\u1eeb h\u1ec7 th\u1ee9c \u1edf b\u01b0\u1edbc 2 t\u00ednh $CE$. <br\/> B\u00e0i gi\u1ea3i:<\/span> <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai14/lv1/img\/H8C3B1_D104.png' \/><\/center> <br\/> Ta c\u00f3: $D \\in AC$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow AC = AD + DC = 2,4 + 1,6 = 4 \\text{(cm)}$ <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 $\\dfrac{1,6}{4} = \\dfrac{CE}{7}$ <br\/> $\\Rightarrow CE = \\dfrac{1,6.7}{4} = 2,8 \\text{(cm)}$ <br\/> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: A. $2,8cm$<\/span>","column":2}]}],"id_ques":1665},{"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":" Cho tam gi\u00e1c $\\triangle MNP$, $E \\in MN$ v\u00e0 $F \\in MP$. Bi\u1ebft $ME = 3cm$; $EN = 4,5cm$; $MF = 6cm$ v\u00e0 $EF \/\/ NP$. T\u00ednh $FP$.","select":[" A. $2,25cm$ "," B. $4cm$","C. $4,5cm$","D. $9cm$"],"hint":" S\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00fd Ta-l\u00e9t","explain":"H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> B\u01b0\u1edbc 1:<\/b>\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Ta-l\u00e9t \u0111\u1ec3 \u0111\u01b0a ra h\u1ec7 th\u1ee9c: $\\dfrac{ME}{EN} = \\dfrac{MF}{FP}$ <br\/> B\u01b0\u1edbc 2:<\/b> T\u1eeb h\u1ec7 th\u1ee9c \u1edf b\u01b0\u1edbc 1 t\u00ednh $FP$. <br\/> B\u00e0i gi\u1ea3i:<\/span> <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai14/lv1/img\/H8C3B1_D105.png' \/><\/center> <br\/> V\u00ec $EF \/\/ NP$ (gi\u1ea3 thi\u1ebft), theo \u0111\u1ecbnh l\u00ed Ta-l\u00e9t ta c\u00f3: <br\/> $\\dfrac{ME}{EN} = \\dfrac{MF}{FP}$ hay $\\dfrac{3}{4,5} = \\dfrac{6}{FP}$ <br\/> $\\Rightarrow FP = \\dfrac{4,5 . 6}{3} = 9 \\text{(cm)}$ <br\/> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D. $9cm$<\/span>","column":2}]}],"id_ques":1666},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00fang hay sai","title_trans":"","temp":"true_false","correct":[["t","f","t"]],"list":[{"point":5,"image":"","col_name":["C\u00e2u h\u1ecfi:","\u0110\u00fang","Sai"],"arr_ques":[" T\u1ec9 s\u1ed1 c\u1ee7a c\u00e1c c\u1eb7p \u0111o\u1ea1n th\u1eb3ng $AB = 5cm$ v\u00e0 $CD = 7cm$ l\u00e0: $\\dfrac{AB}{CD} = \\dfrac{5}{7}$ "," T\u1ec9 s\u1ed1 c\u1ee7a c\u00e1c c\u1eb7p \u0111o\u1ea1n th\u1eb3ng $MN = 4,5cm$ v\u00e0 $PQ = 6cm$ l\u00e0: $\\dfrac{MN}{PQ} = \\dfrac{6}{4,5} = \\dfrac{4}{3}$ "," T\u1ec9 s\u1ed1 c\u1ee7a c\u00e1c c\u1eb7p \u0111o\u1ea1n th\u1eb3ng $OA = 3cm$ v\u00e0 $OB = 6cm$ l\u00e0: $\\dfrac{OA}{OB} = \\dfrac{1}{2} $ "],"hint":"","explain":["T\u1ec9 s\u1ed1 c\u1ee7a c\u00e1c c\u1eb7p \u0111o\u1ea1n th\u1eb3ng $AB = 5cm$ v\u00e0 $CD = 7cm$ l\u00e0: $\\dfrac{AB}{CD} = \\dfrac{5}{7}$ (\u0110\u00daNG)"," <br\/> T\u1ec9 s\u1ed1 c\u1ee7a c\u00e1c c\u1eb7p \u0111o\u1ea1n th\u1eb3ng $MN = 4,5cm$ v\u00e0 $PQ = 6cm$ l\u00e0: $\\dfrac{MN}{PQ} = \\dfrac{6}{4,5} = \\dfrac{4}{3}$ (SAI). V\u00ec T\u1ec9 s\u1ed1 c\u1ee7a c\u00e1c c\u1eb7p \u0111o\u1ea1n th\u1eb3ng $MN = 4,5cm$ v\u00e0 $PQ = 6cm$ l\u00e0: $\\dfrac{MN}{PQ} = \\dfrac{4,5}{6} = \\dfrac{3}{4}$ "," <br\/> T\u1ec9 s\u1ed1 c\u1ee7a c\u00e1c c\u1eb7p \u0111o\u1ea1n th\u1eb3ng $OA = 3cm$ v\u00e0 $OB = 6cm$ l\u00e0: $\\dfrac{OA}{OB} = \\dfrac{1}{2} $ (\u0110\u00daNG). V\u00ec T\u1ec9 s\u1ed1 c\u1ee7a c\u00e1c c\u1eb7p \u0111o\u1ea1n th\u1eb3ng $OA = 3cm$ v\u00e0 $OB = 6cm$ l\u00e0: $\\dfrac{OA}{OB} = \\dfrac{3}{6} = \\dfrac{1}{2} $ "]}]}],"id_ques":1667},{"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":" Cho h\u00ecnh v\u1ebd sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai14/lv1/img\/H8C3B1_D106.png' \/><\/center> <br\/> H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","select":[" A. $\\dfrac{EM}{MF} = \\dfrac{EN}{NP}$ "," B. $\\dfrac{EM}{EF} = \\dfrac{EN}{EP}$","C. $\\dfrac{MF}{EF} = \\dfrac{NP}{EP}$","D. C\u1ea3 A, B, C \u0111\u1ec1u \u0111\u00fang"],"hint":" S\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00fd Ta-l\u00e9t","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai14/lv1/img\/H8C3B1_D106.png' \/><\/center> <br\/> V\u00ec $MN \/\/ FP$ (gi\u1ea3 thi\u1ebft), theo \u0111\u1ecbnh l\u00ed Ta-l\u00e9t ta c\u00f3: <br\/> $\\dfrac{EM}{MF} = \\dfrac{EN}{NP}$; $\\dfrac{EM}{EF} = \\dfrac{EN}{EP}$; $\\dfrac{MF}{EF} = \\dfrac{NP}{EP}$ <br\/> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 D. C\u1ea3 A, B, C \u0111\u1ec1u \u0111\u00fang<\/span><\/span>","column":2}]}],"id_ques":1668},{"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":" Cho h\u00ecnh v\u1ebd sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai14/lv1/img\/H8C3B1_D107.png' \/><\/center> <br\/> H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","select":[" A. $MN \/\/ BC$ "," B. $NP \/\/ AB$","C. $MP \/\/ AC$","D. C\u1ea3 A, C \u0111\u1ec1u \u0111\u00fang"],"hint":" S\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00fd Ta-l\u00e9t \u0111\u1ea3o","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai14/lv1/img\/H8C3B1_D107.png' \/><\/center> <br\/> Ta c\u00f3: <br\/> $\\left.\\begin{array}{l} \\dfrac{AM}{MB} = \\dfrac{6}{2} = 3\\\\ \\dfrac{AN}{NC} = \\dfrac{4,5}{1,5} = 3 \\end{array} \\right\\}$ $\\Rightarrow \\dfrac{AM}{MB} = \\dfrac{AN}{NC}$ <br\/> $\\Rightarrow MN \/\/ BC$ (\u0111\u1ecbnh l\u00ed Ta-l\u00e9t \u0111\u1ea3o) (\u0111\u00e1p \u00e1n A \u0111\u00fang)<\/b> <br\/> $\\left.\\begin{array}{l} \\dfrac{BM}{MA} = \\dfrac{2}{6} = \\dfrac{1}{3}\\\\ \\dfrac{BP}{PC} = \\dfrac{2,25}{6,75} = \\dfrac{1}{3} \\end{array} \\right\\}$ $\\Rightarrow \\dfrac{BM}{MA} = \\dfrac{BP}{PC}$ <br\/> $\\Rightarrow MP \/\/ AC$ (\u0111\u1ecbnh l\u00ed Ta-l\u00e9t \u0111\u1ea3o) (\u0111\u00e1p \u00e1n C \u0111\u00fang)<\/b> <br\/> $\\left.\\begin{array}{l} \\dfrac{CP}{PB} = \\dfrac{6.75}{2,25} = 3\\\\ \\dfrac{CN}{NA} = \\dfrac{1,5}{4,5} = \\dfrac{1}{3} \\end{array} \\right\\}$ $\\Rightarrow \\dfrac{CP}{PB} \\neq \\dfrac{CN}{NA}$ <br\/> $\\Rightarrow$ NP v\u00e0 AB kh\u00f4ng song song v\u1edbi nhau (\u0111\u00e1p \u00e1n B sai)<\/b> <br\/> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 D. C\u1ea3 A, C \u0111\u1ec1u \u0111\u00fang<\/span><\/span>","column":2}]}],"id_ques":1669},{"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/bai14/lv1/img\/H8C3B1_D108.png' \/><\/center> <br\/> Bi\u1ebft $\\dfrac{ME}{MN} = \\dfrac{2}{5}$. T\u00ednh $NP$.","select":[" A. $NP = 12cm$ "," B. $NP = 15cm$","C. $NP = 28cm$","D. $NP = 24cm$"],"hint":" S\u1eed d\u1ee5ng h\u1ec7 qu\u1ea3 c\u1ee7a \u0111\u1ecbnh l\u00fd Ta-l\u00e9t","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai14/lv1/img\/H8C3B1_D108.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\/> $\\Rightarrow \\dfrac{2}{5} = \\dfrac{4,8}{NP}$ <br\/> $\\Rightarrow NP = \\dfrac{5.4,8}{2} = 12 \\text{(cm)}$ <br\/> <br\/> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. $NP = 12cm$<\/span><\/span>","column":2}]}],"id_ques":1670}],"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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