{"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":10,"ques":" <span class='basic_left'> T\u1ec9 s\u1ed1 \u0111\u1ed9 d\u00e0i hai c\u1ea1nh c\u1ee7a h\u00ecnh b\u00ecnh h\u00e0nh l\u00e0 $3 : 4$ v\u00e0 chu vi c\u1ee7a h\u00ecnh b\u00ecnh h\u00e0nh \u0111\u00f3 l\u00e0 $28\\, cm$. \u0110\u1ed9 d\u00e0i hai c\u1ea1nh k\u1ec1 c\u1ee7a h\u00ecnh b\u00ecnh h\u00e0nh l\u00e0: <\/span>","select":["A. $9\\, cm$ v\u00e0 $12\\, cm$ ","B. $6\\, cm$ v\u00e0 $8\\, cm$","C. $7,5\\, cm$ v\u00e0 $10\\, cm$ ","D. $12\\, cm$ v\u00e0 $16\\, cm$ "],"explain":" <span class='basic_left'> G\u1ecdi hai c\u1ea1nh c\u1ee7a h\u00ecnh b\u00ecnh h\u00e0nh l\u00e0: $a$ v\u00e0 $b$ $(a > b > 0)$ (cm) <br\/> Theo gi\u1ea3 thi\u1ebft: <br\/> $a:b=3:4 \\Rightarrow \\dfrac{a}{3}=\\dfrac{b}{4}$ <br\/> V\u00e0 $(a+b).2=28 \\Rightarrow a+b=14$ <br\/> T\u1eeb \u0111\u00f3, ta c\u00f3: <br\/> $\\dfrac{a}{3}=\\dfrac{b}{4}$$=\\dfrac{a+b}{3+4}=\\dfrac{14}{7}=2$ <br\/> $\\Rightarrow a=6\\, (cm); b=8 \\, (cm)$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B. <\/span><\/span> ","column":2}]}],"id_ques":1391},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":10,"ques":" <span class='basic_left'> Cho $ABCD$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh th\u00ec: <\/span>","select":["A. $\\Delta ABC=\\Delta CDA$","B. $S_{ABC}=S_{CDA}$","C. Hai \u0111i\u1ec3m $C$ v\u00e0 $A$ \u0111\u1ed1i x\u1ee9ng v\u1edbi nhau qua trung \u0111i\u1ec3m c\u1ee7a $BD$.","D. C\u1ea3 3 c\u00e2u tr\u00ean \u0111\u1ec1u \u0111\u00fang "],"explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv3/img\/H814_K1_1.jpg' \/><\/center> X\u00e9t $\\Delta ABC$ v\u00e0 $\\Delta CDA$, c\u00f3: <br\/> + $AB=CD$ <br\/> + $\\widehat{B}=\\widehat{D}$ (t\u00ednh ch\u1ea5t h\u00ecnh b\u00ecnh h\u00e0nh) <br\/> + $BC=AD$ (t\u00ednh ch\u1ea5t h\u00ecnh b\u00ecnh h\u00e0nh) <br\/> $\\Rightarrow \\Delta ABC=\\Delta CDA$ (c - g - c) <br\/> $\\Rightarrow$ <b> C\u00e2u A \u0111\u00fang <\/b> <br\/> Do hai tam gi\u00e1c b\u1eb1ng nhau th\u00ec di\u1ec7n t\u00edch c\u1ee7a ch\u00fang b\u1eb1ng nhau. <br\/> $\\Rightarrow $ $S_{ABC}=S_{CDA}$ <br\/> $\\Rightarrow$ <b> C\u00e2u B \u0111\u00fang<\/b> <br\/> Trong h\u00ecnh b\u00ecnh h\u00e0nh hai \u0111\u01b0\u1eddng ch\u00e9o c\u1eaft nhau t\u1ea1i trung \u0111i\u1ec3m c\u1ee7a m\u1ed7i \u0111\u01b0\u1eddng. <br\/> $\\Rightarrow$ <b> C\u00e2u C \u0111\u00fang <\/b> <br\/> C\u1ea3 3 c\u00e2u A, B, C \u0111\u1ec1u \u0111\u00fang. <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D. <\/span><\/span> ","column":1}]}],"id_ques":1392},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":" <span class='basic_left'> Chu vi c\u1ee7a h\u00ecnh b\u00ecnh h\u00e0nh $ABCD$ l\u00e0 $10\\, cm$, chu vi c\u1ee7a $\\Delta ABD$ l\u00e0 $9\\, cm$. \u0110\u1ed9 d\u00e0i c\u1ea1nh $BD$ l\u00e0: <\/span>","select":["A. $1\\, cm$","B. $2\\, cm$","C. $4\\, cm$","D. $6\\, cm$ "],"explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv3/img\/H814_K1_2.jpg' \/><\/center> Chu vi h\u00ecnh b\u00ecnh h\u00e0nh $ABCD$ l\u00e0 $10\\, cm$, t\u1ee9c l\u00e0: <br\/> $(AB+AD).2=10$ <br\/> $\\Rightarrow AB+AD=5\\, (cm)$ <br\/> Chu vi c\u1ee7a $\\Delta ABD$ l\u00e0 $9\\, cm$, t\u1ee9c l\u00e0: <br\/> $AB+AD+BD=9\\, (cm)$ <br\/> $\\Rightarrow BD=9-(AB+AD)$ <br\/> $BD=9-5=4\\, (cm)$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C. <\/span><\/span> ","column":2}]}],"id_ques":1393},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["25"]]],"list":[{"point":10,"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/lv3/img\/H814_K1_3.png' \/><\/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/lv3/img\/H814_K1_3.png' \/><\/center> <span class='basic_left'> Theo t\u00ednh ch\u1ea5t h\u00ecnh b\u00ecnh h\u00e0nh, ta c\u00f3: $\\widehat{A}+\\widehat{B}=180^o$ <br\/> $\\Rightarrow 4x+20^o+2x+10^o=180^o$ <br\/> $\\Rightarrow 6x=150^o$ <br\/> $\\Rightarrow x=25^o$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0: $25$. <\/span><\/span> "}]}],"id_ques":1394},{"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":[[3]],"list":[{"point":10,"ques":" <span class='basic_left'> Cho $\\Delta ABC$, tr\u1ef1c t\u00e2m $H$. C\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi $AB$ t\u1ea1i $B$, vu\u00f4ng g\u00f3c v\u1edbi $AC$ t\u1ea1i $C$ c\u1eaft nhau t\u1ea1i $D$. <br\/><br\/> <b> C\u00e2u 1:<\/b> $BDCH$ 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":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv3/img\/H814_K1_4.jpg' \/><\/center> <span class='basic_left'> Theo gi\u1ea3 thi\u1ebft: $CH\\,\\,\\bot \\,AB;\\,\\,BD\\,\\bot \\,\\,AB\\Rightarrow CH\/\/BD$ <br\/> $BH\\,\\,\\bot \\,\\,AC;\\,\\,CD\\,\\bot \\,\\,AC\\Rightarrow BH\/\/CD$ <br\/> T\u1eeb \u0111\u00f3 suy ra $BHCD$ 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 C. <\/span><\/span> ","column":3}]}],"id_ques":1395},{"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":[[["180"]]],"list":[{"point":10,"width":20,"type_input":"","ques":"<span class='basic_left'> Cho $\\Delta ABC$, tr\u1ef1c t\u00e2m $H$. C\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi $AB$ t\u1ea1i $B$, vu\u00f4ng g\u00f3c v\u1edbi $AC$ t\u1ea1i $C$ c\u1eaft nhau t\u1ea1i $D$. <br\/><br\/> <b> C\u00e2u 2:<\/b> T\u00ednh $\\widehat{BAC}+\\widehat{BDC}$. <br\/><br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $\\widehat{BAC}+\\widehat{BDC}= \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^o$ <\/span> ","hint":" X\u00e9t t\u1ed5ng c\u00e1c g\u00f3c trong t\u1ee9 gi\u00e1c $ABCD$.","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv3/img\/H814_K1_4.jpg' \/><\/center> <span class='basic_left'> Trong t\u1ee9 gi\u00e1c $ABDC$: <br\/> $\\widehat{BAC}+\\widehat{ABD}+\\widehat{ACD}+\\widehat{BDC}={{360}^{o}}$ (t\u1ed5ng c\u00e1c g\u00f3c trong t\u1ee9 gi\u00e1c) <br\/> $\\begin{align} & \\Rightarrow \\widehat{BAC}+{{90}^{o}}+{{90}^{o}}+\\widehat{BDC}={{360}^{o}} \\\\ & \\Rightarrow \\widehat{BAC}+\\widehat{BDC}={{360}^{o}}-{{180}^{o}}={{180}^{o}} \\\\ \\end{align}$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $180$. <\/span><\/span> "}]}],"id_ques":1396},{"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"]]],"list":[{"point":10,"width":20,"type_input":"","ques":"<span class='basic_left'> Cho $\\Delta ABC$, tr\u1ef1c t\u00e2m $H$. C\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi $AB$ t\u1ea1i $B$, vu\u00f4ng g\u00f3c v\u1edbi $AC$ t\u1ea1i $C$ c\u1eaft nhau t\u1ea1i $D$. <br\/><br\/> <b> C\u00e2u 3:<\/b> G\u1ecdi $O$ v\u00e0 $M$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m $AD$ v\u00e0 $BC$. \u0110\u1ed9 d\u00e0i $AH$ g\u1ea5p m\u1ea5y l\u1ea7n \u0111\u1ed9 d\u00e0i $OM$? <br\/><br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $AH\\,=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}\\, OM$ <\/span> ","hint":" X\u00e9t xem $OM$ l\u00e0 g\u00ec trong tam gi\u00e1c $AHD$.","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv3/img\/H814_K1_4.jpg' \/><\/center> <span class='basic_left'> Theo b\u00e0i $BM = CM$ <br\/> M\u00e0 $BHCD$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh (ch\u1ee9ng minh tr\u00ean) n\u00ean $M \\in HD$. <br\/> V\u1eady $H, M, D$ th\u1eb3ng h\u00e0ng. <br\/> X\u00e9t $\\Delta AHD$ c\u00f3: $HM = MD$ <br\/> M\u00e0 $AO = OD$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow OM$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a $\\Delta AHD$ <br\/> $\\Rightarrow OM=\\dfrac{1}{2}AH$ <br\/> $\\Rightarrow AH=2OM$. <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $180$. <\/span><\/span> "}]}],"id_ques":1397},{"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":10,"ques":" <span class='basic_left'> Cho h\u00ecnh thang vu\u00f4ng $ABCD$ ($\\widehat{A}=\\widehat{D}=90^o$, c\u00f3 $AB=\\dfrac{1}{2}CD$. G\u1ecdi $H$ l\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a $D$ tr\u00ean $AC$. G\u1ecdi $M, N$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $HC$ v\u00e0 $HD$. <br\/><br\/> <b> C\u00e2u 1:<\/b> Ta ch\u1ee9ng minh \u0111\u01b0\u1ee3c $DNMC$ l\u00e0 h\u00ecnh thang, $ABMN$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh <b>\u0111\u00fang<\/b> hay <b>sai<\/b>? <\/span>","select":[" \u0110\u00fang"," Sai"],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv3/img\/H814_K1_5a.jpg' \/><\/center> <span class='basic_left'> Do $HM=MC; HN=DN$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow MN\/\/DC$ <br\/> $\\Rightarrow DNMC$ l\u00e0 h\u00ecnh thang. <br\/> Do $MN\/\/ DC$ (ch\u1ee9ng minh tr\u00ean) $\\Rightarrow MN\/\/AB$ (1) <br\/> C\u0169ng theo ch\u1ee9ng minh tr\u00ean th\u00ec $MN$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a $\\Delta CHD$ <br\/> $\\Rightarrow MN=\\dfrac{1}{2}DC$ <br\/> $\\Rightarrow MN=AB\\,\\left(=\\dfrac{1}{2}DC \\right)$ (2) <br\/> T\u1eeb (1) v\u00e0 (2) suy ra $ABMN$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 \u0110\u00fang. <\/span><\/span> ","column":2}]}],"id_ques":1398},{"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":[[["90"]]],"list":[{"point":10,"width":20,"type_input":"","ques":"<span class='basic_left'> Cho h\u00ecnh thang vu\u00f4ng $ABCD$ ($\\widehat{A}=\\widehat{D}=90^o$, c\u00f3 $AB=\\dfrac{1}{2}CD$. G\u1ecdi $H$ l\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a $D$ tr\u00ean $AC$. G\u1ecdi $M, N$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $HC$ v\u00e0 $HD$. <br\/><br\/> <b> C\u00e2u 2:<\/b> T\u00ednh $\\widehat{BMD}$. <br\/><br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $\\widehat{BMD}=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^o$ <\/span> ","hint":"Ch\u1ee9ng minh \u0111i\u1ec3m $N$ l\u00e0 tr\u1ef1c t\u00e2m c\u1ee7a tam gi\u00e1c $ADM$.","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv3/img\/H814_K1_5b.jpg' \/><\/center> <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> Ch\u1ee9ng minh $N$ l\u00e0 tr\u1ef1c t\u00e2m c\u1ee7a $\\Delta ADM$ <br\/> Ch\u1ec9 ra $BM\\bot DM$ <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> X\u00e9t $\\Delta ADM$ c\u00f3: <br\/> + $DN\\bot AM$ (gi\u1ea3 thi\u1ebft) <br\/> + $MN\\bot AD$ (do $MN \/\/ AB$) <br\/> $\\Rightarrow N$ l\u00e0 tr\u1ef1c t\u00e2m c\u1ee7a $\\Delta ADM$ <br\/> $\\Rightarrow AN \\bot DM$ <br\/> M\u00e0 $ABMN$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh n\u00ean $BM \/\/AN$. <br\/> $\\Rightarrow BM \\bot DM$ <br\/> Do \u0111\u00f3: $\\widehat {BMD}=90^o$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $90$. <\/span><\/span> "}]}],"id_ques":1399},{"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":[[["72"]]],"list":[{"point":10,"width":20,"type_input":"","ques":"<span class='basic_left'> Cho h\u00ecnh thang vu\u00f4ng $ABCD$ ($\\widehat{A}=\\widehat{D}=90^o$, c\u00f3 $AB=\\dfrac{1}{2}CD$. G\u1ecdi $H$ l\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a $D$ tr\u00ean $AC$. G\u1ecdi $M, N$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $HC$ v\u00e0 $HD$. <br\/><br\/> <b> C\u00e2u 3:<\/b> $CD=16\\, cm; AD=6\\, cm$ <br\/> $S_{ABCD}=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}\\, (cm^2)$ <\/span> ","hint":"Di\u1ec7n t\u00edch h\u00ecnh thang b\u1eb1ng n\u1eeda t\u00edch t\u1ed5ng hai \u0111\u00e1y v\u1edbi \u0111\u01b0\u1eddng cao.","explain":" V\u1ebd h\u00ecnh <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai4/lv3/img\/H814_K1_5c.jpg' \/><\/center> <span class='basic_left'> $S_{ABCD}=\\dfrac{1}{2}(AB+DC).AD$$=\\dfrac{1}{2}(8+16).6=72\\, (cm^2)$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $72$. <\/span><\/span> "}]}],"id_ques":1400}],"lesson":{"save":0,"level":3}}