{"segment":[{"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'> Ch\u1ecdn kh\u1eb3ng \u0111\u1ecbnh SAI trong c\u00e1c kh\u1eb3ng \u0111\u1ecbnh sau: <\/span>","select":["A. \u0110\u1ed9 d\u00e0i \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang b\u1eb1ng n\u1eeda t\u1ed5ng hai \u0111\u00e1y ","B. \u0110\u1ed9 d\u00e0i \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang b\u1eb1ng n\u1eeda hi\u1ec7u hai \u0111\u00e1y","C. \u0110\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang th\u00ec song song v\u1edbi hai \u0111\u00e1y ","D. \u0110\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang l\u00e0 \u0111o\u1ea1n n\u1ed1i trung \u0111i\u1ec3m hai c\u1ea1nh b\u00ean c\u1ee7a h\u00ecnh thang "],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai3/lv1/img\/H813_D1_1.jpg' \/><\/center> <span class='basic_left'> \u0110\u1ed9 d\u00e0i \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang b\u1eb1ng n\u1eeda t\u1ed5ng hai \u0111\u00e1y. <br\/> \u0110\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang th\u00ec song song v\u1edbi hai \u0111\u00e1y. <br\/> \u0110\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang l\u00e0 \u0111o\u1ea1n n\u1ed1i trung \u0111i\u1ec3m hai c\u1ea1nh b\u00ean c\u1ee7a h\u00ecnh thang. <br\/> C\u00e1c \u0111\u00e1p \u00e1n A, C, D \u0111\u1ec1u \u0111\u00fang. <br\/> Do \u0111\u00f3 \u0111\u00e1n \u00e1n B l\u00e0 sai. <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n ch\u1ecdn l\u00e0 B. <\/span><\/span> ","column":1}]}],"id_ques":1341},{"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'> \u0110i\u1ec1n ti\u1ebfp v\u00e0o ch\u1ed7 tr\u1ed1ng \u0111\u1ec3 \u0111\u01b0\u1ee3c kh\u1eb3ng \u0111\u1ecbnh \u0111\u00fang: <br\/> <b>\u0110\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c l\u00e0 \u0111o\u1ea1n th\u1eb3ng________<\/b> <\/span>","select":["A. N\u1ed1i trung \u0111i\u1ec3m hai c\u1ea1nh c\u1ee7a tam gi\u00e1c ","B. Song song v\u1edbi m\u1ed9t c\u1ea1nh c\u1ee7a tam gi\u00e1c ","C. C\u1eaft hai c\u1ea1nh c\u1ee7a tam gi\u00e1c v\u00e0 song song v\u1edbi c\u1ea1nh c\u00f2n l\u1ea1i "],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai3/lv1/img\/H813_D2_1.jpg' \/><\/center> <span class='basic_left'> \u0110\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c l\u00e0 \u0111o\u1ea1n th\u1eb3ng n\u1ed1i trung \u0111i\u1ec3m hai c\u1ea1nh c\u1ee7a tam gi\u00e1c. <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A. <\/span><\/span> ","column":1}]}],"id_ques":1342},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t.<br\/> Kh\u1eb3ng \u0111\u1ecbnh d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang hay sai","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" <span class='basic_left'> <i> \u0110\u1ecbnh ngh\u0129a: <\/i> \u0110\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua trung \u0111i\u1ec3m m\u1ed9t c\u1ea1nh b\u00ean c\u1ee7a h\u00ecnh thang v\u00e0 song song v\u1edbi hai \u0111\u00e1y. <\/span> <\/span> ","select":["\u0110\u00fang","Sai"],"explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai3/lv1/img\/H813_D1_1.jpg' \/><\/center> <i> \u0110\u1ecbnh ngh\u0129a: <\/i> \u0110\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang l\u00e0 \u0111o\u1ea1n th\u1eb3ng n\u1ed1i trung \u0111i\u1ec3m hai c\u1ea1nh b\u00ean c\u1ee7a h\u00ecnh thang. <br\/> Kh\u1eb3ng \u0111\u1ecbnh: ''\u0110\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua trung \u0111i\u1ec3m m\u1ed9t c\u1ea1nh b\u00ean c\u1ee7a h\u00ecnh thang v\u00e0 song song v\u1edbi hai \u0111\u00e1y'' (t\u00ednh ch\u1ea5t c\u1ee7a \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang). <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 \u0110\u00fang.<\/span>","column":2}]}],"id_ques":1343},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t.<br\/> Kh\u1eb3ng \u0111\u1ecbnh d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang hay sai","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" <span class='basic_left'> Cho $\\Delta ABC$, $AE =EB \\, (E\\in AB)$ v\u00e0 $AF=CF\\,(F\\in AC)$ th\u00ec $EF=\\dfrac{1}{2}BC$. <\/span> <\/span> ","select":["\u0110\u00fang","Sai"],"explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai3/lv1/img\/H813_D2_1.jpg' \/><\/center> Theo b\u00e0i: $AE =EB \\, (E\\in AB)$ v\u00e0 $AF=CF\\,(F\\in AC)$ <br\/> $\\Rightarrow EF$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a $\\Delta ABC$. <br\/> Theo \u0111\u1ecbnh l\u00ed th\u00ec $EF\/\/BC$ v\u00e0 $EF=\\dfrac{1}{2}BC$. <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n l\u00e0 \u0110\u00fang.<\/span>","column":2}]}],"id_ques":1344},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["4"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<span class='basic_left'> Cho h\u00ecnh sau. T\u00ednh $x$. <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai3/lv1/img\/H813_D1_2.jpg' \/><\/center> <br\/> <b> \u0110\u00e1p \u00e1n:<\/b> $x= \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ $(cm)$ ","hint":" X\u00e9t xem $EF$ l\u00e0 g\u00ec c\u1ee7a $\\Delta ABC$. ","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai3/lv1/img\/H813_D1_2.jpg' \/><\/center> <span class='basic_left'> X\u00e9t trong $\\Delta ABC$ c\u00f3: $AE=EB; AF=FC$ <br\/> $\\Rightarrow EF$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a $\\Delta ABC$. <br\/> $\\Rightarrow EF=\\dfrac{1}{2}BC=\\dfrac{1}{2}.8=4$ $(cm)$ <br\/> T\u1ee9c l\u00e0: $x=4\\, (cm)$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $4$. <\/span><\/span> "}]}],"id_ques":1345},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["2"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<span class='basic_left'> Cho h\u00ecnh sau, bi\u1ebft $EF \/\/ BC$. T\u00ednh $x$. <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai3/lv1/img\/H813_D1_3.jpg' \/><\/center> <br\/> <b> \u0110\u00e1p \u00e1n:<\/b> $x= \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ $(cm)$ ","hint":" \u0110\u00e1nh gi\u00e1 $EF$ l\u00e0 g\u00ec \u0111\u1ed1i v\u1edbi $\\Delta ABC$ ","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai3/lv1/img\/H813_D1_3.jpg' \/><\/center> <span class='basic_left'> D\u1ef1a v\u00e0o h\u00ecnh v\u1ebd \u0111\u00e3 cho, ta nh\u1eadn th\u1ea5y: <br\/> $\\left\\{ \\begin{align} & AE=EB\\,\\,\\left( E\\in AB \\right) \\\\ & EF\/\/BC \\\\ \\end{align} \\right.$ <br\/> Suy ra, $EF$ \u0111i qua trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh $AC$ hay $AF =FC$. <br\/> T\u1ee9c l\u00e0: $x=2\\, (cm)$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $2$. <\/span><\/span> "}]}],"id_ques":1346},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["10"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<span class='basic_left'> Cho h\u00ecnh sau. T\u00ednh $x$. <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai3/lv1/img\/H813_D1_4.jpg' \/><\/center> <br\/> <b> \u0110\u00e1p \u00e1n:<\/b> $x= \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ $(cm)$ ","hint":" \u0110\u00e1nh gi\u00e1 $IK$ l\u00e0 g\u00ec \u0111\u1ed1i v\u1edbi $\\Delta ABC$ ","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai3/lv1/img\/H813_D1_4.jpg' \/><\/center> <span class='basic_left'> D\u1ef1a v\u00e0o h\u00ecnh v\u1ebd \u0111\u00e3 cho, ta nh\u1eadn th\u1ea5y: <br\/> $\\left\\{ \\begin{align} & AK=KC\\,\\,\\left( K\\in AC \\right) \\\\ & IK\/\/BC\\,\\,\\left( do\\,\\,\\widehat{AKI}=\\widehat{KCB}=50^o \\right) \\\\ \\end{align} \\right.$ <br\/> Do \u0111\u00f3: $IK$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a $\\Delta ABC$. <br\/> Suy ra: $IK=\\dfrac{1}{2}BC$. <br\/> $\\Rightarrow BC=2IK=2.5=10\\, (cm)$ <br\/> T\u1ee9c l\u00e0: $x=10\\, (cm)$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $10$. <\/span><\/span> "}]}],"id_ques":1347},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["4"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<span class='basic_left'> Cho h\u00ecnh sau, trong \u0111\u00f3 $ABCD$ l\u00e0 h\u00ecnh thang $(AB \/\/ CD)$. T\u00ednh $x$. <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai3/lv1/img\/H813_D1_5.jpg' \/><\/center> <br\/> <b> \u0110\u00e1p \u00e1n:<\/b> $x= \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ $(cm)$ ","hint":" \u0110\u00e1nh gi\u00e1 $IK$ l\u00e0 g\u00ec \u0111\u1ed1i v\u1edbi h\u00ecnh thang $ABCD$. ","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai3/lv1/img\/H813_D1_5.jpg' \/><\/center> <span class='basic_left'> D\u1ef1a v\u00e0o h\u00ecnh v\u1ebd \u0111\u00e3 cho, ta nh\u1eadn th\u1ea5y: <br\/> $\\left\\{ \\begin{align} & AI=ID\\,\\,\\left(I\\in AD \\right) \\\\ & BK=KC\\,\\,\\left( K\\in BC \\right) \\\\ \\end{align} \\right.$ <br\/> Do \u0111\u00f3: $IK$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang $ABCD$. <br\/> Suy ra: $IK=\\dfrac{AB+CD}{2}=\\dfrac{3+5}{2}=4\\,(cm)$ <br\/> T\u1ee9c l\u00e0: $x=4\\, (cm)$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $4$. <\/span><\/span> "}]}],"id_ques":1348},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["6"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<span class='basic_left'> Cho h\u00ecnh sau, trong \u0111\u00f3 $ABCD$ l\u00e0 h\u00ecnh thang $(AB \/\/ CD)$. T\u00ednh $x$. <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai3/lv1/img\/H813_D1_6.jpg' \/><\/center> <b> \u0110\u00e1p \u00e1n:<\/b> $x= \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ $(cm)$ ","hint":" \u0110\u00e1nh gi\u00e1 $HK$ l\u00e0 g\u00ec \u0111\u1ed1i v\u1edbi h\u00ecnh thang $ABCD$ ","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai3/lv1/img\/H813_D1_6.jpg' \/><\/center> <span class='basic_left'> D\u1ef1a v\u00e0o h\u00ecnh v\u1ebd \u0111\u00e3 cho, ta nh\u1eadn th\u1ea5y: <br\/> $\\left\\{ \\begin{align} & BK=KC\\,\\,\\left(K\\in BC \\right) \\\\ & HK \/\/ AB \/\/ CD \\,\\,\\left( \\widehat{AHK}=\\widehat{ADC}=60^o \\right) \\\\ \\end{align} \\right.$ <br\/> Do \u0111\u00f3: $HK$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang $ABCD$. <br\/> Suy ra: $HK=\\dfrac{AB+CD}{2}$ <br\/> $\\Rightarrow AB+CD=2HK$ <br\/> $DC=2HK-AB=2.5-4=6$ $(cm)$ <br\/> T\u1ee9c l\u00e0: $x=6\\, (cm)$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $6$. <\/span><\/span> "}]}],"id_ques":1349},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["6"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<span class='basic_left'> Cho h\u00ecnh sau, trong \u0111\u00f3 $AD=BD; AE=EC$ <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai3/lv1/img\/H813_D1_7.jpg' \/><\/center> T\u00ednh $x$. <br\/> <br\/> <b> \u0110\u00e1p \u00e1n:<\/b> $x= \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ $(cm)$ ","hint":" T\u00ecm \u0111\u1ed9 d\u00e0i $DE$ tr\u01b0\u1edbc sau \u0111\u00f3 t\u1edbi $HK$.","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai3/lv1/img\/H813_D1_7.jpg' \/><\/center> <span class='basic_left'> D\u1ef1a v\u00e0o h\u00ecnh v\u1ebd v\u00e0 \u0111\u1ec1 b\u00e0i \u0111\u00e3 cho, x\u00e9t $\\Delta ABC$ c\u00f3: <br\/> $\\left\\{ \\begin{align} & AD=BD\\,\\,\\left(D\\in AB \\right) \\\\ & AE=EC \\,\\,\\left( E\\in AC \\right) \\\\ \\end{align} \\right.$ <br\/> Do \u0111\u00f3: $DE$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a $\\Delta ABC$. <br\/> Suy ra: $DE=\\dfrac{1}{2}BC=\\dfrac{1}{2}.8=4\\, (cm)$ <br\/> M\u1eb7t kh\u00e1c ta c\u0169ng c\u00f3 $DECB$ l\u00e0 h\u00ecnh thang do $DE \/\/ BC$ <br\/> Ta c\u00f3: <br\/> $\\left\\{ \\begin{align} & DH=BH\\,\\,\\left(H\\in DB \\right) \\\\ & EK=KC \\,\\,\\left( K\\in EC \\right) \\\\ \\end{align} \\right.$ <br\/> Suy ra: $HK$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang $DECB$. <br\/> $\\Rightarrow HK=\\dfrac{DE+BC}{2}$$=\\dfrac{4+8}{2}=6\\, (cm)$ <br\/> T\u1ee9c l\u00e0: $x=6\\, cm$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $6$. <\/span><\/span> "}]}],"id_ques":1350},{"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'> M\u1ed9t h\u00ecnh thang c\u00f3 \u0111\u00e1y l\u1edbn l\u00e0 $5\\, cm$, \u0111\u00e1y nh\u1ecf ng\u1eafn h\u01a1n \u0111\u00e1y l\u1edbn $0,2\\, cm$. \u0110\u1ed9 d\u00e0i \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang \u0111\u00f3 l\u00e0: <\/span>","select":["A. $4,9 \\,cm$ ","B. $4,5\\, cm$ ","C. $3,9\\, cm$ ","C. $3,5\\, cm$ "],"hint":" T\u00ecm \u0111\u1ed9 d\u00e0i \u0111\u00e1y nh\u1ecf tr\u01b0\u1edbc r\u1ed3i suy ra \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng trung b\u00ecnh. ","explain":" <span class='basic_left'> \u0110\u00e1y nh\u1ecf c\u1ee7a h\u00ecnh thang l\u00e0: <br\/> $5-0,2=4,8 \\, (cm)$ <br\/> \u0110\u1ed9 d\u00e0i \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang \u0111\u00f3 l\u00e0: <br\/> $(5+4,8):2=4,9\\, (cm)$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A. <\/span><\/span> ","column":4}]}],"id_ques":1351},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["12"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<span class='basic_left'> Cho $\\Delta HIK$. Bi\u1ebft $MH=MK; NH=NI$ ($M\\in HK; N\\in HI$). Cho $KI=24\\, cm$. T\u00ednh $MN$. <br\/> <br\/> <b> \u0110\u00e1p \u00e1n:<\/b> $MN= \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ $(cm)$ ","hint":" T\u00ecm xem $MN$ l\u00e0 g\u00ec trong $\\Delta HKI$.","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai3/lv1/img\/H813_D1_8.jpg' \/><\/center> <span class='basic_left'> Theo \u0111\u1ec1 b\u00e0i, ta c\u00f3: <br\/> $\\left\\{ \\begin{align} & HM=MK\\,\\,\\left(M\\in HK \\right) \\\\ & HN=NI \\,\\,\\left( N\\in HI \\right) \\\\ \\end{align} \\right.$ <br\/> Suy ra: $MN$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a $\\Delta HKI$. <br\/> $\\Rightarrow MN=\\dfrac{1}{2}KI=\\dfrac{1}{2}.24=12\\, (cm)$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $12$. <\/span><\/span> "}]}],"id_ques":1352},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["56"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<span class='basic_left'> Cho $\\Delta ABC$. Bi\u1ebft $BD=DC; DE \/\/ BA$ ($E\\in AC; D\\in BC$). Cho $AE=28\\, cm$. T\u00ednh $AC$. <br\/> <br\/> <b> \u0110\u00e1p \u00e1n:<\/b> $AC= \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ $(cm)$ ","hint":" T\u00ecm xem $DE$ l\u00e0 g\u00ec trong $\\Delta ABC$.","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai3/lv1/img\/H813_D1_9.jpg' \/><\/center> <span class='basic_left'> Theo \u0111\u1ec1 b\u00e0i, ta c\u00f3: <br\/> $\\left\\{ \\begin{align} & BD=DC\\,\\,\\left(D\\in BC \\right) \\\\ & DE\/\/AB \\,\\,\\left( E\\in AC \\right) \\\\ \\end{align} \\right.$ <br\/> Suy ra: $DE$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a $\\Delta ABC$. <br\/> $\\Rightarrow AE=EC=28\\, (cm)$ <br\/> $\\Rightarrow AC=2AE=56\\, (cm)$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $56$. <\/span><\/span> "}]}],"id_ques":1353},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["35"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<span class='basic_left'> Cho h\u00ecnh thang $GHIK (GH \/\/ IK)$, $KI=30\\, cm; GH = 40\\, cm$. <br\/> Bi\u1ebft $LG=LK; MH=MI\\, (L\\in GK; M \\in HI)$. T\u00ednh $LM$. <br\/> <br\/> <b> \u0110\u00e1p \u00e1n:<\/b> $LM= \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ $(cm)$ ","hint":" T\u00ecm xem $LM$ l\u00e0 g\u00ec trong h\u00ecnh thang $GHIK$.","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai3/lv1/img\/H813_D1_10.jpg' \/><\/center> <span class='basic_left'> Theo \u0111\u1ec1 b\u00e0i, ta c\u00f3: <br\/> $\\left\\{ \\begin{align} & LG=LK\\,\\,\\left(L\\in GK \\right) \\\\ & MH=MI \\,\\,\\left( M \\in HI \\right) \\\\ \\end{align} \\right.$ <br\/> Suy ra: $LM$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang $GHIK$. <br\/> $\\Rightarrow LM=\\dfrac{GH+IK}{2}=\\dfrac{40+30}{2}=35\\, (cm)$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $35$. <\/span><\/span> "}]}],"id_ques":1354},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["16"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<span class='basic_left'> Cho h\u00ecnh thang $ABCD (AB \/\/ CD)$ vu\u00f4ng t\u1ea1i $A$ v\u00e0 $D$; $M\\in AD$ sao cho $AM=MD; MN\\bot AD$. Bi\u1ebft $DC=24\\, cm; MN=20\\, cm$. T\u00ednh $AB$. <br\/> <br\/> <b> \u0110\u00e1p \u00e1n:<\/b> $AB= \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ $(cm)$ ","hint":" X\u00e1c \u0111\u1ecbnh $MN$ l\u00e0 g\u00ec trong h\u00ecnh thang $ABCD$. \u0111\u00f3.","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai3/lv1/img\/H813_D1_11.jpg' \/><\/center> <span class='basic_left'> Theo \u0111\u1ec1 b\u00e0i, ta c\u00f3: <br\/> $\\left\\{ \\begin{align} & AM=MD\\,\\,\\left(M\\in AD \\right) \\\\ & MN \/\/ AB\/\/ CD\\,\\,\\left( MN\\bot AD \\right) \\\\ \\end{align} \\right.$ <br\/>$\\Rightarrow MN$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang $ABCD$. <br\/> $\\Rightarrow MN=\\dfrac{AB+DC}{2}$ <br\/> $\\Rightarrow 2MN=AB+CD$<br\/>$\\Rightarrow AB=2MN-CD=2.20-24=16\\, (cm)$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $16$. <\/span><\/span> "}]}],"id_ques":1355},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t.<br\/> Kh\u1eb3ng \u0111\u1ecbnh d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang hay sai","title_trans":"\u0110\u1ec1 chung cho ba c\u00e2u","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" <span class='basic_left'> Cho $\\Delta ABC$ c\u00e2n t\u1ea1i $A$, g\u1ecdi $D$ v\u00e0 $E$ theo th\u1ee9 t\u1ef1 l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$ v\u00e0 $AC$. <br\/><br\/> <b> C\u00e2u 1:<\/b> Ta ch\u1ee9ng minh \u0111\u01b0\u1ee3c t\u1ee9 gi\u00e1c $BDEC$ l\u00e0 h\u00ecnh thang c\u00e2n. <\/span> <\/span> ","select":["\u0110\u00fang","Sai"],"explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai3/lv1/img\/H813_D1_13.jpg' \/><\/center> Theo b\u00e0i: $AD=DB; AE=EC$ <br\/> $\\Rightarrow$ $DE$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a $\\Delta ABC$. <br\/> $\\Rightarrow DE \/\/ BC$ <br\/> Do v\u1eady: $BDEC$ l\u00e0 h\u00ecnh thang. <br\/> L\u1ea1i c\u00f3: $\\Delta ABC$ c\u00e2n t\u1ea1i $A$ n\u00ean $AB=AC$ <br\/> $\\Rightarrow \\widehat{B}=\\widehat{C}$ <br\/> Do \u0111\u00f3: $BDEC$ l\u00e0 h\u00ecnh thang c\u00e2n. <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 \u0110\u00fang.<\/span>","column":2}]}],"id_ques":1356},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho ba c\u00e2u","temp":"fill_the_blank","correct":[[["4"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<span class='basic_left'> Cho $\\Delta ABC$ c\u00e2n t\u1ea1i $A$, g\u1ecdi $D$ v\u00e0 $E$ theo th\u1ee9 t\u1ef1 l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$ v\u00e0 $AC$. <br\/><br\/> <b> C\u00e2u 2:<\/b> K\u1ebb $DH\\bot BC; EK \\bot BC$, bi\u1ebft $BC=8 \\, cm$. T\u00ednh \u0111\u1ed9 d\u00e0i $KH$. <br\/><br\/> <b> \u0110\u00e1p \u00e1n:<\/b> $KH= \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ $(cm)$ <\/span>","hint":" T\u00ecm m\u1ed1i quan h\u1ec7 gi\u1eefa $DE$ v\u00e0 $HK$.","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai3/lv1/img\/H813_D1_12.jpg' \/><\/center> <span class='basic_left'> Gi\u1ea3 thi\u1ebft \u0111\u00e3 cho: $DH\\bot BC; EK \\bot BC$ $\\Rightarrow DH\/\/EK$ <br\/> M\u00e0 $DE \/\/ HK$ (v\u00ec $DE\/\/BC$).<br\/> $\\Rightarrow DE=KH$ (t\u00ednh ch\u1ea5t \u0111o\u1ea1n ch\u1eafn)<br\/> Theo c\u00e2u 1, ta ch\u1ee9ng minh \u0111\u01b0\u1ee3c $DE$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a $\\Delta ABC$. <br\/> $\\Rightarrow DE =\\dfrac{1}{2}BC=\\dfrac{1}{2}.8=4\\, (cm)$ <br\/> Do v\u1eady: $HK=4\\, (cm)$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $4$. <\/span><\/span> "}]}],"id_ques":1357},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho ba c\u00e2u","temp":"fill_the_blank","correct":[[["2"],["6"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<span class='basic_left'> Cho $\\Delta ABC$ c\u00e2n t\u1ea1i $A$, g\u1ecdi $D$ v\u00e0 $E$ theo th\u1ee9 t\u1ef1 l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$ v\u00e0 $AC$. <br\/><br\/> <b> C\u00e2u 3:<\/b> K\u1ebb $DH\\bot BC; EK \\bot BC$, bi\u1ebft $BC=8 \\, cm$. T\u00ednh \u0111\u1ed9 d\u00e0i $HB, HC$. <br\/><br\/> <b> \u0110\u00e1p \u00e1n:<\/b> <br\/> $HB= \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ $(cm)$ <br\/>$HC= \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ $(cm)$ <\/span>","hint":" T\u00ecm m\u1ed1i quan h\u1ec7 gi\u1eefa $BH$ v\u00e0 $CK$.","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai3/lv1/img\/H813_D1_12.jpg' \/><\/center> <span class='basic_left'> X\u00e9t hai tam gi\u00e1c vu\u00f4ng $DBH$ v\u00e0 $ECK$, c\u00f3: <br\/> + $BD=CE$ (gi\u1ea3 thi\u1ebft) <br\/> + $\\widehat{B}=\\widehat{C}$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow \\Delta DBH=\\Delta ECK$ (c\u1ea1nh huy\u1ec1n - g\u00f3c nh\u1ecdn) <br\/> $\\Rightarrow BH=CK$ (hai c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) <br\/> Do v\u1eady: $BH=\\dfrac{BC-HK}{2}$$=\\dfrac{8-4}{2}=2\\, (cm)$ <br\/> $\\Rightarrow HC=BC-BH=8-2=6\\, (cm)$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng \u0111\u1ec3 \u0111\u01b0\u1ee3c: $HB=2\\, cm; HC=6\\, cm$. <\/span><\/span> "}]}],"id_ques":1358},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t.","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" <span class='basic_left'> Cho $\\Delta ABC$, $\\widehat{A}=60^o;\\widehat{B}=70^o$, $D$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$, $E$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AC$. <br\/><br\/> <b> C\u00e2u 1:<\/b> T\u1ee9 gi\u00e1c $BDEC$ l\u00e0 h\u00ecnh g\u00ec? <\/span> <\/span> ","select":["A. H\u00ecnh thang","B. H\u00ecnh thang c\u00e2n","C. H\u00ecnh thang vu\u00f4ng"],"explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai3/lv1/img\/H813_D1_14.jpg' \/><\/center> Theo b\u00e0i, ta c\u00f3: <br\/> + $AD=BD$ (gi\u1ea3 thi\u1ebft) <br\/> + $AE=EC$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow $ $DE$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a $\\Delta ABC$. <br\/> $\\Rightarrow DE\/\/BC$ <br\/> T\u1ee9 gi\u00e1c $BDEC$ l\u00e0 h\u00ecnh thang. <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A.<\/span>","column":3}]}],"id_ques":1359},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"fill_the_blank","correct":[[["110"],["130"]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<span class='basic_left'> Cho $\\Delta ABC$, $\\widehat{A}=60^o;\\widehat{B}=70^o$, $D$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$, $E$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AC$. <br\/><br\/> <b> C\u00e2u 2:<\/b> T\u00ednh $\\widehat{BDE}, \\widehat{DEC}$. <br\/><br\/> <b> \u0110\u00e1p \u00e1n: <\/b> <br\/> $\\widehat{BDE}=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^o$ <br\/> $\\widehat{DEC}=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^o$ <\/span>","hint":" Hai g\u00f3c k\u1ec1 m\u1ed9t c\u1ea1nh b\u00ean c\u1ee7a h\u00ecnh thang c\u00f3 t\u1ed5ng s\u1ed1 \u0111o l\u00e0 $180^o$.","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai3/lv1/img\/H813_D1_14.jpg' \/><\/center> <span class='basic_left'> Theo c\u00e2u 1, ta \u0111\u00e3 ch\u1ee9ng minh \u0111\u01b0\u1ee3c: $BDEC$ l\u00e0 h\u00ecnh thang. <br\/> $\\Rightarrow \\widehat{B}+\\widehat{BDE}=180^o$ <br\/> $\\Rightarrow \\widehat{BDE}=180^o-70^o=110^o$<br\/> X\u00e9t $\\Delta ABC$: <br\/> $\\widehat{A}+\\widehat{B}+\\widehat{C}=180^o$ (t\u1ed5ng ba g\u00f3c trong tam gi\u00e1c) <br\/> $\\Rightarrow \\widehat{C}=180^o-60^o-70^o=50^o$ <br\/> X\u00e9t trong h\u00ecnh thang $BDEC$: <br\/> $\\widehat{C}+\\widehat{DEC}=180^o$ <br\/> $\\Rightarrow \\widehat{DEC}=180^o-50^o=130^o$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t t\u1eeb tr\u00ean xu\u1ed1ng d\u01b0\u1edbi l\u00e0: $110$ v\u00e0 $130$. <\/span><\/span> "}]}],"id_ques":1360}],"lesson":{"save":0,"level":1}}