Cho tam gi\u00e1c ABC c\u1ed1 \u0111\u1ecbnh v\u00e0 m\u1ed9t \u0111i\u1ec3m S thay \u0111\u1ed5i. Th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i ch\u00f3p S.ABC c\u00f3 thay \u0111\u1ed5i hay kh\u00f4ng n\u1ebfu:<\/p>\n

a) \u0110\u1ec9nh S di chuy\u1ec3n tr\u00ean m\u1ed9t m\u1eb7t ph\u1eb3ng song song v\u1edbi m\u1eb7t ph\u1eb3ng (ABC)?<\/p>\n

b) \u0110\u1ec9nh S di chuy\u1ec3n tr\u00ean m\u1ed9t m\u1eb7t ph\u1eb3ng song song v\u1edbi ch\u1ec9 m\u1ed9t c\u1ea1nh \u0111\u00e1y?<\/p>\n

c) \u0110\u1ec9nh S di chuy\u1ec3n tr\u00ean m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng song song v\u1edbi m\u1ed9t c\u1ea1nh \u0111\u00e1p?<\/p>\n

Trong \u0111\u00f3 S_{\u0394ABC<\/sub>\u00a0kh\u00f4ng \u0111\u1ed5i, h = d(S; (ABC))<\/p>\n}

a) Khi S di chuy\u1ec3n tr\u00ean (\u03b1)\/\/ (ABC)) th\u00ec d(S, (ABC)) = (d(\u03b1);(ABC))kh\u00f4ng \u0111\u1ed5i n\u00ean VV_{S.ABC<\/sub>\u00a0kh\u00f4ng \u0111\u1ed5i.<\/p>\n}

b) Khi S di chuy\u1ec3n tr\u00ean m\u1ed9t m\u1eb7t ph\u1eb3ng song song v\u1edbi m\u1ed9t c\u1ea1nh \u0111\u00e1y. M\u1eb7t ph\u1eb3ng n\u00e0y c\u00f3 th\u1ec3 kh\u00f4ng song song v\u1edbi mp (ABC).<\/p>\n

Khi \u0111\u00f3 h = d(S: (ABC)) c\u00f3 th\u1ec3 thay \u0111\u1ed5i n\u00ean V_{S.ABC<\/sub>\u00a0c\u00f3 th\u1ec3 thay \u0111\u1ed5i.<\/p>\n}

c) Gi\u1ea3 s\u1eed S di chuy\u1ec3n tr\u00ean d v\u00e0 d\/\/ AC (d \/\/ AC => d \/\/(ABC)) d(S, (ABC)) , (ABC)=d(d; (ABC)) kh\u00f4ng \u0111\u1ed5i n\u00ean VV_{S.ABC<\/sub>\u00a0kh\u00f4ng \u0111\u1ed5i.<\/p>\n}

B\u00e0i 16 (trang 28 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao):<\/b>\u00a0H\u00e3y chia m\u1ed9t kh\u1ed1i t\u1ee9 di\u1ec7n th\u00e0nh hai kh\u1ed1i t\u1ee9 di\u1ec7n sao cho t\u1ec9 s\u1ed1 th\u1ec3 t\u00edch c\u1ee7a hai kh\u1ed1i n\u00e0y b\u1eb1ng s\u1ed1 k > 0 cho tr\u01b0\u1edbc.<\/p>\n

<\/div>\n
$\"\"$ <\/p>\n
G\u1ecdi M l\u00e0 m\u1ed9t \u0111i\u1ec3m tr\u00ean c\u1ea1nh AB kh\u00e1c hai \u0111\u1ea7u n\u00fat). Khi \u0111\u00f3 (SMC) chia t\u1ee9 di\u1ec7n S.ABC th\u00e0nh hai t\u1ee9 di\u1ec7n S.AMC v\u00e0 S. BMC l\u1ea7n l\u01b0\u1ee3t v\u1edbi th\u1ec3 t\u00edch V_{1<\/sub>,_{2<\/sub><\/p>\n}}
V\u00ec d(S, (AMC) = d(S,(BMC)) n\u00ean<\/p>\n
$\"\"$ <\/p>\n
K\u1ebft lu\u1eadn: L\u1ea5y \u0111i\u1ec3m M tr\u00ean AB sao cho AM = k MB. Khi \u0111\u00f3, kh\u1ed1i t\u1ee9 di\u1ec7n SABC \u0111\u01b0\u1ee3c chia th\u00e0nh hai kh\u1ed1i t\u1ee9 di\u1ec7n SAMC v\u00e0 SBMC th\u1ecfa y\u00eau c\u1ea7u b\u00e0i to\u00e1n.<\/p>\n
B\u00e0i 17 (trang 28 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao):<\/b><\/p>\n
T\u00ednh th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i h\u1ed9p ABCD.A\u2019B\u2019C\u2019D\u2019 bi\u1ebft r\u1eb1ng AA\u2019B\u2019D\u2019 l\u00e0 kh\u1ed1i t\u1ee9 di\u1ec7n \u0111\u1ec1u c\u1ea1nh a.<\/p>\n
$\"\"$ <\/p>\n
L\u1eddi gi\u1ea3i:<\/b><\/p>\n
V\u00ec h = d (ABCD); (A\u2019B\u2019C\u2019D\u2019) = d(A, (A\u2019B\u2019D\u2019) v\u00e0 S_{\u0394A’ B’ C’ D’<\/sub>=2.S_{\u0394A’ B’ D’<\/sub><\/p>\n}}
$\"\"$ <\/p>\n
B\u00e0i 18 (trang 28 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao):<\/b>\u00a0T\u00ednh th\u1ec3 t\u00edch c\u1ee7a m\u1ed9t kh\u1ed1i n \u2013 c\u00f3 t\u1ea5t c\u1ea3 c\u00e1c c\u1ea1nh \u0111\u1ec1u b\u1eb1ng a.<\/p>\n
$\"Gi\u1ea3i$ <\/p>\n
L\u1eddi gi\u1ea3i:<\/b><\/p>\n
<\/iframe><\/ins><\/ins><\/ins><\/div>\n– X\u00e9t l\u0103ng tr\u1ee5 n \u2013 gi\u00e1c \u0111\u1ec1u.<\/p>\nA1<\/sub>\u00a0A2<\/sub>..A_n A1<\/sub>‘ A2<\/sub>‘\u2026An<\/sub>‘ c\u00f3 t\u1ea5t c\u1ea3 c\u00e1c c\u1ea1nh b\u1eb1ng a.<\/p>\nTa c\u00f3: V = S.h, trong \u0111\u00f3<\/p>\nS l\u00e0 di\u1ec7n t\u00edch n \u2013 gi\u00e1c \u0111i\u1ec1u A1<\/sub>\u00a0A2<\/sub>\u2026An<\/sub>\u00a0c\u1ea1nh a.<\/p>\nh l\u00e0 chi\u1ec1u cao.<\/p>\nV l\u00e0 th\u1ec3 t\u00edch c\u1ee7a l\u0103ng tr\u1ee5.<\/p>\n<img decoding=\"async\" src=\"http:\/\/vietjack.com\/giai-toan-12-nang-cao\/images\/bai-18-trang-28-sgk-hinh-hoc-12-nang-cao-2.PNG\" alt=\"Gi\u1ea3i To\u00e1n 12 n\u00e2ng cao | Gi\u1ea3i b\u00e0i t\u1eadp To\u00e1n l\u1edbp 12 n\u00e2ng cao\" \/><\/p>\n– Theo \u0111\u1ec1 ra: h = a<\/p>\nS = n. S_(\u0394OA1<\/sub>\u00a0A2<\/sub>\u00a0) (O l\u00e0 t\u00e2m c\u1ee7a \u0111\u00e1p A1<\/sub>\u00a0A2<\/sub>\u2026An<\/sub>)<\/p>\n<img decoding=\"async\" src=\"http:\/\/vietjack.com\/giai-toan-12-nang-cao\/images\/bai-18-trang-28-sgk-hinh-hoc-12-nang-cao-1.PNG\" alt=\"Gi\u1ea3i To\u00e1n 12 n\u00e2ng cao | Gi\u1ea3i b\u00e0i t\u1eadp To\u00e1n l\u1edbp 12 n\u00e2ng cao\" \/><\/p>\nB\u00e0i 19 (trang 28 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao):<\/b><\/p>\nCho kh\u1ed1i l\u0103ng tr\u1ee5 \u0111\u1ee9ng ABC.A\u2019B\u2019C\u2019 c\u00f3 \u0111\u00e1y l\u00e0 tam gi\u00e1c ABc vu\u00f4ng t\u1ea1i A, AC = b, g\u00f3c ACB=60o<\/sup>. D\u01b0\u1eddng th\u1eb3ng BC\u2019 t\u1ea1o mp (AACC\u2019) m\u1ed9t g\u00f3c 30o<\/sup>.<\/p>\na) T\u00ednh \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n th\u1eb3ng AC\u2019<\/p>\nb) T\u00ednh th\u1ec3 t\u00edch kh\u1ed1i l\u0103ng tr\u1ee5 \u0111\u00e3 cho.<\/p>\nL\u1eddi gi\u1ea3i:<\/b><\/p>\n<div><\/div>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-22426\" src=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-206.png\" alt=\"\" width=\"270\" height=\"292\" \/><\/p>\na) Do ABC.A\u2019B\u2019C\u2019 l\u00e0 l\u0103ng tr\u1ee5 \u0111\u1ee9ng n\u00ean AA\u2019 \u22a5 AB m\u00e0 AC \u22a5 AB.<\/p>\nAB \u22a5 (ACC\u2019A\u2019)<\/p>\ng\u00f3c BC’A=30o<\/sup>\u00a0v\u00e0 \u0394ABC’ vu\u00f4ng t\u1ea1i A.<\/p>\nAC\u2019 = AB. Cot 30o<\/sup><\/p>\nX\u00e9t \u0394ABC: AB = AC.tan (g\u00f3c ACB)=b \u221a3<\/p>\nV\u1eady AC\u2019 = b \u221a3; \u221a3=3b<\/p>\nb) VABC.A’B’C’<\/sub>=S\u0394ABC<\/sub>.h: trong \u0111\u00f3<\/p>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-22427\" src=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/2-113.png\" alt=\"\" width=\"281\" height=\"135\" \/><\/p>\nB\u00e0i 20 (trang 28 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao):<\/b><\/p>\nCho kh\u1ed1i l\u0103ng tr\u1ee5 tam gi\u00e1c ABC.A\u2019B\u2019C\u2019 c\u00f3 \u0111\u00e1y l\u00e0 tam gi\u00e1c \u0111\u1ec1u c\u1ea1nh a. \u0111i\u1ec3m A\u2019 c\u00e1ch \u0111\u1ec1u 3 \u0111i\u1ec3m A, B, C, c\u1ea1nh b\u00ean AA\u2019 t\u1ea1o v\u1edbi m\u1eb7t ph\u1ea7n \u0111\u00e1y m\u1ed9t g\u00f3c 600<\/sup>.<\/p>\na) T\u00ednh th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i l\u0103ng tr\u1ee5 \u0111\u00f3.<\/p>\nb) Ch\u1ee9ng minh r\u1eb1ng m\u1eb7t b\u00ean BCC\u2019B\u2019 l\u00e0 m\u1ed9t h\u00ecnh ch\u1eef nh\u1eadt.<\/p>\nc) T\u00ednh t\u1ed5ng di\u1ec7n t\u00edch c\u00e1c m\u1eb7t b\u00ean c\u1ee7a h\u00ecnh l\u0103ng tr\u1ee5 ABC.A\u2019B\u2019C\u2019 (t\u1ed5ng \u0111\u00f3 g\u1ecdi l\u00e0 di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh (ho\u1eb7c kh\u1ed1i l\u0103ng tr\u1ee5 \u0111\u00e3 cho).<\/p>\nL\u1eddi gi\u1ea3i:<\/b><\/p>\n<div><\/div>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-22428\" src=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-207.png\" alt=\"\" width=\"186\" height=\"264\" \/><\/p>\na) G\u1ecdi O l\u00e0 t\u00e2m c\u1ee7a tam gi\u00e1c ABC, v\u00ec OA = OB = OC n\u00ean A’ O \u22a5 (ABC)<\/p>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-22429\" src=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/2-114.png\" alt=\"\" width=\"277\" height=\"186\" \/><\/p>\nb) Ta c\u00f3: BC \u22a5 AO n\u00ean BC \u22a5 AA’ (\u0111\u1ecbnh l\u00ed 3 \u0111\u01b0\u1eddng vu\u00f4ng g\u00f3c)<\/p>\nL\u1ea1i c\u00f3 AA\u2019 \/\/CC\u2019 => BC \u22a5 CC\u2019<\/p>\nT\u1ee9 gi\u00e1c BB\u2019C\u2019C l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh c\u00f3 m\u1ed9t g\u00f3c vu\u00f4ng n\u00ean l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt.<\/p>\nc) Sxq<\/sub>=2SAA’ B’ B<\/sub>+SBB’ C’ C<\/sub><\/p>\nG\u1ecdi H l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AB \u0111\u1ec3 th\u1ea5y<\/p>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-22430\" src=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/3-60.png\" alt=\"\" width=\"436\" height=\"143\" srcset=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/3-60.png 436w, https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/3-60-300x98.png 300w\" sizes=\"(max-width: 436px) 100vw, 436px\" \/><\/p>\nB\u00e0i 21 (trang 28 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao):<\/b><\/p>\nCho \u0111i\u1ec3m M n\u1eb1m trong h\u00ecnh t\u1ee9 di\u1ec7n \u0111\u1ec1u ABCD. Ch\u1ee9ng minh r\u1eb1ng t\u1ed5ng c\u00e1c kho\u1ea3ng c\u00e1ch t\u1eeb M t\u1edbi b\u1ed1n m\u1eb7t c\u1ee7a h\u00ecnh t\u1ee9 di\u1ec7n l\u00e0 m\u1ed9t s\u1ed1 kh\u00f4ng ph\u1ee5 thu\u1ed9c v\u00e0o v\u1ecb tr\u00ed c\u1ee7a \u0111i\u1ec3m M. T\u1ed5ng \u0111\u00f3 b\u1eb1ng bao nhi\u00eau n\u1ea5u c\u1ea1nh c\u1ee7a t\u1ee9 di\u1ec7n \u0111\u1ec1u b\u1eb1ng a?<\/p>\nL\u1eddi gi\u1ea3i:<\/b><\/p>\n<div><\/div>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-22431\" src=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-208.png\" alt=\"\" width=\"280\" height=\"247\" \/><\/p>\nG\u1ecdi h1<\/sub>,h2<\/sub>,h3<\/sub>,h4<\/sub>\u00a0l\u1ea7n l\u01b0\u1ee3t l\u00e0 kho\u1ea3ng c\u00e1c t\u1eeb M \u0111\u1ebfn (ABC), (ACD), (ABD), (BCD). Kh\u1ed1i t\u1ee9 di\u1ec7n ABCD \u0111\u01b0\u1ee3c chia th\u00e0nh 4 kh\u1ed1i t\u1ee9 di\u1ec7n MABC, MACD, MABD, MBCD.<\/p>\nTa c\u00f3:<\/p>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-22432\" src=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/2-115.png\" alt=\"\" width=\"455\" height=\"79\" srcset=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/2-115.png 455w, https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/2-115-300x52.png 300w\" sizes=\"(max-width: 455px) 100vw, 455px\" \/><\/p>\nL\u1ea1i v\u00ec S\u0394ABC<\/sub>=S\u0394ACD<\/sub>=S\u0394ABD<\/sub>=S\u0394BCD<\/sub><\/p>\nN\u00ean VABCD<\/sub>=(1\/3).S_\u0394ABC (h1<\/sub>+h2<\/sub>+h3<\/sub>+h4<\/sub>) (1)<\/p>\nG\u1ecdi h l\u00e0 chi\u1ec1u cao c\u1ee7a t\u1ee9 di\u1ec7n \u0111\u1ec1u, ta c\u00f3:<\/p>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-22433\" src=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/3-61.png\" alt=\"\" width=\"267\" height=\"53\" srcset=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/3-61.png 267w, https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/3-61-265x53.png 265w\" sizes=\"(max-width: 267px) 100vw, 267px\" \/><\/p>\nT\u1eeb (1) v\u00e0 (2) c\u00f3: h1<\/sub>+h2<\/sub>+h3<\/sub>+h4<\/sub>=h<\/p>\nN\u1ebfu c\u1ea1nh c\u1ee7a t\u1ee9 di\u1ec7n \u0111\u1ec1u b\u1eb1ng a th\u00ec h a\u221a6\/3<\/p>\nB\u00e0i 22 (trang 28 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao):<\/b><\/p>\nCho kh\u1ed1i l\u0103ng tr\u1ee5 tam gi\u00e1c \u0111\u1ec1u ABC.A\u2019B\u2019C\u2019. g\u1ecdi M l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AA\u2019. M\u1eb7t ph\u1eb3ng \u0111i qua M, B\u2019, C chia kh\u1ed1i l\u0103ng tr\u1ee5 th\u00e0nh hai ph\u1ea7n. T\u00ednh t\u1ec9 s\u1ed1 c\u1ee7a th\u1ec3 t\u00edch c\u1ee7a hai ph\u1ea7n \u0111\u00f3.<\/p>\nL\u1eddi gi\u1ea3i:<\/b><\/p>\n<div><\/div>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-22434\" src=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-209.png\" alt=\"\" width=\"375\" height=\"231\" srcset=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-209.png 375w, https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-209-300x185.png 300w, https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-209-356x220.png 356w\" sizes=\"(max-width: 375px) 100vw, 375px\" \/><\/p>\nG\u1ecdi V, S, h l\u1ea7n l\u01b0\u1ee3t l\u00e0 th\u1ec3 t\u00edch v\u00e0 di\u1ec7n t\u00edch \u0111\u00e1y, chi\u1ec1u cao c\u1ee7a l\u0103ng tr\u1ee5. V1<\/sub>,V2<\/sub>\u00a0l\u1ea7n l\u01b0\u1ee3t l\u00e0 th\u1ec3 t\u00edch ph\u1ea7n l\u0103ng tr\u1ee5 b\u00ean tr\u00ean, b\u00ean d\u01b0\u1edbi thi\u1ebft di\u1ec7n MB\u2019C<\/p>\nE = CM \u2229C’A’, do M l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AA\u2019 n\u00ean A\u2019E = A\u2019C\u2019<\/p>\nS\u0394EA’B’<\/sub>=S\u0394A’B’C’<\/sub>\u00a0=S<\/p>\nTa c\u00f3:<\/p>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-22435\" src=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/2-116.png\" alt=\"\" width=\"282\" height=\"207\" srcset=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/2-116.png 282w, https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/2-116-80x60.png 80w\" sizes=\"(max-width: 282px) 100vw, 282px\" \/><\/p>\nB\u00e0i 23 (trang 29 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao):<\/b><\/p>\nCho kh\u1ed1i ch\u00f3p tam gi\u00e1c S.ABC. Tr\u00ean ba \u0111\u01b0\u1eddng th\u1eb3ng SA, SB, SC l\u1ea7n l\u01b0\u1ee3t l\u1ea5y ba \u0111i\u1ec3m A\u2019, B\u2019, C\u2019 kh\u00e1c v\u1edbi S. g\u1ecdi V v\u00e0 V\u2019 l\u1ea7n l\u01b0\u1ee3t l\u00e0 th\u1ec3 t\u00edch c\u1ee7a c\u00e1c kh\u1ed1i ch\u00f3p S.ABC v\u00e0 S.A\u2019B\u2019C\u2019<\/p>\nCh\u1ee9ng minh r\u1eb1ng:<\/p>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-22438\" src=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-211.png\" alt=\"\" width=\"166\" height=\"65\" \/><\/p>\nL\u1eddi gi\u1ea3i:<\/b><\/p>\n<div><\/div>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-22436\" src=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-210.png\" alt=\"\" width=\"278\" height=\"301\" srcset=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-210.png 278w, https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-210-277x300.png 277w\" sizes=\"(max-width: 278px) 100vw, 278px\" \/><\/p>\nTa c\u00f3:<\/p>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-22439\" src=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/2-118.png\" alt=\"\" width=\"266\" height=\"56\" srcset=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/2-118.png 266w, https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/2-118-265x56.png 265w\" sizes=\"(max-width: 266px) 100vw, 266px\" \/><\/p>\nK\u1ebb CH, C\u2019H\u2019 vu\u00f4ng g\u00f3c v\u1edbi (SAB) (H, H\u2019 \u2208 (SAB)) => CH \/\/ C\u2019H\u2019 v\u00e0 S, H, H\u2019 th\u1eb3ng h\u00e0ng n\u00ean<\/p>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-22440\" src=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/3-62.png\" alt=\"\" width=\"302\" height=\"231\" srcset=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/3-62.png 302w, https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/3-62-300x229.png 300w, https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/3-62-80x60.png 80w\" sizes=\"(max-width: 302px) 100vw, 302px\" \/><\/p>\nT\u1eeb (1), (2) v\u00e0 (3) suy ra:<\/p>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-22441\" src=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/5-22.png\" alt=\"\" width=\"161\" height=\"51\" \/><\/p>\nB\u00e0i 24 (trang 29 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao):<\/b><\/p>\nKh\u1ed1i ch\u00f3p S.ABCD c\u00f3 \u0111\u00e1y l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh, M l\u00e0 trung \u0111i\u1ec3m c\u1ea1nh SC. M\u1eb7t ph\u1eb3ng (P) \u0111i qua AM, song song v\u1edbi BD, chia kh\u1ed1i ch\u00f3p th\u00e0nh hai ph\u1ea7n. T\u00ednh t\u1ec9 s\u1ed1 th\u1ec3 t\u00edch c\u1ee7a hai ph\u1ea7n \u0111\u00f3.<\/p>\nL\u1eddi gi\u1ea3i:<\/b><\/p>\n<div><\/div>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-22442\" src=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-212.png\" alt=\"\" width=\"309\" height=\"215\" srcset=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-212.png 309w, https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-212-300x209.png 300w, https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-212-100x70.png 100w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><\/p>\nG\u1ecdi B\u2019= (P) \u2229SB; D\u2019 = (P) \u2229SD;O=AC \u2229BD<\/p>\nKhi \u0111\u00f3: B\u2019D\u2019, AM, SO \u0111\u1ed3ng quy t\u1ea1i tr\u1ecdng t\u00e2m G c\u1ee7a \u0394SAC v\u00e0 B\u2019D\u2019 \/\/ BD (do (P) \/\/ BD)<\/p>\nC\u00e1ch 1.<\/p>\nTa c\u00f3:<\/p>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-22443\" src=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/2-119.png\" alt=\"\" width=\"221\" height=\"53\" srcset=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/2-119.png 221w, https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/2-119-218x53.png 218w\" sizes=\"(max-width: 221px) 100vw, 221px\" \/><\/p>\nL\u1ea1i c\u00f3: GB\u2019 = GD\u2019<\/p>\n=> S\u0394AB’M<\/sub>=S\u0394AD’M<\/sub>\u00a0\u00a0\u00a0 (2)<\/p>\nT\u1eeb (1) v\u00e0 (2) suy ra:<\/p>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-22444\" src=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/3-63.png\" alt=\"\" width=\"345\" height=\"431\" srcset=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/3-63.png 345w, https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/3-63-240x300.png 240w, https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/3-63-336x420.png 336w\" sizes=\"(max-width: 345px) 100vw, 345px\" \/><\/p>\nB\u00e0i 25 (trang 29 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao):<\/b><\/p>\nCh\u1ee9ng minh r\u1eb1ng n\u1ebfu c\u00f3 ph\u00e9p v\u1ecb t\u1ef1 s\u1ed1 k bi\u1ebfn t\u1ee9 di\u1ec7n ABCD th\u00e0nh t\u1ee9 di\u1ec7n A\u2019B\u2019C\u2019D\u2019 th\u00ec:<\/p>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-22449\" src=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-214.png\" alt=\"\" width=\"165\" height=\"57\" \/><\/p>\nL\u1eddi gi\u1ea3i:<\/b><\/p>\n<div><\/div>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-22445\" src=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-213.png\" alt=\"\" width=\"426\" height=\"234\" srcset=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-213.png 426w, https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-213-300x165.png 300w\" sizes=\"(max-width: 426px) 100vw, 426px\" \/><\/p>\nG\u1ecdi H l\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a A tr\u00ean (BCD). Gi\u1ea3 s\u1eed ph\u00e9p v\u1ecb t\u1ef1 t\u1ec9 s\u1ed1 k bi\u1ebfn A, B, C, D, H l\u1ea7n l\u01b0\u1ee3t th\u00e0nh A\u2019, B\u2019, C\u2019, D\u2019, H\u2019.<\/p>\nV\u00ec H \u2208(BCD) n\u00ean H\u2019 \u2208(B’C’D’). H\u01a1n n\u1eefa, theo t\u00ednh ch\u1ea5t c\u1ee7a ph\u00e9p v\u1ecb t\u1ef1 th\u00ec A\u2019H\u2019 song song ho\u1eb7c tr\u00f9ng h\u1ee3p v\u1edbi AH; (B\u2019C\u2019D\u2019) song song ho\u1eb7c tr\u00f9ng h\u1ee3p v\u1edbi (BCD) m\u00e0 AH \u22a5 (BCD) n\u00ean A’H’ \u22a5 (B’C’D’). V\u1eady A\u2019H\u2019 l\u00e0 \u0111\u01b0\u1eddng cao c\u1ee7a t\u1ee9 di\u1ec7n (A\u2019B\u2019C\u2019D\u2019) (1)<\/p>\nM\u1eb7t kh\u00e1c, d\u1ec5 th\u1ea5y:<\/p>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-22446\" src=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/2-120.png\" alt=\"\" width=\"225\" height=\"37\" srcset=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/2-120.png 225w, https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/2-120-218x37.png 218w\" sizes=\"(max-width: 225px) 100vw, 225px\" \/><\/p>\nH\u01a1n n\u1eefa, c\u0169ng t\u1eeb t\u00ednh ch\u1ea5t c\u1ee7a ph\u00e9p v\u1ecb t\u1eeb ta c\u00f3:<\/p>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-22447\" src=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/3-64.png\" alt=\"\" width=\"259\" height=\"59\" \/><\/p>\nT\u1eeb (1), (2), (3) ta c\u00f3:<\/p>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-22448\" src=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/4-33.png\" alt=\"\" width=\"300\" height=\"203\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"B\u00e0i 15 (trang 28 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao): Cho tam gi\u00e1c ABC c\u1ed1 \u0111\u1ecbnh v\u00e0 m\u1ed9t \u0111i\u1ec3m S thay \u0111\u1ed5i. Th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i ch\u00f3p S.ABC c\u00f3 thay \u0111\u1ed5i hay kh\u00f4ng n\u1ebfu: a) \u0110\u1ec9nh S di chuy\u1ec3n tr\u00ean m\u1ed9t m\u1eb7t ph\u1eb3ng song song v\u1edbi m\u1eb7t ph\u1eb3ng (ABC)? b) \u0110\u1ec9nh S di chuy\u1ec3n tr\u00ean […]<\/p>\n","protected":false},"author":3,"featured_media":22420,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"tdm_status":"","tdm_grid_status":""},"categories":[1302],"tags":[1392,1393],"yoast_head":"\n<title>H\u00ecnh h\u1ecdc - Ch\u01b0\u01a1ng 1 - B\u00e0i 4 - Th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i \u0111a dien<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-1-bai-4-the-tich-cua-khoi-da-dien\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"H\u00ecnh h\u1ecdc - Ch\u01b0\u01a1ng 1 - B\u00e0i 4 - Th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i \u0111a dien\" \/>\n<meta property=\"og:description\" content=\"B\u00e0i 15 (trang 28 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao): Cho tam gi\u00e1c ABC c\u1ed1 \u0111\u1ecbnh v\u00e0 m\u1ed9t \u0111i\u1ec3m S thay \u0111\u1ed5i. 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