{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"\u0110i\u1ec3m c\u00e1ch \u0111\u1ec1u hai \u0111\u1ea7u m\u00fat c\u1ee7a \u0111o\u1ea1n th\u1eb3ng th\u00ec n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng \u0111\u00f3. <b> \u0110\u00fang <\/b> hay <b> sai <\/b>? ","select":["A. \u0110\u00daNG ","B. SAI"],"hint":"D\u1ef1a v\u00e0o t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng","explain":" Theo \u0111\u1ecbnh l\u00fd \u0111\u1ea3o v\u1ec1 t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng: \u0110i\u1ec3m c\u00e1ch \u0111\u1ec1u hai \u0111\u1ea7u m\u00fat c\u1ee7a \u0111o\u1ea1n th\u1eb3ng th\u00ec n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng \u0111\u00f3 <br\/> V\u1eady kh\u1eb3ng \u0111\u1ecbnh tr\u00ean l\u00e0 <span class='basic_pink'> \u0110\u00daNG <\/span> ","column":2}]}],"id_ques":1951},{"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":"T\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m c\u00e1ch \u0111\u1ec1u hai \u0111\u1ea7u m\u00fat c\u1ee7a m\u1ed9t \u0111o\u1ea1n th\u1eb3ng l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng \u0111\u00f3. <b> \u0110\u00fang <\/b> hay <b> sai <\/b>? ","select":["A. \u0110\u00daNG ","B. SAI"],"hint":"D\u1ef1a v\u00e0o t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng","explain":" T\u1eeb \u0111\u1ecbnh l\u00fd thu\u1eadn v\u00e0 \u0111\u1ea3o v\u1ec1 t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng, ta c\u00f3: T\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m c\u00e1ch \u0111\u1ec1u hai \u0111\u1ea7u m\u00fat c\u1ee7a m\u1ed9t \u0111o\u1ea1n th\u1eb3ng l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng \u0111\u00f3. <br\/> V\u1eady kh\u1eb3ng \u0111\u1ecbnh tr\u00ean l\u00e0 <span class='basic_pink'> \u0110\u00daNG <\/span> ","column":2}]}],"id_ques":1952},{"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: <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai22/lv1/img\/H7C3B22_D01.png' \/><\/center> <br\/> B\u1ea1n Lan v\u1ebd \u0111\u01b0\u1eddng trung tr\u1ef1c $MN$ c\u1ee7a \u0111o\u1ea1n th\u1eb3ng $AB$ nh\u01b0 tr\u00ean h\u00ecnh v\u1ebd (cung tr\u00f2n t\u00e2m $A$ v\u00e0 cung tr\u00f2n t\u00e2m $B$ c\u00f3 c\u00f9ng b\u00e1n k\u00ednh). <b> \u0110\u00fang <\/b> hay <b> sai <\/b>? ","select":["A. \u0110\u00daNG ","B. SAI"],"hint":"","explain":" <span class='basic_left'> Ta c\u00f3 th\u1ec3 v\u1ebd \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng $AB$ nh\u01b0 sau: <br\/> +) L\u1ea5y $A$ l\u00e0m t\u00e2m v\u1ebd cung tr\u00f2n b\u00e1n k\u00ednh l\u1edbn h\u01a1n $\\dfrac{1}{2}AB$, sau \u0111\u00f3 l\u1ea5y $B$ l\u00e0m t\u00e2m v\u1ebd cung tr\u00f2n c\u00f9ng b\u00e1n k\u00ednh \u0111\u00f3. Hai cung tr\u00f2n n\u00e0y c\u1eaft nhau t\u1ea1i hai \u0111i\u1ec3m g\u1ecdi l\u00e0 $M$ v\u00e0 $N$ <br\/> +) D\u00f9ng th\u01b0\u1edbc th\u1eb3ng v\u1ebd \u0111\u01b0\u1eddng th\u1eb3ng $MN$, \u0111\u00f3 l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng $AB$ <br\/> Do \u0111\u00f3 c\u00e1ch v\u1ebd c\u1ee7a b\u1ea1n Lan l\u00e0 <span class='basic_pink'> \u0110\u00daNG <\/span> <br\/> <span class='basic_green'> <i> L\u01b0u \u00fd: <br\/> +) Khi v\u1ebd hai cung tr\u00f2n tr\u00ean ta ph\u1ea3i l\u1ea5y b\u00e1n k\u00ednh l\u1edbn h\u01a1n $\\dfrac{1}{2}AB$ th\u00ec hai cung tr\u00f2n \u0111\u00f3 m\u1edbi c\u00f3 hai \u0111i\u1ec3m chung <br\/> +) Giao \u0111i\u1ec3m c\u1ee7a $AB$ v\u00e0 $MN$ c\u0169ng ch\u00ednh l\u00e0 trung \u0111i\u1ec3m c\u1ee7a \u0111o\u1ea1n th\u1eb3ng $AB$ n\u00ean c\u00e1ch v\u1ebd tr\u00ean c\u0169ng ch\u00ednh l\u00e0 c\u00e1ch d\u1ef1ng trung \u0111i\u1ec3m c\u1ee7a \u0111o\u1ea1n th\u1eb3ng b\u1eb1ng th\u01b0\u1edbc v\u00e0 compa <\/i> <\/span> ","column":2}]}],"id_ques":1953},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["3"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" G\u1ecdi $I$ l\u00e0 \u0111i\u1ec3m n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng $AB$. Cho \u0111o\u1ea1n th\u1eb3ng $IA$ c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng $3cm$. H\u1ecfi \u0111\u1ed9 d\u00e0i $IB$ b\u1eb1ng bao nhi\u00eau? <br\/> <b> \u0110\u00e1p \u00e1n l\u00e0: <\/b> $IB = $ _input_ $cm$ ","hint":"","explain":" V\u00ec $I$ n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng $AB$ n\u00ean $IA = IB = 3cm$ <br\/> <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n l\u00e0: $3$ <\/span> "}]}],"id_ques":1954},{"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 hai \u0111i\u1ec3m $M; N$ n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng $AB$, g\u1ecdi $H$ l\u00e0 giao \u0111i\u1ec3m c\u1ee7a $AB$ v\u00e0 $MN$. <br\/> Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y \u0111\u00fang? ","select":["A. $MA = MB$ ","B. $AH = HB$ ","C. $\\triangle{AMN} = \\triangle{BMN}$ ","D. C\u1ea3 $3$ \u0111\u00e1p \u00e1n tr\u00ean \u0111\u1ec1u \u0111\u00fang "],"hint":"D\u1ef1a v\u00e0o t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng","explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai22/lv1/img\/H7C3B22_D02.png' \/><\/center> <br\/> Theo gi\u1ea3 thi\u1ebft $M, N$ thu\u1ed9c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng $AB$ v\u00e0 $H$ l\u00e0 giao \u0111i\u1ec3m c\u1ee7a $AB$ v\u00e0 $MN$ <br\/> Suy ra, $HA = HB$, $MA = MB$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c) <br\/> X\u00e9t $\\triangle{AMN}$ v\u00e0 $\\triangle{BMN}$ c\u00f3: <br\/> $MA = MB$ <br\/> $NA = NB$ <br\/> $MN$ l\u00e0 c\u1ea1nh chung <br\/> $\\Rightarrow$ $\\triangle{AMN} = \\triangle{BMN}$ (c.c.c) <br\/> <span class='basic_pink'> Do \u0111\u00f3 \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D <\/span> ","column":2}]}],"id_ques":1955},{"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":"Hai \u0111i\u1ec3m $M$ v\u00e0 $N$ thu\u1ed9c n\u1eeda m\u1eb7t ph\u1eb3ng c\u00f3 b\u1edd ch\u1ee9a \u0111\u01b0\u1eddng th\u1eb3ng $xy$. L\u1ea5y \u0111i\u1ec3m $L$ \u0111\u1ed1i x\u1ee9ng v\u1edbi \u0111i\u1ec3m $M$ qua $xy$. G\u1ecdi $I$ l\u00e0 m\u1ed9t \u0111i\u1ec3m b\u1ea5t k\u00ec thu\u1ed9c $xy$. H\u00e3y so s\u00e1nh $IM + IN$ v\u1edbi $LN$. ","select":["A. $IM + IN < LN$ ","B. $IM + IN \\geq LN$ "],"hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Ch\u1ec9 ra $IM = IL$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> Ch\u1ec9 ra $IN + IL \\geq LN$ <br\/> <b> B\u01b0\u1edbc 3: <\/b> T\u1eeb b\u01b0\u1edbc 1 v\u00e0 b\u01b0\u1edbc 2 suy ra \u0111\u01b0\u1ee3c $IM + IN \\geq LN$ <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai22/lv1/img\/H7C3B22_D03.png' \/><\/center> Theo gi\u1ea3 thi\u1ebft $L$ \u0111\u1ed1i x\u1ee9ng v\u1edbi $M$ qua $xy$ <br\/> N\u00ean $xy$ l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $ML$ <br\/> V\u00ec $I \\in xy$ (gt) n\u00ean $IM = IL$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng) (1) <br\/> V\u1edbi ba \u0111i\u1ec3m $I; L; N$ ta c\u00f3: $IL + IN \\geq LN$ (2) <br\/> T\u1eeb (1) v\u00e0 (2), ta c\u00f3: $IM + IN \\geq MN$ <br\/> G\u1ecdi $O$ l\u00e0 giao \u0111i\u1ec3m c\u1ee7a $LN$ v\u00e0 $xy$; $IM + IN = LN$ $\\Leftrightarrow$ $I \\equiv O$ <br\/> <span class='basic_pink'> Do \u0111\u00f3 \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: B <\/span> <br\/> ","column":2}]}],"id_ques":1956},{"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 $MA = MB$. Khi \u0111\u00f3 $M$ thu\u1ed9c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AB$. <b> \u0110\u00fang <\/b> hay <b> sai <\/b>? ","select":["A. \u0110\u00daNG ","B. SAI "],"hint":"X\u00e9t hai tr\u01b0\u1eddng h\u1ee3p $M \\in AB$ v\u00e0 $M \\notin AB$","explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai22/lv1/img\/H7C3B22_D04.png' \/><\/center> <b> Tr\u01b0\u1eddng h\u1ee3p 1: <\/b> N\u1ebfu $M \\in AB$ th\u00ec v\u00ec $MA = MB$ (gt) suy ra $M$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$ (\u0111\u1ecbnh ngh\u0129a) <br\/> Do \u0111\u00f3 $M$ thu\u1ed9c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AB$ <br\/> <b> Tr\u01b0\u1eddng h\u1ee3p 2: <\/b> $M \\notin AB$, k\u1ebb $MH \\perp AB$ <br\/> X\u00e9t tam gi\u00e1c vu\u00f4ng $AMH$ v\u00e0 tam gi\u00e1c vu\u00f4ng $BMH$ c\u00f3: <br\/> $MH$ chung <br\/> $MA = MB$ (gt) <br\/> $\\Rightarrow$ $\\triangle{AMH} = \\triangle{BMH}$ (c\u1ea1nh huy\u1ec1n - c\u1ea1nh g\u00f3c vu\u00f4ng) <br\/> $\\Rightarrow$ $HA = HB$ (hai c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) <br\/> $\\Rightarrow$ $MH$ l\u00e0 trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng $AB$ (\u0111\u1ecbnh ngh\u0129a) <br\/> V\u1eady kh\u1eb3ng \u0111\u1ecbnh $M$ thu\u1ed9c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AB$ l\u00e0 <span class='basic_pink'> \u0110\u00daNG <\/span> <br\/> <span class='basic_green'> <i> Nh\u1eadn x\u00e9t: Nh\u01b0 v\u1eady \u0111\u1ec3 ch\u1ee9ng minh \u0111\u01b0\u1eddng th\u1eb3ng $d$ l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng $AB$ ch\u00fang ta c\u00f3 th\u1ec3 l\u1ef1a ch\u1ecdn m\u1ed9t trong hai c\u00e1ch sau: <br\/> +) C\u00e1ch 1: Ch\u1ee9ng minh $d$ \u0111i qua trung \u0111i\u1ec3m $M$ c\u1ee7a $AB$ v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi $AB$ <br\/> +) C\u00e1ch 2: L\u1ea5y hai \u0111i\u1ec3m $P$, $Q$ tr\u00ean $d$. Ta \u0111i ch\u1ee9ng minh $PA = PB$ v\u00e0 $QA = QB$ <\/i> <\/span> ","column":2}]}],"id_ques":1957},{"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 $MNP$ vu\u00f4ng t\u1ea1i $M$ c\u00f3 \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c $PE$. K\u1ebb $EH$ vu\u00f4ng g\u00f3c v\u1edbi $NP$ ($H \\in NP$), g\u1ecdi $K$ l\u00e0 giao \u0111i\u1ec3m c\u1ee7a $PM$ v\u00e0 $HE$. Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y \u0111\u00fang?","select":["A. $\\triangle{PME} = \\triangle{PHE}$","B. $PE$ l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $MH$ ","C. $KE = NE$","D. C\u1ea3 3 \u0111\u00e1p \u00e1n tr\u00ean \u0111\u1ec1u \u0111\u00fang"],"hint":"","explain":" <span class='basic_left'> <span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b> B\u01b0\u1edbc 1: <\/b> X\u00e9t $\\triangle{PME}$ v\u00e0 $\\triangle{PHE}$ <br\/> <b> B\u01b0\u1edbc 2: <\/b>So s\u00e1nh c\u00e1c c\u1eb7p \u0111o\u1ea1n th\u1eb3ng $PM; PH$ v\u00e0 $ME; HE$ <br\/> <b> B\u01b0\u1edbc 3: <\/b> X\u00e9t $\\triangle{MEK}$ v\u00e0 $\\triangle{HEN}$ <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai22/lv1/img\/H7C3B22_D06.png' \/><\/center> <br\/> $\\blacktriangleright$ X\u00e9t hai tam gi\u00e1c vu\u00f4ng $\\triangle{PME}$ v\u00e0 $\\triangle{PHE}$ c\u00f3: <br\/> $\\begin{cases} PE \\hspace{0,2cm} \\text{chung} \\\\ \\widehat{P_{1}} = \\widehat{P_{2}} (gt) \\end{cases}$ <br\/>$\\Rightarrow$ $\\triangle{PME} = \\triangle{PHE}$ (c\u1ea1nh huy\u1ec1n - g\u00f3c nh\u1ecdn) $\\Rightarrow$ <b> (\u0110\u00e1p \u00e1n A \u0111\u00fang) <\/b> <br\/> $\\blacktriangleright$ Ta c\u00f3: $PM = PH$ v\u00e0 $ME = HE$ (v\u00ec $\\triangle{PME} = \\triangle{PHE}$) <br\/> $\\Rightarrow$ $PE$ l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $MH$ (t\u00ednh ch\u1ea5t) $\\Rightarrow$ <b> (\u0110\u00e1p \u00e1n B \u0111\u00fang) <\/b> <br\/> $\\blacktriangleright$ X\u00e9t hai tam gi\u00e1c vu\u00f4ng $\\triangle{MEK}$ v\u00e0 $\\triangle{HEN}$ c\u00f3: <br\/> $\\begin{cases} \\widehat{E_{1}} = \\widehat{E_{2}} (\\text{\u0111\u1ed1i} \\hspace{0,2cm} \\text{\u0111\u1ec9nh}) \\\\ ME = EH (\\triangle{PME} = \\triangle{PHE}) \\end{cases}$ <br\/> $\\Rightarrow$ $\\triangle{MEK} = \\triangle{HEN}$ (c\u1ea1nh g\u00f3c vu\u00f4ng - g\u00f3c nh\u1ecdn) <br\/> $\\Rightarrow$ $KE = NE$ (hai c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) $\\Rightarrow$ <b> (\u0110\u00e1p \u00e1n C \u0111\u00fang) <\/b> <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n ph\u1ea3i ch\u1ecdn l\u00e0: D <\/span> ","column":2}]}],"id_ques":1958},{"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 tam gi\u00e1c $ABC$. Hai \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AB$ v\u00e0 $AC$ c\u1eaft nhau t\u1ea1i $O$. B\u1ea1n Mai kh\u1eb3ng \u0111\u1ecbnh $O$ kh\u00f4ng thu\u1ed9c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $BC$. <b> \u0110\u00fang <\/b> hay <b> sai <\/b>?","select":["A. \u0110\u00daNG","B. SAI "],"hint":"So s\u00e1nh $OB$ v\u00e0 $OC$","explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai22/lv1/img\/H7C3B22_D07.png' \/><\/center> <br\/> G\u1ecdi $K; H$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB; AC$ <br\/> Ta c\u00f3: $OK$ l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AB$ (gt) $\\Rightarrow$ $OA = OB$ (1) <br\/> $OH$ l\u00e0 \u0111\u01b0\u1eddng trug tr\u1ef1c c\u1ee7a $AC$ (gt) $\\Rightarrow$ $OA = OC$ (2) <br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow$ $OB = OC$ n\u00ean $O$ thu\u1ed9c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $BC$ (\u0111\u1ecbnh l\u00fd \u0111\u1ea3o) <br\/> V\u1eady kh\u1eb3ng \u0111\u1ecbnh $O$ kh\u00f4ng thu\u1ed9c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $BC$ l\u00e0 <span class='basic_pink'> SAI <\/span> ","column":2}]}],"id_ques":1959},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["40"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" Cho tam gi\u00e1c $ABC$ c\u00f3 $\\widehat{B} - \\widehat{C} = 40^{o}$. \u0110\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $BC$ c\u1eaft $AC$ \u1edf $I$. T\u00ednh s\u1ed1 \u0111o g\u00f3c $ABI$. <br\/> <b> \u0110\u00e1p \u00e1n l\u00e0: <\/b> $\\widehat{ABI}$ _input_ $^o$ ","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 $\\widehat{IBC} = \\widehat{C}$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ednh $\\widehat{ABI}$ <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai22/lv1/img\/H7C3B22_D08.png' \/><\/center> <br\/> V\u00ec $I$ thu\u1ed9c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $BC$ (gt) <br\/> Suy ra: $IB = IC$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c) <br\/> $\\triangle{BIC}$ c\u00f3 $IB = IC$ n\u00ean $\\triangle{BIC}$ c\u00e2n t\u1ea1i $I$ (\u0111\u1ecbnh ngh\u0129a) <br\/> $\\Rightarrow$ $\\widehat{C} = \\widehat{B_{2}}$ (t\u00ednh ch\u1ea5t tam gi\u00e1c c\u00e2n) <br\/> Ta c\u00f3: $\\widehat{ABI} = \\widehat{ABC} - \\widehat{B_{2}} = \\widehat{ABC} - \\widehat{C} = 40^{o}$ (v\u00ec $\\widehat{B_{2}} = \\widehat{C}$) <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n l\u00e0: $40$ <\/span> "}]}],"id_ques":1960},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["20"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" Tam gi\u00e1c $ABC$ c\u00f3 $AB = 12cm; BC = 8cm$. Qua trung \u0111i\u1ec3m $M$ c\u1ee7a $AC$, k\u1ebb \u0111\u01b0\u1eddng vu\u00f4ng g\u00f3c v\u1edbi $AC$, c\u1eaft $AB$ t\u1ea1i $I$. T\u00ednh chu vi tam gi\u00e1c $IBC$. <br\/> <b> \u0110\u00e1p \u00e1n l\u00e0: <\/b> _input_ $cm$ ","hint":"Ch\u1ec9 ra $IM$ l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AC$","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 $IM$ l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AC$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u1eeb b\u01b0\u1edbc 1 suy ra $IC = IA$, t\u1eeb \u0111\u00f3 t\u00ednh chu vi tam gi\u00e1c $IBC$ <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai22/lv1/img\/H7C3B22_D09.png' \/><\/center> <br\/> Ta c\u00f3: $MA = MC$ (gt) v\u00e0 $MI \\perp AC$ <br\/> $\\Rightarrow$ $MI$ l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AC$ (\u0111\u1ecbnh ngh\u0129a) <br\/> $\\Rightarrow$ $IA = IC$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c) <br\/> Chu vi tam gi\u00e1c $IBC$ b\u1eb1ng: <br\/> $IB + IC + BC = IB + IA + BC = AB + BC = 12 + 8 = 20 (cm)$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n l\u00e0: $20$ <\/span> "}]}],"id_ques":1961},{"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":"Tr\u00ean \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng $PQ$ l\u1ea5y hai \u0111i\u1ec3m ph\u00e2n bi\u1ec7t $M; N$. Khi \u0111\u00f3 kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y \u0111\u00fang?","select":["A. $\\widehat{MNP} \\neq \\widehat{MNQ}$ ","B. $\\widehat{PMN} \\neq \\widehat{QMN}$ ","C. $\\widehat{MPN} \\neq \\widehat{MQN}$ ","D. $\\triangle{MNP} = \\triangle{MNQ}$ "],"hint":"D\u1ef1a v\u00e0o t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng","explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai22/lv1/img\/H7C3B22_D10.png' \/><\/center> <br\/> G\u1ecdi $d$ l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng $PQ$ <br\/> V\u00ec $M; N \\in d$ n\u00ean $MP = MQ; NP = NQ$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c) <br\/> X\u00e9t $\\triangle{MNP}$ v\u00e0 $\\triangle{MNQ}$ c\u00f3: <br\/> $\\begin{cases} MP = MQ \\\\ NP = NQ \\\\ MN \\hspace{0,2cm} \\text{chung} \\end{cases}$ <br\/> $\\Rightarrow$ $\\triangle{MNP} = \\triangle{MNQ}$ (c.c.c) $\\Rightarrow$ <b> D \u0111\u00fang <\/b> <br\/> $\\Rightarrow$ $\\widehat{MNP} = \\widehat{MNQ}$ (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng) $\\Rightarrow$ <b> A sai <\/b> <br\/> $\\widehat{PMN} = \\widehat{QMN}$ (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng) $\\Rightarrow$ <b> B sai <\/b> <br\/> $\\widehat{MPN} = \\widehat{MQN}$ (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng) $\\Rightarrow$ <b> C sai <\/b> <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D <\/span> ","column":2}]}],"id_ques":1962},{"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: <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai22/lv1/img\/H7C3B22_D11.png' \/><\/center> <br\/> H\u00e3y ch\u1ecdn kh\u1eb3ng \u0111\u1ecbnh \u0111\u00fang?","select":["A. $AN$ l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng $MH$ ","B. $MH$ l\u00e0 \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{AMN}$ ","C. $MH$ l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AN$ ","D. $\\widehat{AMH} = \\widehat{NMH}$ "],"hint":"D\u1ef1a v\u00e0o t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng v\u00e0 \u0111\u1ecbnh ngh\u0129a \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c","explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai22/lv1/img\/H7C3B22_D11A.png' \/><\/center> <br\/> $\\blacktriangleright$ Ta c\u00f3 $AM = AH$ (gt) <br\/> $\\Rightarrow$ $A$ thu\u1ed9c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng $MH$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c) (1) <br\/> $NM = NH$ (gt) <br\/> $\\Rightarrow$ $N$ thu\u1ed9c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng $MH$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c) (2) <br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow$ $AN$ l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $MH$ $\\Rightarrow$ <b> \u0110\u00e1p \u00e1n A \u0111\u00fang <\/b> <br\/> $\\blacktriangleright$ Tr\u00ean tia \u0111\u1ed1i c\u1ee7a tia $OA$ l\u1ea5y \u0111i\u1ec3m $I$ sao cho $MA = MI$ <br\/> X\u00e9t $\\triangle{AMI}$ c\u00f3 $MA = MI$ n\u00ean $\\triangle{AMI}$ c\u00e2n t\u1ea1i $M$ <br\/> C\u00f3 $MO \\perp AI$ ($AN$ l\u00e0 trung tr\u1ef1c c\u1ee7a $MH$) <br\/> $\\Rightarrow$ $MO$ l\u00e0 \u0111\u01b0\u1eddng cao c\u1ee7a $\\triangle{AMI}$ <br\/> $\\Rightarrow$ $MO$ l\u00e0 \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{AMI}$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng cao xu\u1ea5t ph\u00e1t t\u1eeb \u0111\u1ec9nh trong tam gi\u00e1c c\u00e2n) (3)<br\/> V\u00ec $MI = MA$ m\u00e0 $MA \\neq MN$ n\u00ean $MI \\neq MN$ (4) <br\/> T\u1eeb (3) v\u00e0 (4) $\\Rightarrow$ $MH$ kh\u00f4ng l\u00e0 \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{AMN}$ $\\Rightarrow$ <b> \u0110\u00e1p \u00e1n B; D sai <\/b> <br\/> $\\blacktriangleright$ V\u00ec $MA \\ne MN$ (gt) $\\Rightarrow$ $M$ kh\u00f4ng thu\u1ed9c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AN$ <br\/> $\\Rightarrow$ $MH$ kh\u00f4ng l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AN$ $\\Rightarrow$ <b> \u0110\u00e1p \u00e1n C sai <\/b> <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: A <\/span> ","column":2}]}],"id_ques":1963},{"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":" \u0110\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a c\u1ea1nh $DF$ trong tam gi\u00e1c $DEF$ c\u1eaft c\u1ea1nh $EF$ t\u1ea1i $M$. Bi\u1ebft $DM = 10cm, EF = 13cm$. Khi \u0111\u00f3, \u0111\u1ed9 d\u00e0i c\u1ea1nh $EM$ v\u00e0 $MF$ b\u1eb1ng bao nhi\u00eau? ","select":["A. $EM = 8cm; MF = 5cm$ ","B. $EM = 5cm; MF = 8cm$ ","C. $EM = 3cm; MF = 10cm$ ","D. $EM = 10cm; MF = 3cm$ "],"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 $MD = MF$ r\u1ed3i t\u00ednh $MF$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ednh $ME$ <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai22/lv1/img\/H7C3B22_D12.png' \/><\/center> <br\/> G\u1ecdi $I$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh $DF$ <br\/> V\u00ec $M$ thu\u1ed9c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a c\u1ea1nh $DF$ (gi\u1ea3 thi\u1ebft) n\u00ean $MD = MF$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c) <br\/> $\\Rightarrow$ $MF = MD = 10cm$ <br\/> M\u1eb7t kh\u00e1c v\u00ec $M \\in EF$ n\u00ean $EM + MF = EF$ <br\/> $\\begin{align} \\Rightarrow EM &= EF - MF \\\\ &= 13 - 10 \\\\ &= 3 (cm) \\end{align}$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: C. $EM = 3cm; MF = 10cm$ <\/span> ","column":2}]}],"id_ques":1964},{"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 $HIK$ c\u00f3 $\\widehat{K} = 60^{o}$. \u0110\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a c\u1ea1nh $HK$ c\u1eaft c\u1ea1nh $IK$ t\u1ea1i $E$, g\u1ecdi $D$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh $HK$. H\u00e3y ch\u1ecdn kh\u1eb3ng \u0111\u1ecbnh \u0111\u00fang?","select":["A. $\\triangle{HEK}$ vu\u00f4ng t\u1ea1i $E$ ","B. $\\widehat{HEK} = 120^{o}$ ","C. $DE = DH = DK$ ","D. $\\triangle{HEK}$ \u0111\u1ec1u"],"hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> X\u00e9t $\\widehat{HEK}$ d\u1ef1a v\u00e0o vi\u1ec7c ch\u1ee9ng minh $EH = EK$ <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai22/lv1/img\/H7C3B22_D13.png' \/><\/center> <br\/> V\u00ec $ED$ l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a c\u1ea1nh $HK$ <br\/> $\\Rightarrow$ $ED \\perp HK$ (\u0111\u1ecbnh ngh\u0129a) <br\/> $EH = EK$ (t\u00ednh ch\u1ea5t) <br\/> Tam gi\u00e1c $HEK$ c\u00f3 $EH = EK$ n\u00ean $\\triangle{HEK}$ c\u00e2n t\u1ea1i $E$ (\u0111\u1ecbnh ngh\u0129a) <br\/> $\\triangle{HEK}$ c\u00e2n t\u1ea1i $E$ c\u00f3 $\\widehat{K} = 60^{o}$ $\\Rightarrow$ $\\triangle{HEK}$ \u0111\u1ec1u (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) <br\/> $\\Rightarrow$ $\\widehat{EHK} = \\widehat{HEK} = \\widehat{EKH} = 60^{o}$ (t\u00ednh ch\u1ea5t) <br\/> $\\Rightarrow$ <b> \u0110\u00e1p \u00e1n A, B sai; \u0111\u00e1p \u00e1n D \u0111\u00fang <\/b> <br\/> V\u00ec $\\triangle{HEK}$ kh\u00f4ng ph\u1ea3i tam gi\u00e1c vu\u00f4ng n\u00ean $DE \\neq HD = DK$ <br\/> $\\Rightarrow$ <b> \u0110\u00e1p \u00e1n C sai <\/b> <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D. $\\triangle{HEK}$ \u0111\u1ec1u <\/span> ","column":2}]}],"id_ques":1965},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["36"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" Cho tam gi\u00e1c $HMP$, c\u00e1c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $MH$ v\u00e0 $MP$ c\u1eaft nhau t\u1ea1i $O$. Bi\u1ebft \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n $OM$ l\u00e0 $12cm$. T\u00ednh \u0111\u1ed9 d\u00e0i $OM + OH + OP$ <br\/> <b> \u0110\u00e1p \u00e1n l\u00e0: <\/b> $OM + OH + OP = $ _input_ $cm$ ","hint":"D\u1ef1a v\u00e0o t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c","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 $OM = OH = OP$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ednh $OM + OH + OP$ <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai22/lv1/img\/H7C3B22_D14.png' \/><\/center> <br\/> G\u1ecdi $I$, $K$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $MH; MP$ <br\/> Khi \u0111\u00f3, $IO$ l\u00e0 trung tr\u1ef1c c\u1ee7a $MH$ $\\Rightarrow$ $OM = OH$ (t\u00ednh ch\u1ea5t) (1) <br\/> $KO$ l\u00e0 trung tr\u1ef1c c\u1ee7a $MP$ $\\Rightarrow$ $OM = OP$ (t\u00ednh ch\u1ea5t) (2) <br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow$ $OH = OP = OM = 12cm$ <br\/> $\\Rightarrow$ $OH + OM + OP = 12 + 12 + 12 = 36(cm)$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n l\u00e0: $36$ <\/span> "}]}],"id_ques":1966},{"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: <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai22/lv1/img\/H7C3B22_D15.png' \/><\/center> <br\/> \u0110i\u1ec3m $O$ tr\u00ean h\u00ecnh v\u1ebd thu\u1ed9c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a c\u1ea1nh $AC$. <b> \u0110\u00fang <\/b> hay <b> sai <\/b>? ","select":["A. \u0110\u00daNG ","B. SAI "],"hint":"D\u1ef1a v\u00e0o t\u00ednh ch\u1ea5t ba \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a m\u1ed9t tam gi\u00e1c","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 $OA = OB$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> Ch\u1ee9ng minh $OB = OC$ <br\/> <b> B\u01b0\u1edbc 3: <\/b> Ch\u1ee9ng minh $O$ thu\u1ed9c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a c\u1ea1nh $AC$ <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai22/lv1/img\/H7C3B22_D15.png' \/><\/center> <br\/> Theo h\u00ecnh v\u1ebd ta c\u00f3: <br\/> $\\begin{cases} KA = KB \\\\ OK \\perp AB \\end{cases}$ <br\/> $\\Rightarrow$ $OK$ l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a c\u1ea1nh $AB$ (\u0111\u1ecbnh ngh\u0129a) <br\/> $\\Rightarrow$ $OA = OB$ (t\u00ednh ch\u1ea5t) (1) <br\/> $\\begin{cases} HB = HC \\\\ OH \\perp BC \\end{cases}$ <br\/> $\\Rightarrow$ $OH$ l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a c\u1ea1nh $BC$ (\u0111\u1ecbnh ngh\u0129a) <br\/> $\\Rightarrow$ $OB = OC$ (t\u00ednh ch\u1ea5t) (2)<br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow$ $OA = OC$ do \u0111\u00f3 \u0111i\u1ec3m $O$ n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a c\u1ea1nh $AC$ <br\/> V\u1eady kh\u1eb3ng \u0111\u1ecbnh tr\u00ean l\u00e0 <span class='basic_pink'> \u0110\u00daNG <\/span> ","column":2}]}],"id_ques":1967},{"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":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai22/lv1/img\/H7C3B22_D16.png' \/><\/center> <br\/>Bi\u1ebft $AB < AC$, trong c\u00e1c kh\u1eb3ng \u0111\u1ecbnh sau kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sai? ","select":["A. $MA = MB = MC$ ","B. $KM$ l\u00e0 trung tr\u1ef1c c\u1ee7a $AB$ ","C. $HM$ l\u00e0 trung tr\u1ef1c c\u1ee7a $AC$","D. $AM \\perp HK$"],"hint":"","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai22/lv1/img\/H7C3B22_D16.png' \/><\/center> <br\/> Theo h\u00ecnh v\u1ebd ta c\u00f3: <br\/> $\\blacktriangleright$ $\\triangle{ABC}$ vu\u00f4ng t\u1ea1i $A$ c\u00f3 $MB = MC$ <br\/> $\\Rightarrow$ $AM$ l\u00e0 \u0111\u01b0\u1eddng trung tuy\u1ebfn <br\/> $\\Rightarrow$ $MA = MB = MC$ (t\u00ednh ch\u1ea5t trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) <br\/> $\\Rightarrow$ <b> \u0110\u00e1p \u00e1n A \u0111\u00fang <\/b> <br\/> $\\blacktriangleright$ X\u00e9t hai tam gi\u00e1c vu\u00f4ng $MHA$ v\u00e0 $MHC$ c\u00f3: <br\/> $\\begin{cases} MH \\hspace{0,2cm} \\text{chung} \\\\ MA = MC \\end{cases}$ <br\/> $\\Rightarrow$ $\\triangle{MHA} = \\triangle{MHC}$ (c\u1ea1nh huy\u1ec1n - c\u1ea1nh g\u00f3c vu\u00f4ng) <br\/> $\\Rightarrow$ $HA = HC$ (hai c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) <br\/> V\u00ec $\\begin{cases} MH \\perp AC (gt) \\\\ HA = HC \\end{cases}$ $\\Rightarrow$ $HM$ l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a c\u1ea1nh $AC$ (\u0111\u1ecbnh ngh\u0129a) <br\/> $\\Rightarrow$ <b> \u0110\u00e1p \u00e1n C \u0111\u00fang <\/b> <br\/> $\\blacktriangleright$ Ch\u1ee9ng minh t\u01b0\u01a1ng t\u1ef1 ta c\u00f3 $KM$ l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a c\u1ea1nh $AB$ <br\/> $\\Rightarrow$ <b> \u0110\u00e1p \u00e1n B \u0111\u00fang <\/b> <br\/> $\\blacktriangleright$ Theo gi\u1ea3 thi\u1ebft $AB < AC$ (1) <br\/> $\\triangle{ABC}$ c\u00f3: $HC = HA = \\dfrac{1}{2}AC$ ($HM$ l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AC$) (2) <br\/> $KA = KB = \\dfrac{1}{2}AB$ ($KM$ l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AB$) (3)<br\/> T\u1eeb (1), (2), (3) $\\Rightarrow$ $KA < HA$ <br\/> T\u1ee9 gi\u00e1c $AKMH$ c\u00f3 $\\widehat{MKA} = \\widehat{KAH} = \\widehat{AHM} = 90^{o}$ v\u00e0 $KA < HA$ <br\/> Suy ra t\u1ee9 gi\u00e1c $AHMK$ kh\u00f4ng ph\u1ea3i h\u00ecnh vu\u00f4ng <br\/> N\u00ean $AM$ kh\u00f4ng vu\u00f4ng g\u00f3c v\u1edbi $KH$ <br\/> $\\Rightarrow$ <b> \u0110\u00e1p \u00e1n D sai <\/b> <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n sai l\u00e0: D <\/span> ","column":2}]}],"id_ques":1968},{"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 \u0111o\u1ea1n th\u1eb3ng $AB = 6cm$, $M$ l\u00e0 \u0111i\u1ec3m n\u1eb1m tr\u00ean trung tr\u1ef1c c\u1ee7a $AB$, $I$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$, $MA = 5cm$. Nh\u01b0 v\u1eady k\u1ebft qu\u1ea3 n\u00e0o trong c\u00e1c k\u1ebft qu\u1ea3 sau \u0111\u00e2y l\u00e0 sai? ","select":["A. $MB = 5cm$ ","B. $MI = MA = MB$ ","C. $MI = 4cm$","D. $\\widehat{AMI} = \\widehat{BMI}$"],"hint":"","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai22/lv1/img\/H7C3B22_D17.png' \/><\/center> <br\/> $\\blacktriangleright$ $M$ thu\u1ed9c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AB$ (gt) n\u00ean $MB = MA = 5cm$ <b> (\u0110\u00e1p \u00e1n A \u0111\u00fang) <\/b> <br\/> $\\blacktriangleright$ $I$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$ n\u00ean $IA = IB = \\dfrac{AB}{2} = \\dfrac{6}{2} = 3(cm)$ <br\/> $\\triangle{AMI}$ vu\u00f4ng t\u1ea1i $I$, c\u00f3: <br\/> $MI^2 + AI^2 = AM^2$ (\u0111\u1ecbnh l\u00fd Pitago) <br\/> $\\Rightarrow$ $MI^2 = AM^2 - AI^2 = 5^2 - 3^2 = 16$ <br\/> Suy ra $MI = 4cm$ <b> (\u0110\u00e1p \u00e1n C \u0111\u00fang) <\/b> <br\/> $\\blacktriangleright$ $\\triangle{AMB}$ c\u00f3 $MA = MB$ n\u00ean c\u00e2n t\u1ea1i $M$ (\u0111\u1ecbnh ngh\u0129a) <br\/> $\\Rightarrow$ $MI$ v\u1eeba l\u00e0 trung tuy\u1ebfn v\u00e0 l\u00e0 \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $AMB$ (t\u00ednh ch\u1ea5t) <br\/> $\\Rightarrow$ $\\widehat{AMI} = \\widehat{BMI}$ (\u0111\u1ecbnh ngh\u0129a) <b> (\u0110\u00e1p \u00e1n D \u0111\u00fang) <\/b> <br\/> $\\blacktriangleright$ $MI \\neq MA = MB$ (v\u00ec $4 \\neq 5$) <b> (\u0110\u00e1p \u00e1n B sai) <\/b>) <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n sai l\u00e0: B <\/span> ","column":2}]}],"id_ques":1969},{"time":24,"part":[{"title":"H\u00e3y s\u1eafp x\u1ebfp c\u00e1c \u00fd sau \u0111\u1ec3 \u0111\u01b0\u1ee3c th\u1ee9 t\u1ef1 \u0111\u00fang","title_trans":" Cho tam gi\u00e1c $ABC$ kh\u00f4ng l\u00e0 tam gi\u00e1c vu\u00f4ng. \u0110\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a c\u1ea1nh $AB$ v\u00e0 $AC$ c\u1eaft nhau t\u1ea1i $O$, c\u1eaft c\u1ea1nh $BC$ l\u1ea7n l\u01b0\u1ee3t \u1edf $M$ v\u00e0 $N$. H\u00e3y s\u1eafp x\u1ebfp c\u00e1c \u00fd ch\u1ee9ng minh $AO$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $MAN$.","temp":"sequence","correct":[[[3],[6],[1],[5],[2],[4]]],"list":[{"point":5,"image":"https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai22/lv1/img\/H7C3B22_D18.png","left":["$\\Rightarrow$ $\\widehat{A_{1}} = \\widehat{B_{1}}$ (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng) (1) "," T\u1eeb (1), (2), (3) $\\Rightarrow$ $\\widehat{A_{1}} = \\widehat{A_{2}}$, v\u1eady $AO$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $MAN$","Theo gi\u1ea3 thi\u1ebft $M$ v\u00e0 $O$ thu\u1ed9c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AB$ n\u00ean ta c\u00f3: <br\/> $MA = MB$ v\u00e0 $OA = OB$ (t\u00ednh ch\u1ea5t) ","$\\triangle{OBC}$ c\u00f3 $OB = OC$ (c\u00f9ng b\u1eb1ng $OA$) n\u00ean $\\triangle{OBC}$ c\u00e2n t\u1ea1i $B$ (\u0111\u1ecbnh ngh\u0129a) <br\/> $\\Rightarrow$ $\\widehat{B_{1}} = \\widehat{C_{1}}$ (t\u00ednh ch\u1ea5t) (3) ","X\u00e9t $\\triangle{OMA}$ v\u00e0 $\\triangle{OMB}$ c\u00f3: <br\/> $\\begin{cases} OA = OB \\\\ MA = MB \\\\ MO \\hspace{0,2cm} \\text{chung} \\end{cases}$ $\\Rightarrow$ $\\triangle{OMA} = \\triangle{OMB}$ (c.c.c) "," Ch\u1ee9ng minh t\u01b0\u01a1ng t\u1ef1 ta \u0111\u01b0\u1ee3c $\\widehat{A_{2}} = \\widehat{C_{1}}$ (2) "],"top":110,"hint":"Ch\u1ee9ng minh $\\widehat{MAO} = \\widehat{NAO}$","explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai22/lv1/img\/H7C3B22_D18.png' \/><\/center> <br\/> $\\blacktriangleright$ Theo gi\u1ea3 thi\u1ebft $M$ v\u00e0 $O$ thu\u1ed9c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AB$ n\u00ean ta c\u00f3: <br\/> $MA = MB$ v\u00e0 $OA = OB$ (t\u00ednh ch\u1ea5t) <br\/> $\\blacktriangleright$ X\u00e9t $\\triangle{OMA}$ v\u00e0 $\\triangle{OMB}$ c\u00f3: <br\/> $\\begin{cases} OA = OB \\\\ MA = MB \\\\ MO \\hspace{0,2cm} \\text{chung} \\end{cases}$ <br\/> $\\Rightarrow$ $\\triangle{OMA} = \\triangle{OMB}$ (c.c.c) <br\/> $\\Rightarrow$ $\\widehat{A_{1}} = \\widehat{B_{1}}$ (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng) (1) <br\/> Ch\u1ee9ng minh t\u01b0\u01a1ng t\u1ef1 ta \u0111\u01b0\u1ee3c $\\widehat{A_{2}} = \\widehat{C_{1}}$ (2) <br\/> $\\blacktriangleright$ $\\triangle{OBC}$ c\u00f3 $OB = OC$ n\u00ean $\\triangle{OBC}$ c\u00e2n t\u1ea1i $B$ (\u0111\u1ecbnh ngh\u0129a) <br\/> $\\Rightarrow$ $\\widehat{B_{1}} = \\widehat{C_{1}}$ (t\u00ednh ch\u1ea5t) (3) <br\/> $\\blacktriangleright$ T\u1eeb (1), (2), (3) $\\Rightarrow$ $\\widehat{A_{1}} = \\widehat{A_{2}}$, v\u1eady $AO$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $MAN$"}]}],"id_ques":1970}],"lesson":{"save":0,"level":1}}