{"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":" <span class='basic_left'> Ch\u1ecdn kh\u1eb3ng \u0111\u1ecbnh sai trong c\u00e1c kh\u1eb3ng \u0111\u1ecbnh sau: <\/span>","select":["A. H\u00ecnh b\u00ecnh h\u00e0nh l\u00e0 t\u1ee9 gi\u00e1c c\u00f3 hai \u0111\u01b0\u1eddng ch\u00e9o b\u1eb1ng nhau v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi nhau ","B. H\u00ecnh b\u00ecnh h\u00e0nh l\u00e0 t\u1ee9 gi\u00e1c c\u00f3 c\u00e1c c\u1ea1nh \u0111\u1ed1i b\u1eb1ng nhau","C. H\u00ecnh b\u00ecnh h\u00e0nh l\u00e0 t\u1ee9 gi\u00e1c c\u00f3 c\u00e1c g\u00f3c \u0111\u1ed1i b\u1eb1ng nhau ","D. H\u00ecnh b\u00ecnh h\u00e0nh l\u00e0 t\u1ee9 gi\u00e1c c\u00f3 c\u00e1c c\u1ea1nh \u0111\u1ed1i song song "],"explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv1/img\/H814_D2_1a.jpg' \/><\/center> C\u00e2u A sai. Trong h\u00ecnh b\u00ecnh h\u00e0nh hai \u0111\u01b0\u1eddng ch\u00e9o kh\u00f4ng b\u1eb1ng nhau v\u00e0 c\u0169ng kh\u00f4ng vu\u00f4ng g\u00f3c v\u1edbi nhau. <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A. <\/span><\/span> ","column":1}]}],"id_ques":1371},{"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'> Theo d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft th\u00ec kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y sai? <\/span>","select":["A. T\u1ee9 gi\u00e1c c\u00f3 hai c\u1eb7p c\u1ea1nh \u0111\u1ed1i song song l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh ","B. H\u00ecnh thang c\u00f3 hai g\u00f3c k\u1ec1 m\u1ed9t \u0111\u00e1y b\u1eb1ng nhau l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh","C. T\u1ee9 gi\u00e1c c\u00f3 hai c\u1eb7p c\u1ea1nh \u0111\u1ed1i b\u1eb1ng nhau l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh ","D. T\u1ee9 gi\u00e1c c\u00f3 hai c\u1eb7p g\u00f3c \u0111\u1ed1i b\u1eb1ng nhau l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh"],"explain":" <span class='basic_left'> C\u00e2u B sai. V\u00ec: H\u00ecnh thang c\u00f3 hai g\u00f3c k\u1ec1 m\u1ed9t \u0111\u00e1y b\u1eb1ng nhau l\u00e0 h\u00ecnh thang c\u00e2n. <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B. <\/span><\/span> ","column":1}]}],"id_ques":1372},{"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'> T\u1ee9 gi\u00e1c $ABCD$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh n\u1ebfu: <\/span>","select":["A. $\\widehat{A}=\\widehat{C}$ ","B. $AB=CD; BC=AD$","C. $AB\/\/CD$ ","D. $BC=AD$"],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv1/img\/H814_D2_1.jpg' \/><\/center> <span class='basic_left'> T\u1ee9 gi\u00e1c $ABCD$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh n\u1ebfu: $AB=CD; BC=AD$. <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B. <\/span><\/span> ","column":2}]}],"id_ques":1373},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["D"],["C"]]],"list":[{"point":5,"width":20,"type_input":"","ques":"<span class='basic_left'> T\u1ee9 gi\u00e1c $ABCD$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh n\u1ebfu: <br\/> $\\left\\{ \\begin{align} & \\widehat{B}=\\widehat{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}} \\\\ & \\widehat{A}=\\widehat{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}} \\\\ \\end{align} \\right.$ <\/span> ","hint":" D\u1ef1a v\u00e0o d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft h\u00ecnh b\u00ecnh h\u00e0nh.","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv1/img\/H814_D1_1.jpg' \/><\/center> <span class='basic_left'> T\u1ee9 gi\u00e1c $ABCD$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh n\u1ebfu: <br\/> $\\left\\{ \\begin{align} & \\widehat{B}=\\widehat{D} \\\\ & \\widehat{A}=\\widehat{C} \\\\ \\end{align} \\right.$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $D$ v\u00e0 $C$. <\/span><\/span> "}]}],"id_ques":1374},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["120"],["60"]]],"list":[{"point":5,"width":20,"type_input":"","ques":"<span class='basic_left'> H\u00ecnh b\u00ecnh h\u00e0nh $ABCD$ c\u00f3 $\\widehat{A}=2\\widehat{B}$. S\u1ed1 \u0111o c\u00e1c g\u00f3c h\u00ecnh b\u00ecnh h\u00e0nh $ABCD$ l\u00e0: <br\/> <br\/> $\\left\\{ \\begin{align} & \\widehat{A}=\\widehat{C}=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^o \\\\ & \\widehat{B}=\\widehat{D}=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^o \\\\ \\end{align} \\right.$ <\/span> ","hint":" Trong h\u00ecnh b\u00ecnh h\u00e0nh hai g\u00f3c k\u1ec1 m\u1ed9t c\u1ea1nh c\u00f3 s\u1ed1 \u0111o l\u00e0 $180^o$.","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv1/img\/H814_D1_1.jpg' \/><\/center> <span class='basic_left'> H\u00ecnh b\u00ecnh h\u00e0nh $ABCD$ c\u00f3: $\\widehat{A}+\\widehat{B}=180^o$ <br\/> K\u1ebft h\u1ee3p v\u1edbi \u0111\u1ec1 b\u00e0i: $\\widehat{A}=2\\widehat{B}$ <br\/> $\\Rightarrow \\left\\{ \\begin{align} & \\widehat{A}=120^o \\\\ & \\widehat{B}=60^o \\\\ \\end{align} \\right.$ <br\/> Theo t\u00ednh ch\u1ea5t h\u00ecnh b\u00ecnh h\u00e0nh: <br\/> $\\Rightarrow \\left\\{ \\begin{align} & \\widehat{A}=\\widehat{C}=120^o \\\\ & \\widehat{B}=\\widehat{D}=60^o \\\\ \\end{align} \\right.$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o c\u00e1c \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 $120$ v\u00e0 $60$. <\/span><\/span> "}]}],"id_ques":1375},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["="]]],"list":[{"point":5,"width":20,"type_input":"","ques":"<span class='basic_left'> H\u00ecnh b\u00ecnh h\u00e0nh $ABCD$ c\u00f3 $H$ v\u00e0 $K$ l\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a $A$ v\u00e0 $C$ xu\u1ed1ng $BD$. So s\u00e1nh $AH$ v\u00e0 $CK$. <br\/> <br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $AH\\, \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\, CK$ (\u0110i\u1ec1n d\u1ea5u >, < ho\u1eb7c = ) <\/span> ","hint":" G\u1ecdi giao \u0111i\u1ec3m hai \u0111\u01b0\u1eddng ch\u00e9o l\u00e0 $O$.","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv1/img\/H814_D1_2.jpg' \/><\/center> <span class='basic_left'> H\u00ecnh b\u00ecnh h\u00e0nh $ABCD$ c\u00f3: $AC\\cap BD=O$ <br\/> X\u00e9t hai tam gi\u00e1c vu\u00f4ng $\\Delta AOH$ v\u00e0 $\\Delta COK$ c\u00f3: <br\/> + $AO=CO$ (t\u00ednh ch\u1ea5t h\u00ecnh b\u00ecnh h\u00e0nh $ABCD$) <br\/> + $\\widehat{AOH}=\\widehat{COK}$ (\u0111\u1ed1i \u0111\u1ec9nh) <br\/> $\\Rightarrow \\Delta AOH=\\Delta COK$ (c\u1ea1nh huy\u1ec1n - g\u00f3c nh\u1ecdn). <br\/> $\\Rightarrow AH=CK$ (hai c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng d\u1ea5u ' = '. <\/span><\/span> "}]}],"id_ques":1376},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["8"]]],"list":[{"point":5,"width":20,"type_input":"","ques":"<span class='basic_left'> H\u00ecnh b\u00ecnh h\u00e0nh $IKLM$ nh\u01b0 h\u00ecnh v\u1ebd sau. T\u00ednh $x$. <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv1/img\/H814_D1_3.jpg' \/><\/center> <br\/> <b> \u0110\u00e1p \u00e1n: <\/b> <br\/> $x=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ <\/span> ","hint":" Trong h\u00ecnh b\u00ecnh h\u00e0nh, c\u00e1c c\u1ea1nh \u0111\u1ed1i song song v\u00e0 c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng nhau.","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv1/img\/H814_D1_3.jpg' \/><\/center> <span class='basic_left'> Theo b\u00e0i c\u00f3 $IKLM$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh n\u00ean: $LK=IM$ (t\u00ednh ch\u1ea5t) <br\/> $\\Rightarrow 8x-16=6x$ <br\/> $\\Rightarrow 2x=16$ <br\/> $\\Rightarrow x=16:2=8$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $8$. <\/span><\/span> "}]}],"id_ques":1377},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["8"]]],"list":[{"point":5,"width":20,"type_input":"","ques":"<span class='basic_left'> H\u00ecnh b\u00ecnh h\u00e0nh $ABCD$ nh\u01b0 h\u00ecnh v\u1ebd sau. T\u00ednh $AB$. <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv1/img\/H814_D1_4.jpg' \/><\/center> <br\/> <b> \u0110\u00e1p \u00e1n: <\/b> <br\/> $AB=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ <\/span> ","hint":" Trong h\u00ecnh b\u00ecnh h\u00e0nh, c\u00e1c c\u1ea1nh \u0111\u1ed1i song song v\u00e0 c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng nhau.","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv1/img\/H814_D1_4.jpg' \/><\/center> <span class='basic_left'> Theo b\u00e0i c\u00f3 $ABCD$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh n\u00ean: $AB=CD$ (t\u00ednh ch\u1ea5t)<br\/> $\\Rightarrow 2x=x+4$ <br\/> $\\Rightarrow x=4$ <br\/> Do \u0111\u00f3: $AB=2x=2.4=8$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $8$. <\/span><\/span> "}]}],"id_ques":1378},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["106"]]],"list":[{"point":5,"width":20,"type_input":"","ques":"<span class='basic_left'> H\u00ecnh b\u00ecnh h\u00e0nh $ABCD$ nh\u01b0 h\u00ecnh v\u1ebd sau. T\u00ednh $x$. <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv1/img\/H814_D1_5.jpg' \/><\/center> <br\/> <b> \u0110\u00e1p \u00e1n: <\/b> <br\/> $x=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^o$ <\/span> ","hint":" Trong h\u00ecnh b\u00ecnh h\u00e0nh, hai g\u00f3c k\u1ec1 m\u1ed9t c\u1ea1nh c\u00f3 t\u1ed5ng s\u1ed1 \u0111o l\u00e0 $180^o$.","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv1/img\/H814_D1_5.jpg' \/><\/center> <span class='basic_left'> Theo b\u00e0i c\u00f3 $ABCD$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh n\u00ean: $\\widehat{C}+\\widehat{D}=180^o$ (t\u00ednh ch\u1ea5t) <br\/> $\\widehat{C}=180^o-74^o$ <br\/> $\\Rightarrow \\widehat{C}=106^o$ hay $x=106^o$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $106$. <\/span><\/span> "}]}],"id_ques":1379},{"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":[[3]],"list":[{"point":5,"ques":" <span class='basic_left'> Cho t\u1ee9 gi\u00e1c $ABCD$. G\u1ecdi $E, F, G, H$ theo th\u1ee9 t\u1ef1 l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $BD, AB, AC, CD$. <br\/><br\/> <b> C\u00e2u 1:<\/b> T\u1ee9 gi\u00e1c $EFGH$ l\u00e0 h\u00ecnh g\u00ec? <\/span>","select":["A. H\u00ecnh thang","B. H\u00ecnh thang c\u00e2n","C. H\u00ecnh b\u00ecnh h\u00e0nh"],"explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv1/img\/H814_D1_6.jpg' \/><\/center> Theo gi\u1ea3 thi\u1ebft: $AF = BF; DE = BE$ n\u00ean $EF$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a $\\Delta ABD$. <br\/> $\\Rightarrow E\\,F\/\/AD;\\,\\,\\,E\\,F=\\dfrac{1}{2}AD$ (1) <br\/> $AG = GC; DH = HC$ n\u00ean $GH$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a $\\Delta ACD$. <br\/> $\\Rightarrow GH\/\/AD;\\,GH=\\dfrac{1}{2}AD$ (2)<br\/> T\u1eeb (1) v\u00e0 (2) suy ra $EF \/\/ GH$ v\u00e0 $EF=GH$<br\/> $\\Rightarrow EFGH$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh. <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n l\u00e0 C.<\/span>","column":3}]}],"id_ques":1380},{"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'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv1/img\/H814_D1_6.jpg' \/><\/center><br\/> Cho t\u1ee9 gi\u00e1c $ABCD$. G\u1ecdi $E, F, G, H$ theo th\u1ee9 t\u1ef1 l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $BD, AB, AC, CD$. <br\/><br\/> <b> C\u00e2u 2:<\/b> Cho $AD=a; BC=b$. Chu vi c\u1ee7a $EFGH$ l\u00e0: <\/span>","select":["A. $a+b$","B. $a-b$","C. $\\dfrac{a+b}{2}$"],"hint":" Theo t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung b\u00ecnh, t\u00ednh c\u00e1c c\u1ea1nh c\u1ee7a $EFGH$ theo $AC$ v\u00e0 $BC$.","explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv1/img\/H814_D1_6.jpg' \/><\/center> Theo c\u00e2u 1, ta ch\u1ee9ng minh \u0111\u01b0\u1ee3c $EFGH$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh v\u00e0: <br\/> $\\text{EF=GH=}\\dfrac{1}{2}AD=\\dfrac{1}{2}a$$\\Rightarrow E\\,F+GH=a$ <br\/> $EH=FG=\\dfrac{1}{2}BC=\\dfrac{1}{2}b$<br\/> $\\Rightarrow EH+FG=b$ <br\/> Chu vi h\u00ecnh b\u00ecnh h\u00e0nh $EFGH$: <br\/> $EF + FG + GH + EH = a + b$. <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n l\u00e0 A.<\/span>","column":3}]}],"id_ques":1381},{"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":[[["FC","CF"]]],"list":[{"point":5,"width":20,"type_input":"","ques":"<span class='basic_left'> Cho h\u00ecnh b\u00ecnh h\u00e0nh $ABCD$, $O$ l\u00e0 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng ch\u00e9o, $E$ v\u00e0 $F$ theo th\u1ee9 t\u1ef1 l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $OD$ v\u00e0 $OB$. <br\/><br\/> <b> C\u00e2u 1:<\/b> $AE$ song song v\u00e0 b\u1eb1ng $\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ <\/span> ","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv1/img\/H814_D1_7a.jpg' \/><\/center> <span class='basic_left'> Do $O = AC \\cap BD$ n\u00ean $DO = OB$ <br\/> M\u00e0 $E$ v\u00e0 $F$ theo th\u1ee9 t\u1ef1 l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $OD$ v\u00e0 $OB$ n\u00ean $DE = EO = OF = BF$. <br\/> X\u00e9t t\u1ee9 gi\u00e1c $AFCE$ c\u00f3: $AO = OC; OE = OF$ n\u00ean $AFCE$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh. <br\/> Do \u0111\u00f3: $AE \/\/ CF$ v\u00e0 $AE=CF$. <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $CF$. <\/span><\/span> "}]}],"id_ques":1382},{"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":[[["2"]]],"list":[{"point":5,"width":20,"type_input":"","ques":"<span class='basic_left'> Cho h\u00ecnh b\u00ecnh h\u00e0nh $ABCD, O$ l\u00e0 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng ch\u00e9o, $E$ v\u00e0 $F$ theo th\u1ee9 t\u1ef1 l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $OD$ v\u00e0 $OB$. <br\/><br\/> <b> C\u00e2u 2:<\/b> $AE\\cap DC=K$. H\u1ecfi \u0111\u1ed9 d\u00e0i $KC$ g\u1ea5p m\u1ea5y l\u1ea7n \u0111\u1ed9 d\u00e0i $DK$?<br\/><br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $KC=\\, \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}\\, DK$ <\/span> ","hint":" G\u1ecdi $H$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $CK$.","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv1/img\/H814_D1_7.jpg' \/><\/center> <span class='basic_left'> G\u1ecdi $H$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $KC$. <br\/> Trong $\\Delta ACK$ c\u00f3: $OA = OC$ (gi\u1ea3 thi\u1ebft); $HC = HK$ (c\u00e1ch v\u1ebd) <br\/> $\\Rightarrow OH$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a $\\Delta ACK$ <br\/> $\\Rightarrow OH \/\/ AK$ <br\/> Trong $\\Delta DOH$ c\u00f3: $DE = EO; EK \/\/ OH$ (do $OH \/\/ AK$) n\u00ean $DK = KH$. <br\/> V\u1eady $DK = KH = HC$ $\\Rightarrow DK=\\dfrac{1}{2}KC$ <br\/> $\\Rightarrow CK=2DK$ <br\/> <span class='basic_pink'>V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $2$. <\/span><\/span> "}]}],"id_ques":1383},{"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":[[["120"]]],"list":[{"point":5,"width":20,"type_input":"","ques":"<span class='basic_left'> Cho $\\Delta ABC$ \u0111\u1ec1u. Tr\u00ean c\u1ea1nh $AB, AC, BC$ l\u1ea5y l\u1ea7n l\u01b0\u1ee3t c\u00e1c \u0111i\u1ec3m $D, E$ v\u00e0 $F$ sao cho: $\\widehat{EDF}=60^o$; $\\widehat{DFC}=120^o$. <br\/><br\/> <b> C\u00e2u 1:<\/b> T\u00ednh s\u1ed1 \u0111o c\u1ee7a $\\widehat{DEC}$. <br\/><br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $\\widehat{DEC}=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^o$ <\/span> ","hint":" X\u00e9t t\u1ee9 gi\u00e1c $DECF$ \u0111\u1ec3 t\u00ednh g\u00f3c $DEC$.","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv1/img\/H814_D1_8.jpg' \/><\/center> <span class='basic_left'> Do $\\Delta ABC$ \u0111\u1ec1u n\u00ean: $\\widehat{A}=\\widehat{B}=\\widehat{C}=60^o$ <br\/> X\u00e9t t\u1ee9 gi\u00e1c $DECF$: <br\/> $\\widehat{EDF}+\\widehat{DFC}+\\widehat{C}+\\widehat {DEC}=360^o$ (t\u1ed5ng c\u00e1c g\u00f3c trong t\u1ee9 gi\u00e1c) <br\/> $\\Rightarrow \\widehat{DEC}=360^o-60^o-120^o-60^o$ <br\/> $\\Rightarrow \\widehat{DEC}=120^o$. <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $120$. <\/span><\/span> "}]}],"id_ques":1384},{"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 hai c\u00e2u","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" <span class='basic_left'> Cho $\\Delta ABC$ \u0111\u1ec1u. Tr\u00ean c\u1ea1nh $AB, AC, BC$ l\u1ea5y l\u1ea7n l\u01b0\u1ee3t c\u00e1c \u0111i\u1ec3m $D, E$ v\u00e0 $F$ sao cho: $\\widehat{EDF}=60^o$; $\\widehat{DFC}=120^o$. <br\/><br\/> <b> C\u00e2u 2:<\/b> T\u1ee9 gi\u00e1c $DECF$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh. <\/span>","select":["\u0110\u00fang","Sai"],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv1/img\/H814_D1_8.jpg' \/><\/center> <span class='basic_left'> Theo c\u00e2u 1, ta t\u00ednh \u0111\u01b0\u1ee3c c\u00e1c g\u00f3c c\u1ee7a t\u1ee9 gi\u00e1c $DECF$. <br\/> Ta th\u1ea5y: <br\/> $\\widehat{EDF}=\\widehat{C}=60^o$ <br\/> $\\widehat{DFC}=\\widehat{DEC}=120^o$. <br\/> Do \u0111\u00f3: $DECF$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft). <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 \u0110\u00fang. <\/span><\/span> ","column":2}]}],"id_ques":1385},{"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":[[["="]]],"list":[{"point":5,"width":20,"type_input":"","ques":"<span class='basic_left'> Cho h\u00ecnh b\u00ecnh h\u00e0nh $ABCD$, $O$ l\u00e0 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng ch\u00e9o. \u0110\u01b0\u1eddng th\u1eb3ng b\u1ea5t k\u00ec qua $O$ c\u1eaft $AB$ \u1edf $M$ v\u00e0 $CD$ \u1edf $N$. <br\/><br\/> <b> C\u00e2u 1:<\/b> So s\u00e1nh $OM$ v\u1edbi $ON$. <br\/><br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $OM \\, \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\, ON$ (\u0110i\u1ec1n d\u1ea5u >; < ho\u1eb7c =) <\/span> ","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv1/img\/H814_D1_9a.jpg' \/><\/center> <span class='basic_left'> X\u00e9t $\\Delta AOM$ v\u00e0 $\\Delta CON$: <br\/> + $\\widehat{O_1}=\\widehat{O_2}$ (\u0111\u1ed1i \u0111\u1ec9nh) <br\/> + $AO=OC$ (gi\u1ea3 thi\u1ebft)<br\/> + $\\widehat {A_1}=\\widehat{C_1}$ (so le trong) <br\/> $\\Rightarrow \\Delta AOM=\\Delta CON$ (g - c - g) <br\/> $\\Rightarrow OM=ON$ (hai c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng). <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng d\u1ea5u '='. <\/span><\/span> "}]}],"id_ques":1386},{"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 hai c\u00e2u","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" <span class='basic_left'> Cho h\u00ecnh b\u00ecnh h\u00e0nh $ABCD$, $O$ l\u00e0 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng ch\u00e9o. \u0110\u01b0\u1eddng th\u1eb3ng b\u1ea5t k\u00ec qua $O$ c\u1eaft $AB$ \u1edf $M$ v\u00e0 $CD$ \u1edf $N$. <br\/><br\/> <b> C\u00e2u 2:<\/b> T\u1ee9 gi\u00e1c $AMCN$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh. <\/span>","select":["\u0110\u00fang","Sai"],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv1/img\/H814_D1_9.jpg' \/><\/center> <span class='basic_left'> Theo c\u00e2u 1, ta ch\u1ee9ng minh \u0111\u01b0\u1ee3c: $OM=ON$ <br\/> H\u01a1n n\u1eefa: $OA=OC$ (gi\u1ea3 thi\u1ebft) <br\/> M\u00e0 $MN$ v\u00e0 $AC$ l\u00e0 c\u00e1c \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a t\u1ee9 gi\u00e1c $AMCN$ ($AC\\cap MN=O$). <br\/> $\\Rightarrow AMCN$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft). <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 \u0110\u00fang. <\/span><\/span> ","column":2}]}],"id_ques":1387},{"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 \u1edf $A$. T\u1eeb $M\\in BC$ k\u1ebb $MD\/\/AC$ v\u00e0 $ME\/\/AB$ ($D\\in AB; E \\in AC$) <br\/><br\/> <b> C\u00e2u 1:<\/b> T\u1ee9 gi\u00e1c $ADME$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh. <\/span>","select":["\u0110\u00fang","Sai"],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv1/img\/H814_D1_10.jpg' \/><\/center> <span class='basic_left'> Theo gi\u1ea3 thi\u1ebft: <br\/> + $ AD \/\/ ME$ <br\/> + $ AE \/\/ MD $ (do $AC \/\/ MD$) <br\/> $\\Rightarrow ADME$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft). <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 \u0110\u00fang. <\/span><\/span> ","column":2}]}],"id_ques":1388},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t.","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 \u1edf $A$. T\u1eeb $M\\in BC$ k\u1ebb $MD\/\/AC$ v\u00e0 $ME\/\/AB$ ($D\\in AB; E \\in AC$). <br\/><br\/> <b> C\u00e2u 2:<\/b> $\\Delta EMC$ l\u00e0 tam gi\u00e1c g\u00ec? <\/span>","select":["A. Tam gi\u00e1c c\u00e2n","B. Tam gi\u00e1c vu\u00f4ng","C. Tam gi\u00e1c \u0111\u1ec1u"],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv1/img\/H814_D1_10.jpg' \/><\/center> <span class='basic_left'> Do $ ME \/\/ AB$ n\u00ean $\\widehat{B}=\\widehat{EMC}$ (\u0111\u1ed3ng v\u1ecb) <br\/> M\u00e0 $\\widehat{B}=\\widehat{C}$ ($\\Delta ABC$ c\u00e2n \u1edf $A$) <br\/> $\\Rightarrow \\widehat{C}=\\widehat{EMC}$ <br\/> $\\Rightarrow \\Delta EMC$ c\u00e2n t\u1ea1i $E$. <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A. <\/span><\/span> ","column":3}]}],"id_ques":1389},{"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":[[["="]]],"list":[{"point":5,"width":20,"type_input":"","ques":"<span class='basic_left'> <span class='basic_left'> Cho $\\Delta ABC$ c\u00e2n \u1edf $A$. T\u1eeb $M\\in BC$ k\u1ebb $MD\/\/AC$ v\u00e0 $ME\/\/AB$ ($D\\in AB; E \\in AC$) <br\/><br\/> <b> C\u00e2u 3:<\/b> So s\u00e1nh t\u1ed5ng $MD+ME$ v\u1edbi $AC$. <br\/><br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $(MD+ME) \\, \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\, AC$ (\u0110i\u1ec1n d\u1ea5u >; < ho\u1eb7c =) <\/span> ","hint":" So s\u00e1nh t\u1eebng c\u1eb7p \u0111o\u1ea1n th\u1eb3ng: $ME$ v\u1edbi $EC$; $DM$ v\u1edbi $AE$","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv1/img\/H814_D1_10.jpg' \/><\/center> <span class='basic_left'> Theo c\u00e2u 2, ta ch\u1ee9ng minh \u0111\u01b0\u1ee3c: $\\Delta EMC$ c\u00e2n t\u1ea1i $E$.<br\/> $\\Rightarrow ME=EC$ <br\/> M\u1eb7t kh\u00e1c do $AEMD$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh (ch\u1ee9ng minh c\u00e2u 1). <br\/> $\\Rightarrow MD=AE$ <br\/> Do \u0111\u00f3: $MD+ME=AE+EC=AC$ <br\/> $\\Rightarrow (MD+ME)=AC$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng d\u1ea5u '='. <\/span><\/span> "}]}],"id_ques":1390}],"lesson":{"save":0,"level":1}}