{"segment":[{"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":"C\u1ea7n \u00edt nh\u1ea5t m\u1ea5y m\u00e0u \u0111\u1ec3 s\u01a1n t\u1ea5t c\u1ea3 c\u00e1c m\u1eb7t c\u1ee7a m\u1ed9t h\u00ecnh l\u1eadp ph\u01b0\u01a1ng sao cho kh\u00f4ng c\u00f3 hai m\u1eb7t k\u1ec1 nhau n\u00e0o \u0111\u01b0\u1ee3c s\u01a1n c\u00f9ng m\u00e0u?","select":["A. $1$","B. $2$","C. $3$","D. $4$"],"hint":"","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai20/lv3/img\/H8_B20_K1.1.png' \/><\/center>T\u1ea1i \u0111\u1ec9nh $B$ c\u1ee7a h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt. Ta th\u1ea5y c\u00f3 $3$ m\u1eb7t \u0111\u00f4i m\u1ed9t k\u1ec1 nhau. Do v\u1eady c\u1ea7n \u00edt nh\u1ea5t $3$ m\u00e0u \u0111\u1ec3 s\u01a1n $3$ m\u1eb7t sao cho kh\u00f4ng c\u00f3 hai m\u1eb7t n\u00e0o k\u1ec1 nhau \u0111\u01b0\u1ee3c s\u01a1n c\u00f9ng m\u00e0u.<br\/>C\u00e1c m\u1eb7t c\u00f2n l\u1ea1i s\u01a1n m\u00e0u gi\u1ed1ng v\u1edbi m\u00e0u c\u1ee7a m\u1eb7t \u0111\u1ed1i di\u1ec7n.<br\/>Nh\u01b0 v\u1eady v\u1edbi h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt c\u1ea7n \u00edt nh\u1ea5t $3$ m\u00e0u \u0111\u1ec3 s\u01a1n t\u1ea5t c\u1ea3 c\u00e1c m\u1eb7t m\u00e0 kh\u00f4ng c\u00f3 hai m\u1eb7t k\u1ec1 nhau \u0111\u01b0\u1ee3c s\u01a1n c\u00f9ng m\u00e0u.<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><\/span>","column":2}]}],"id_ques":1830},{"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":"C\u00f3 bao nhi\u00eau d\u1ea5u ch\u1ea5m tr\u00f2n c\u1ea7n \u0111i\u1ec1n v\u00e0o c\u00e1c m\u1eb7t $?1; ?2; ?3$ trong h\u00ecnh khai tri\u1ec3n c\u1ee7a vi\u00ean x\u00fac x\u1eafc h\u00ecnh l\u1eadp ph\u01b0\u01a1ng, bi\u1ebft r\u1eb1ng t\u1ed5ng hai s\u1ed1 \u1edf hai m\u1eb7t \u0111\u1ed1i di\u1ec7n c\u1ee7a vi\u00ean x\u00fac x\u1eafc b\u1eb1ng $7$.<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai20/lv3/img\/H8_B20_K1.2.png' \/><\/center><br\/>S\u1ed1 d\u1ea5u ch\u1ea5m tr\u00f2n c\u1ea7n \u0111i\u1ec1n theo th\u1ee9 t\u1ef1 l\u00e0:","select":["A. $4;5;6$","B. $4;6;5$","C. $6;4;5$","D. $5;4;6$"],"hint":"C\u00f3 th\u1ec3 c\u1eaft h\u00ecnh khai tri\u1ec3n b\u1eb1ng gi\u1ea5y r\u1ed3i gh\u00e9p l\u1ea1i.","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai20/lv3/img\/H8_B20_K1.2a.png' \/><\/center><br\/>V\u00ec t\u1ed5ng hai m\u1eb7t \u0111\u1ed1i di\u1ec7n l\u00e0 $7$ ch\u1ea5m tr\u00f2n n\u00ean ta c\u00f3 th\u1ec3 t\u00ecm ra c\u00e1c m\u1eb7t \u0111\u1ed1i di\u1ec7n v\u1edbi c\u00e1c m\u1eb7t ghi s\u1ed1 nh\u01b0 sau:<br\/>- M\u1eb7t $?1$ k\u1ec1 v\u1edbi m\u1eb7t ghi $2$ ch\u1ea5m v\u00e0 m\u1eb7t $1$ ch\u1ea5m n\u00ean \u0111\u1ed1i di\u1ec7n v\u1edbi m\u1eb7t ghi $3$ ch\u1ea5m. Suy ra m\u1eb7t $?1$ l\u00e0 m\u1eb7t ghi $4$ ch\u1ea5m.<br\/>- M\u1eb7t $?2$ k\u1ec1 v\u1edbi m\u1eb7t ghi $3$ ch\u1ea5m v\u00e0 m\u1eb7t ghi $2$ ch\u1ea5m n\u00ean \u0111\u1ed1i di\u1ec7n m\u1eb7t ghi $1$ ch\u1ea5m. Suy ra m\u1eb7t $?2$ ghi $6$ ch\u1ea5m.<br\/>- M\u1eb7t $?3$ ghi $5$ ch\u1ea5m.<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B<\/span><\/span>","column":2}]}],"id_ques":1831},{"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":"Cho h\u00ecnh l\u1eadp ph\u01b0\u01a1ng $ABCD.A\u2019B\u2019C\u2019D\u2019$. Tam gi\u00e1c $A\u2019DC\u2019$ l\u00e0 tam gi\u00e1c g\u00ec?<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai20/lv3/img\/H8_B20_K1.3.png' \/><\/center>","select":["A. Tam gi\u00e1c vu\u00f4ng","B. Tam gi\u00e1c c\u00e2n","C. Tam gi\u00e1c \u0111\u1ec1u"],"hint":"Gi\u1ea3 s\u1eed \u0111\u1ed9 d\u00e0i c\u1ea1nh h\u00ecnh l\u1eadp ph\u01b0\u01a1ng l\u00e0 $a$. T\u00ednh \u0111\u1ed9 d\u00e0i m\u1ed7i c\u1ea1nh c\u1ee7a tam gi\u00e1c $A'DC'$","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai20/lv3/img\/H8_B20_K1.3.png' \/><\/center><br\/>Gi\u1ea3 s\u1eed \u0111\u1ed9 d\u00e0i h\u00ecnh l\u1eadp ph\u01b0\u01a1ng $ABCD.A'B'C'D'$ l\u00e0 $a$ (\u0111\u01a1n v\u1ecb \u0111\u1ed9 d\u00e0i)<br\/>X\u00e9t tam gi\u00e1c $ADA'$ vu\u00f4ng t\u1ea1i $A$ c\u00f3 $AD=AA'=a$.<br\/>\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3:<br\/>$A'D^2=AA'^2+AD^2\\\\ \\Rightarrow A'D^2=a^2+a^2\\\\ \\Leftrightarrow A'D^2=2a^2\\\\ \\Leftrightarrow A'D=a\\sqrt {2}$<br\/>T\u01b0\u01a1ng t\u1ef1, ta c\u00f3: <br\/>Tam gi\u00e1c $A'D'C'$ vu\u00f4ng t\u1ea1i $D'$ c\u00f3 $A'D'=D'C'=a$.<br\/>Suy ra $A'C'=a\\sqrt {2}$<br\/>Tam gi\u00e1c $DD'C'$ vu\u00f4ng t\u1ea1i $D'$ c\u00f3 $DD'=D'C'=a$.<br\/>Suy ra $DC'=a\\sqrt {2}$<br\/>X\u00e9t tam gi\u00e1c $A'DC'$ c\u00f3 $A'D=A'C'=DC'=a\\sqrt{2}$<br\/>V\u1eady tam gi\u00e1c $A'DC'$ l\u00e0 tam gi\u00e1c \u0111\u1ec1u.<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><\/span>","column":3}]}],"id_ques":1832},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank_random","correct":[[["4"],["5"],["6"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"Cho h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt $ABCD.A\u2019B\u2019C\u2019D\u2019$. Di\u1ec7n t\u00edch c\u00e1c m\u1eb7t $ABCD$; $BCC\u2019B\u2019$ v\u00e0 $DD'C'C$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 $30 cm^2$; $20 cm^2$; $24 cm^2$. T\u00ednh c\u00e1c k\u00edch th\u01b0\u1edbc c\u1ee7a h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt.<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai20/lv3/img\/H8_B20_K1.5.png' \/><\/center><br\/><b> \u0110\u00e1p s\u1ed1: <\/b> _input_ ($cm$); _input_ ($cm$); _input_ ($cm$)","hint":"Bi\u1ec3u di\u1ec5n di\u1ec7n t\u00edch 3 m\u1eb7t theo k\u00edch th\u01b0\u1edbc h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt.","explain":"<span class='basic_left'><br\/><span class='basic_green'>H\u01b0\u1edbng d\u1eabn<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> Bi\u1ec3u di\u1ec5n \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh c\u1ee7a h\u00ecnh h\u1ed9p theo k\u00edch th\u01b0\u1edbc $a;b;c$.<br\/><b>B\u01b0\u1edbc 2:<\/b> Bi\u1ec3u di\u1ec5n di\u1ec7n t\u00edch c\u00e1c m\u1eb7t theo $a;b;c$<br\/><b>B\u01b0\u1edbc 3:<\/b>T\u00ednh t\u00edch di\u1ec7n t\u00edch $3$ m\u1eb7t c\u1ee7a h\u00ecnh ch\u1eef nh\u1eadt.<br\/><b>B\u01b0\u1edbc 4:<\/b> T\u00ednh m\u1ed7i k\u00edch th\u01b0\u1edbc t\u1eeb th\u1ec3 t\u00edch v\u00e0 di\u1ec7n t\u00edch c\u00e1c m\u1eb7t.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>Gi\u1ea3 s\u1eed h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt $ABCD.A'B'C'D'$ c\u00f3 c\u00e1c k\u00edch th\u01b0\u1edbc l\u1ea7n l\u01b0\u1ee3t l\u00e0 $AB=a\\,(cm)$; $BC=b\\,(cm)$; $CC'=c\\,(cm)$<br\/>Khi \u0111\u00f3, ta c\u00f3:<br\/>$S_{ABCD}=a.b=30\\,(cm^2) \\,\\,(1)$<br\/>$S_{BCC'B'}=b.c=20\\,(cm^2)\\,\\,(2)$<br\/>$S_{DD'C'C}=a.c=24\\,(cm^2)\\,\\,(3)$<br\/>Suy ra $ab.bc.ca=30.20.24=14400\\Leftrightarrow (abc)^2=14400\\Leftrightarrow abc=120\\,(cm^3)\\,\\,(4)$<br\/>V\u1eady th\u1ec3 t\u00edch h\u00ecnh h\u1ed9p l\u00e0 $120\\,cm^3$<br\/>T\u1eeb (1) v\u00e0 (4) ta c\u00f3: $c=\\dfrac{abc}{ab}=\\dfrac{120}{30}=4\\,(cm)$<br\/>T\u1eeb (2) v\u00e0 (4) ta c\u00f3: $a=\\dfrac{abc}{bc}=\\dfrac{120}{20}=6\\,(cm)$<br\/>T\u1eeb (3) v\u00e0 (4) ta c\u00f3: $b=\\dfrac{abc}{ac}=\\dfrac{120}{24}=5\\,(cm)$<br\/>V\u1eady h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt c\u00f3 k\u00edch th\u01b0\u1edbc l\u00e0 $4;5;6\\,cm$<br\/><span class='basic_pink'>V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $4;5;6$<\/span><\/span>"}]}],"id_ques":1833},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["2700"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"M\u1ed9t h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt c\u00f3 t\u1ed5ng ba k\u00edch th\u01b0\u1edbc b\u1eb1ng $60\\,cm$ v\u00e0 \u0111\u01b0\u1eddng ch\u00e9o b\u1eb1ng $30\\,cm$ t\u00ednh di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt.<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai20/lv3/img\/H8_B20_K1.6.png' \/><\/center><br\/><b> Tr\u1ea3 l\u1eddi:<\/b>_input_ ($cm^2$)","hint":"Vi\u1ebft c\u00f4ng th\u1ee9c t\u00ednh \u0111\u01b0\u1eddng ch\u00e9o l\u1edbn v\u00e0 di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh h\u1ed9p. <br\/>V\u1eadn d\u1ee5ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c m\u1edf r\u1ed9ng $(a+b+c)^2$","explain":"<span class='basic_left'><br\/><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> Bi\u1ec3u di\u1ec5n c\u00f4ng th\u1ee9c t\u00ednh \u0111\u01b0\u1eddng ch\u00e9o h\u00ecnh h\u1ed9p theo k\u00edch th\u01b0\u1edbc $a;b;c$<br\/><b>B\u01b0\u1edbc 2:<\/b> S\u1eed d\u1ee5ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c $(a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ca $ <br\/><b>B\u01b0\u1edbc 3:<\/b> T\u00ednh th\u1ec3 t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh h\u1ed9p.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>Gi\u1ea3 s\u1eed h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt c\u00f3 k\u00edch th\u01b0\u1edbc l\u00e0 $a;b;c$ ($cm$)<br\/>Ta d\u1ec5 d\u00e0ng ch\u1ee9ng minh \u0111\u01b0\u1ee3c \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng ch\u00e9o l\u1edbn l\u00e0 $\\sqrt {a^2+b^2+c^2}$ ($cm$)<br\/>Suy ra, $\\sqrt{a^2+b^2+c^2}=30\\Leftrightarrow a^2+b^2+c^2=900$<br\/>Theo gi\u1ea3 thi\u1ebft ta c\u00f3, $a+b+c=60$<br\/>Khi \u0111\u00f3, ta c\u00f3: $(a+b+c)^2=60^2\\\\ \\Leftrightarrow a^2+b^2+c^2+2ab+2bc+2ca=3600\\\\ \\Leftrightarrow 900+2(ab+bc+ca)=2700\\\\ \\Leftrightarrow 2(ab+bc+ca)=2700\\,(cm^2)$<br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $2700$<\/span><br\/><span class='basic_green'>Ghi nh\u1edb:<\/span> Trong h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt $ABCD.A'B'C'D'$ c\u00f3 $4$ \u0111\u01b0\u1eddng ch\u00e9o l\u1edbn c\u1eaft nhau t\u1ea1i trung \u0111i\u1ec3m c\u1ee7a m\u1ed7i \u0111\u01b0\u1eddng l\u00e0: $AC';\\,BD';\\,CA';\\,$ v\u00e0 $DB'$<br\/><b><i>Ch\u1ee9ng minh c\u00f4ng th\u1ee9c t\u00ednh \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng ch\u00e9o<\/i><\/b><br\/>X\u00e9t h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt $ABCD.A'B'C'D'$ c\u00f3 c\u00e1c k\u00edch th\u01b0\u1edbc: $AA'=a;\\,AB=b;\\,AD=c$. T\u00ednh $AC'$<br\/>X\u00e9t tam gi\u00e1c $A'B'C'$ vu\u00f4ng t\u1ea1i $B'$. \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3:<br\/>$A'C'^2=A'B'^2+B'C'^2\\Rightarrow A'C'^2=b^2+c^2$<br\/>X\u00e9t tam gi\u00e1c $AA'C'$ vu\u00f4ng t\u1ea1i $A'$. \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3:<br\/>$AC'=AA'^2+A'C'^2\\Rightarrow AC'^2=a^2+b^2+c^2\\Leftrightarrow AC'=\\sqrt {a^2+b^2+c^2}$<\/span>"}]}],"id_ques":1834},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":"H\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt $ABCD.A'B'C'D'$ c\u00f3 \u0111\u00e1y l\u00e0 h\u00ecnh vu\u00f4ng c\u1ea1nh $12cm$ v\u00e0 $BD=BB\u2019$. T\u00ednh s\u1ed1 \u0111o g\u00f3c $A\u2019DB\u2019$.<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai20/lv3/img\/H8_B20_K1.7.png' \/><\/center>","select":["A. $30^o$","B. $45^o$","C. $60^o$","D. $20^o$"],"hint":"Tam gi\u00e1c $A'DB'$ vu\u00f4ng t\u1ea1i $A'$. K\u1ebb $BD$, t\u00ednh \u0111\u1ed9 d\u00e0i $B'D$","explain":" <span class='basic_left'><br\/><span class='basic_green'>H\u01b0\u1edbng d\u1eabn<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> K\u1ebb $BD$. T\u00ednh $BD$<br\/><b>B\u01b0\u1edbc 2:<\/b> T\u00ednh $DB'$<br\/><b>B\u01b0\u1edbc 3:<\/b> Nh\u1eadn x\u00e9t t\u1ec9 l\u1ec7 hai c\u1ea1nh $A'B'$ v\u00e0 $B'D$.<br\/>Trong tam gi\u00e1c vu\u00f4ng, n\u1ebfu c\u1ea1nh g\u00f3c vu\u00f4ng v\u00e0 c\u1ea1nh huy\u1ec1n t\u1ec9 l\u1ec7 v\u1edbi $1:2$ th\u00ec g\u00f3c \u0111\u1ed1i di\u1ec7n c\u1ea1nh g\u00f3c vu\u00f4ng \u0111\u00f3 $30^o$.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai20/lv3/img\/H8_B20_K1.7.png' \/><\/center><br\/>K\u1ebb $BD$.<br\/>X\u00e9t tam gi\u00e1c $ABD$ vu\u00f4ng t\u1ea1i $A$ c\u00f3 $AD=AB=12\\,cm$.<br\/>\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3:<br\/>$BD^2=AB^2+AD^2\\\\ \\Rightarrow BD^2=12^2+12^2\\\\ \\Leftrightarrow BD^2=2.12^2\\\\ \\Leftrightarrow BD=12\\sqrt {2}\\,(cm)$<br\/>T\u01b0\u01a1ng t\u1ef1, ta c\u00f3: <br\/>Tam gi\u00e1c $BDB'$ vu\u00f4ng t\u1ea1i $B$ c\u00f3 $BD=BB'=12\\sqrt{2}\\,cm$.<br\/>Suy ra $DB'=24\\,(cm)$<br\/>Ta c\u00f3: $A'B'\\bot AA'; \\,A'B'\\bot A'D'\\Rightarrow A'B'\\bot mp(ADD'A')\\Rightarrow A'B'\\bot A'D$<br\/>X\u00e9t tam gi\u00e1c $A'DB'$ vu\u00f4ng t\u1ea1i $A'$ c\u00f3 $A'B'=\\dfrac{1}{2}B'D\\,\\,(12=\\dfrac{1}{2}.24)$<br\/>Suy ra $\\widehat{A'DB'}=30^o$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A<\/span><br\/><span class='basic_green'>L\u01b0u \u00fd: <\/span><br\/>- Trong tam gi\u00e1c vu\u00f4ng, n\u1ebfu c\u1ea1nh g\u00f3c vu\u00f4ng v\u00e0 c\u1ea1nh huy\u1ec1n t\u1ec9 l\u1ec7 v\u1edbi $1:2$ th\u00ec g\u00f3c \u0111\u1ed1i di\u1ec7n c\u1ea1nh g\u00f3c vu\u00f4ng \u0111\u00f3 $30^o$.<br\/>- Trong tam gi\u00e1c vu\u00f4ng, n\u1ebfu c\u1ea1nh g\u00f3c vu\u00f4ng v\u00e0 c\u1ea1nh huy\u1ec1n t\u1ec9 l\u1ec7 v\u1edbi $\\sqrt {3}:2$ th\u00ec g\u00f3c \u0111\u1ed1i di\u1ec7n c\u1ea1nh g\u00f3c vu\u00f4ng \u0111\u00f3 $60^o$.<\/span>","column":2}]}],"id_ques":1835},{"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":"M\u1ed9t h\u00ecnh l\u1eadp ph\u01b0\u01a1ng c\u1ea1nh $5 cm$ \u0111\u1eb7t tr\u00ean b\u00e0n. T\u00ednh qu\u00e3ng \u0111\u01b0\u1eddng ng\u1eafn nh\u1ea5t m\u00e0 con ki\u1ebfn ph\u1ea3i b\u00f2 t\u1eeb \u0111\u1ec9nh $A$ \u0111\u1ebfn trung \u0111i\u1ec3m $M$ c\u1ea1nh $CC\u2019$.<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai20/lv3/img\/H8_B20_K1.9.png' \/><\/center>","select":["A. $7,07\\,cm$","B. $9,01\\,cm$","C. $12,5\\,cm$","D. $15\\,cm$"],"hint":"X\u00e9t tr\u00ean t\u1eebng m\u1eb7t ph\u1eb3ng m\u00e0 con ki\u1ebfn c\u00f3 th\u1ec3 b\u00f2 qua. Tr\u1ea3i ph\u1eb3ng c\u00e1c m\u1eb7t ph\u1eb3ng v\u00e0 x\u00e1c \u0111\u1ecbnh qu\u00e3ng \u0111\u01b0\u1eddng ng\u1eafn nh\u1ea5t.","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai20/lv3/img\/H8_B20_K1.8.png' \/><\/center><br\/>Gi\u1ea3 s\u1eeda con ki\u1ebfn b\u00f2 qua m\u1eb7t ph\u1eb3ng $ABCD$ v\u00e0 m\u1eb7t ph\u1eb3ng $BCC'B'$ (c\u00e1c m\u1eb7t ph\u1eb3ng kh\u00e1c t\u01b0\u01a1ng t\u1ef1). <br\/>Ta tr\u1ea3i ph\u1eb3ng hai m\u1eb7t ph\u1eb3ng ta \u0111\u01b0\u1ee3c h\u00ecnh v\u1ebd minh h\u1ecda qu\u00e3ng \u0111\u01b0\u1eddng ng\u1eafn nh\u1ea5t c\u1ee7a con ki\u1ebfn l\u00e0 $AM$<br\/>X\u00e9t tam gi\u00e1c $ADM$ vu\u00f4ng t\u1ea1i $D$ c\u00f3 $AD=5\\,cm;\\,DM=DC+CM=7,5\\,cm$<br\/>\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3: $AM=\\sqrt{AD^2+DM^2}\\Rightarrow AM=\\sqrt{5^2+7,5^2}=9,01\\,(cm)$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B<\/span><\/span>","column":2}]}],"id_ques":1836},{"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":"Cho h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt $ABCD.A'B'C'D'$. T\u1ee9 gi\u00e1c $ADC'B'$ l\u00e0 h\u00ecnh g\u00ec?<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai20/lv3/img\/H8_B20_K1.10.png' \/><\/center>","select":["A. H\u00ecnh b\u00ecnh h\u00e0nh","B. H\u00ecnh ch\u1eef nh\u1eadt","C. H\u00ecnh vu\u00f4ng","D. H\u00ecnh thoi"],"hint":"","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai20/lv3/img\/H8_B20_K1.10.png' \/><\/center><br\/>T\u1ee9 gi\u00e1c $ADC'B'$ c\u00f3 $AD\/\/B'C'$ (v\u00ec c\u00f9ng song song v\u1edbi $BC$); $AD=B'C'$ (t\u00ednh ch\u1ea5t h\u00ecnh l\u1eadp ph\u01b0\u01a1ng) n\u00ean $ADC'B'$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh.<br\/>Ta c\u00f3: $AD\\bot ABB'A'$ (v\u00ec $AD$ vu\u00f4ng g\u00f3c v\u1edbi hai \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft nhau $AB$ v\u00e0 $AA'$) n\u00ean $AD\\bot AB'$.<br\/>H\u00ecnh b\u00ecnh h\u00e0nh $ADC'B'$ c\u00f3 $\\widehat{DAB'}=90^o$ n\u00ean l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt.<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B<\/span><\/span>","column":2}]}],"id_ques":1837},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0110\u00fang ho\u1eb7c Sai","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":"N\u1ebfu m\u1ed7i c\u1ea1nh c\u1ee7a h\u00ecnh l\u1eadp ph\u01b0\u01a1ng gi\u1ea3m $30\\%$ th\u00ec th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh l\u1eadp ph\u01b0\u01a1ng gi\u1ea3m $30\\%$. <b>\u0110\u00fang<\/b> hay <b>Sai<\/b>?","select":["\u0110\u00fang","Sai"],"hint":"G\u1ecdi \u0111\u1ed9 d\u00e0i m\u1ed9t c\u1ea1nh l\u00e0 $a$. T\u00ednh th\u1ec3 t\u00edch ban \u0111\u1ea7u v\u00e0 sau khi thay \u0111\u1ed5i r\u1ed3i so s\u00e1nh.","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai20/lv3/img\/H8_B20_K1.11.png' \/><\/center>Gi\u1ea3 s\u1eed h\u00ecnh l\u1eadp ph\u01b0\u01a1ng c\u00f3 c\u1ea1nh d\u00e0i $a\\,(cm)$<br\/>Th\u1ec3 t\u00edch h\u00ecnh l\u1eadp ph\u01b0\u01a1ng l\u00e0 $a^3\\,(cm^3)$<br\/>M\u1ed7i c\u1ea1nh h\u00ecnh l\u1eadp ph\u01b0\u01a1ng gi\u1ea3m $30\\%$ th\u00ec \u0111\u1ed9 d\u00e0i m\u1ed7i c\u1ea1nh l\u00e0 $a-30\\%a=70\\%a=0,7a\\,(cm)$<br\/>Th\u1ec3 t\u00edch h\u00ecnh l\u1eadp ph\u01b0\u01a1ng sau khi thay \u0111\u1ed5i k\u00edch th\u01b0\u1edbc l\u00e0 $(0,7a)^3=0,343a^3\\,(cm^3)$<br\/>V\u1eady th\u1ec3 t\u00edch h\u00ecnh l\u1eadp ph\u01b0\u01a1ng gi\u1ea3m $a^3-0,343a^3=0,657a^3\\,(cm^3)$<br\/>Do v\u1eady th\u1ec3 t\u00edch gi\u1ea3m $65,7\\%$<br\/><span class='basic_pink'>V\u1eady kh\u1eb3ng \u0111\u1ecbnh tr\u00ean l\u00e0 Sai.<\/span><\/span>","column":2}]}],"id_ques":1838},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["10"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"H\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt $ABCD.A'B'C'D'$ c\u00f3 $AA\u2019=2$; $AC=14$. $A\u2019B\u2019CD$ l\u00e0 h\u00ecnh vu\u00f4ng. T\u00ednh \u0111\u1ed9 d\u00e0i $CD$.<br\/><b> \u0110\u00e1p s\u1ed1: <\/b> _input_ ($cm$)","hint":"\u0110\u1eb7t $CD=A'D=x$","explain":"<span class='basic_left'><br\/><span class='basic_green'>H\u01b0\u1edbng d\u1eabn<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> \u0110\u1eb7t $CD=A'D=x$<br\/><b>B\u01b0\u1edbc 2:<\/b> \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago v\u00e0o tam gi\u00e1c $AA'D$, t\u00ednh $AD^2$<br\/><b>B\u01b0\u1edbc 3:<\/b> \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago v\u00e0o tam gi\u00e1c $ACD$, t\u00ednh $CD$<br\/><b>B\u01b0\u1edbc 4:<\/b> K\u1ebft lu\u1eadn.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai20/lv3/img\/H8_B20_K1.14.png' \/><\/center><br\/>$A'B'CD$ l\u00e0 h\u00ecnh vu\u00f4ng n\u00ean $CD=A'D$.<br\/>\u0110\u1eb7t $CD=A'D=x$<br\/>X\u00e9t tam gi\u00e1c $AA'D$ vu\u00f4ng t\u1ea1i $A$. \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3: <br\/>$AD^2=A'D^2-AA'^2=x^2-2^2=x^2-4$<br\/>Tam gi\u00e1c $ACD$ vu\u00f4ng t\u1ea1i $D$ n\u00ean theo \u0111\u1ecbnh l\u00fd Pytago, ta c\u00f3: <br\/>$AD^2+CD^2=AC^2\\Rightarrow x^2-4+x^2=14^2\\Leftrightarrow 2x^2=200\\Leftrightarrow x^2=100\\Leftrightarrow x=10$<br\/>V\u1eady $CD=10$<br\/><span class='basic_pink'>V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $10$<\/span><\/span>"}]}],"id_ques":1839}],"lesson":{"save":0,"level":3}}