https://cxcosmetics.com.au/pub/ https://icesco.seecs.nust.edu.pk/wp-includes/css/ https://bkad.bengkuluutarakab.go.id/js/ https://www.wartanusantara.org/data-coinmarketcap-bitcoin-menguat-naik-741-dalam-24-jam/ https://land.ubiz.ua/assets/img/ https://inlislite.perpus.palopokota.go.id/cgacor/ https://www.kakamega.go.ke/nul/ https://task.travis.enkosoft.com/ https://www.kungfuology.com/home/plugins/ https://ncc.potensi-utama.ac.id/wp-content/plugins/ https://ji-touch.ru/storage/xgacor/ https://designeroutletathens.gr/admin_assets/xqris/ https://sisule.dprd-bungokab.go.id/gacorx/ https://www.wartanusantara.org/film-vina-sebelum-7-hari-menjadi-perbincangan-hangat-di-media-sosial/ https://www.wartanusantara.org/colour-music-fest-vol-2-siap-meriahkan-karawang-pada-18-mei-2024/ https://www.wartanusantara.org/10-cara-memulai-bisnis-dari-nol-hingga-sukses-untuk-pemula/ https:https://www.wartanusantara.org/terobosan-emosi-ragam-film-indonesia-bulan-ini/
{"id":22464,"date":"2018-03-19T18:13:54","date_gmt":"2018-03-19T11:13:54","guid":{"rendered":"https:\/\/lop12.edu.vn\/?p=22464"},"modified":"2018-03-19T18:13:54","modified_gmt":"2018-03-19T11:13:54","slug":"hinh-hoc-chuong-1-bai-2-phep-doi-xung-qua-mat-phang-va-su-bang-nhau-cua-cac-khoi-da-dien","status":"publish","type":"post","link":"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-1-bai-2-phep-doi-xung-qua-mat-phang-va-su-bang-nhau-cua-cac-khoi-da-dien\/","title":{"rendered":"H\u00ecnh h\u1ecdc – Ch\u01b0\u01a1ng 1 – B\u00e0i 2: Ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua m\u1eb7t ph\u1eb3ng v\u00e0 s\u1ef1 b\u1eb1ng nhau c\u1ee7a c\u00e1c kh\u1ed1i \u0111a di\u1ec7n"},"content":{"rendered":"

B\u00e0i 6 (trang 15 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao):<\/b><\/p>\n

G\u1ecdi \u0110 l\u00e0 ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua mp (P) v\u00e0 a l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng n\u00e0o \u0111\u00f3. Gi\u1ea3 s\u1eed \u0110 bi\u1ebfn a th\u00e0nh \u0111\u01b0\u1eddng th\u1eb3ng a\u2019. tr\u01b0\u1eddng h\u1ee3p n\u00e0o th\u00ec:<\/p>\n

a) a tr\u00f9ng a\u2019 \u00a0\u00a0\u00a0 b) a song song v\u1edbi a\u2019<\/p>\n

c) a c\u1eaft a\u2019 \u00a0\u00a0\u00a0 d) a v\u00e0 a\u2019 ch\u00e9o nhau<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

\"\"<\/div>\n
<\/div>\n

\"\"<\/p>\n

Gi\u1eefa a v\u00e0 (P) x\u1ea3y ra c\u00e1c kh\u1ea3 n\u0103ng sau:<\/p>\n

+ a \u2282 (P), khi \u0111\u00f3, l\u1ea5y \u0111i\u1ec3m A b\u1ea5t k\u00ec tr\u00ean a th\u00ec A\u2208 (P) n\u00ean \u0110 bi\u1ebfn A th\u00e0nh A’\u2261 A. v\u1eady \u0110 bi\u1ebfn a th\u00e0nh a\u2019 \u2261a<\/p>\n

+ a \/\/ (P). l\u1ea5y 2 \u0111i\u1ec3m A, B ph\u00e2n bi\u1ec7t tr\u00ean a gi\u1ea3 s\u1eed \u0110 bi\u1ebfn A th\u00e0nh A\u2019, E th\u00e0nh B\u2019. Ta th\u1ea5y t\u1ee9 gi\u00e1c ABB\u2019A\u2019 l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt n\u1ebfu A\u2019B\u2019 \/\/ AB hay a\u2019 \/\/ a<\/p>\n

+ a \u22a5 (P). l\u1ea5y A b\u1ea5t k\u00ec tr\u00ean a. n\u1ebfu \u0110 bi\u1ebfn A th\u00e0nh A\u2019 th\u00ec AA\u2019 \u22a5 (P) m\u00e0 a \u22a5 (P), (A) \u2208 a => A’\u2208 a=> a’=a<\/p>\n

+ a c\u1eaft (P) t\u1ea1i I nh\u01b0ng kh\u00f4ng vu\u00f4ng g\u00f3c v\u1edbi (P). Khi \u0111\u00f3, \u0110 bi\u1ebfn I th\u00e0nh ch\u00ednh n\u00f3 (v\u00ec I \u2208(P) v\u00e0 bi\u1ebfn A \u2208a (v\u1edbi A kh\u00f4ng tr\u00f9ng I) th\u00e0nh A\u2019 sao cho (P) l\u00e0 m\u1eb7t ph\u1eb3ng trung tr\u1ef1c c\u1ee7a AA\u2019. V\u1eady \u0110 bi\u1ebfn AI th\u00e0nh A\u2019I.<\/p>\n

Do a kh\u00f4ng vu\u00f4ng g\u00f3c v\u1edbi (P) n\u00ean d\u1ec5 th\u1ea5y A, I, A\u2019 kh\u00f4ng th\u1eb3ng h\u00e0ng hay AI, A\u2019I c\u1eaft nhau t\u1ea1i I t\u1ee9c a, a\u2019 c\u1eaft nhau.<\/p>\n

V\u1eady: a) a tr\u00f9ng v\u1edbi a\u2019 n\u1ebfu a \u2282 (P) ho\u1eb7c a \u22a5 (P).<\/p>\n

b) a\/\/ a\u2019 n\u1ebfu a \/\/ (P)<\/p>\n

c) a c\u1eaft a\u2019 n\u1ebfu a c\u1eaft (P) nh\u01b0ng a kh\u00f4ng vu\u00f4ng g\u00f3c v\u1edbi (P).<\/p>\n

d) a, a\u2019 ch\u00e9o nhau kh\u00f4ng x\u1ea3y ra.<\/p>\n

B\u00e0i 7 (trang 15 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao):<\/b><\/p>\n

T\u00ecm c\u00e1c m\u1eb7t ph\u1eb3ng \u0111\u1ed1i x\u1ee9ng c\u1ee7a c\u00e1c h\u00ecnh sau \u0111\u00e2y:<\/p>\n

a) h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u.<\/p>\n

b) h\u00ecnh ch\u00f3p c\u00fat tam gi\u00e1c \u0111\u1ec1u.<\/p>\n

c) h\u00ecnh h\u1ed9p ch\u1eef m\u00e0 kh\u00f4ng c\u00f3 m\u1eb7t n\u00e0o l\u00e0 h\u00ecnh vu\u00f4ng.<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

<\/div>\n

\"\"<\/p>\n

a) x\u00e9t h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u S.ABCD<\/p>\n

– D\u1ec5 th\u1ea5y (SAC) l\u00e0 m\u1eb7t ph\u1eb3ng trung tr\u1ef1c c\u1ee7a BD n\u00ean ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua (SAC) bi\u1ebfn c\u00e1c \u0111\u1ec9nh S, A, B, C D l\u1ea7n l\u01b0\u1ee3t th\u00e0nh c\u00e1c \u0111\u1ec9nh S, A, D, C, B hay bi\u1ebfn h\u00ecnh ch\u00f3p S.ABCD th\u00e0nh ch\u00ednh n\u00f3. V\u1eady (SAC) l\u00e0 m\u1ed9t m\u1eb7t ph\u1eb3ng \u0111\u1ed1i x\u1ee9ng c\u1ee7a h\u00ecnh ch\u00f3p S.ABCD.<\/p>\n

T\u01b0\u01a1ng t\u1ef1 (SBD) c\u0169ng l\u00e0 m\u1ed9t mp \u0111\u1ed1i x\u1ee9ng c\u1ee7a h\u00ecnh ch\u00f3p S.ABCD .<\/p>\n

– L\u1ea1i c\u00f3, m\u1eb7t ph\u1eb3ng trung tr\u1ef1c c\u1ee7a c\u1ea1nh AB \u0111\u1ed3ng th\u1eddi l\u00e0 m\u1eb7t ph\u1eb3ng trung tr\u1ef1c c\u1ee7a c\u1ea1nh CD v\u00e0 ch\u1ee9a S n\u00ean \u0111\u00f3 l\u00e0 m\u1ed9t m\u1eb7t \u0111\u1ed1i x\u1ee9ng c\u1ee7a h\u00ecnh ch\u00f3p S.ABCD. t\u01b0\u01a1ng t\u1ef1 m\u1eb7t ph\u1eb3ng trung tr\u1ef1c c\u1ee7a AD c\u0169ng l\u00e0 m\u1ed9t m\u1eb7t ph\u1eb3ng \u0111\u1ed1i x\u1ee9ng c\u1ee7a h\u00ecnh ch\u00f3p S.ABCD.<\/p>\n

– K\u1ebft lu\u1eadn: H\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u S.ABCD c\u00f3 4 m\u1eb7t ph\u1eb3ng \u0111\u1ed1i x\u1ee9ng l\u00e0 (SAC), (SBD) , m\u1eb7t ph\u1eb3ng trung tr\u1ef1c c\u1ee7a c\u1ea1nh AD v\u00e0 AD.<\/p>\n

\"Gi\u1ea3i<\/p>\n

b) X\u00e9t h\u00ecnh ch\u00f3p c\u1ee5t tam gi\u00e1c \u0111\u1ec1u ABC.A\u2019B\u2019C\u2019<\/p>\n

G\u1ecdi S l\u00e0 \u0111i\u1ec3m \u0111\u1ed3ng quy c\u1ee7a AA\u2019, BB\u2019, CC\u2019, M, N, P l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a BC, CA, AB.<\/p>\n

Ta c\u00f3 (SAM) l\u00e0 m\u1eb7t ph\u1eb3ng trung tr\u1ef1c c\u1ee7a BC, c\u0169ng l\u00e0 m\u1eb7t ph\u1eb3ng trung tr\u1ef1c c\u1ee7a B\u2019C\u2019.<\/p>\n

M\u1eb7t kh\u00e1c, A\u2019 \u2208 SA => A\u2019 \u2208 mp (SAM). V\u1eady ph\u00e9p \u0111\u00f4i x\u1ee9ng qua mp(SAM) bi\u1ebfn c\u00e1c \u0111\u1ec9nh A, B, C, A\u2019, B\u2019, C\u2019 l\u1ea7n l\u01b0\u1ee3t th\u00e0nh A, B, C, A\u2019, C\u2019, B\u2019 do \u0111\u00f3 bi\u1ebfn h\u00ecnh ch\u00f3p c\u1ee5t tam gi\u00e1c \u0111\u1ec1u ABC.A\u2019B\u2019C\u2019 th\u00e0nh ch\u00ednh n\u00f3 hay (SAM) l\u00e0 m\u1ed9t mp \u0111\u1ed1i x\u1ee9ng l\u00e0 (SAM), (SBN), (SCP).<\/p>\n

\"Gi\u1ea3i<\/p>\n

c) X\u00e9t h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt ABCD.A\u2019B\u2019C\u2019D\u2019 m\u00e0 kh\u00f4ng c\u00f3 m\u1eb7t n\u00e0o l\u00e0 h\u00ecnh vu\u00f4ng.<\/p>\n

– G\u1ecdi (P) l\u00e0 m\u1eb7t ph\u1eb3ng trung tr\u1ef1c c\u1ee7a c\u1ea1nh AB th\u00ec (P) c\u0169ng l\u00e0 m\u1eb7t ph\u1eb3ng trung tr\u1ef1c c\u1ee7a c\u00e1c c\u1ea1nh CD, D\u2019C\u2019, A\u2019B\u2019 n\u1ebfu cho ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua (P) bi\u1ebfn A, B, C, D, A\u2019, B\u2019, C\u2019, D\u2019 l\u1ea7n l\u01b0\u1ee3t th\u00e0nh B, A, D, C, B\u2019, A\u2019, D\u2019, C\u2019 hay ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua (P) bi\u1ebfn h\u00ecnh h\u1ed9p c\u1ee7a h\u00ecnh ch\u1eef nh\u1eadt ABCD.A\u2019B\u2019C\u2019D\u2019 th\u00e0nh ch\u00ednh n\u00f3. V\u1eady (P) l\u00e0 m\u1ed9t m\u1eb7t ph\u1eb3ng \u0111\u1ed1i x\u1ee9ng c\u1ee7a h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt.<\/p>\n

T\u01b0\u01a1ng t\u1ef1, m\u1eb7t ph\u1eb3ng trung tr\u1ef1c c\u1ee7a c\u00e1c c\u1ea1nh AA\u2019, AD c\u0169ng l\u00e0 c\u00e1c m\u1eb7t ph\u1eb3ng \u0111\u1ed1i x\u1ee9ng c\u1ee7a h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt ABCD.A\u2019B\u2019C\u2019D\u2019.<\/p>\n

K\u1ebft lu\u1eadn: h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt m\u00e0 kh\u00f4ng c\u00f3 m\u1eb7t ph\u1eb3ng n\u00e0o vu\u00f4ng g\u00f3c c\u00f3 3 m\u1eb7t ph\u1eb3ng \u0111\u1ed1i x\u1ee9ng l\u00e0 3 m\u1eb7t ph\u1eb3ng trung tr\u1ef1c c\u1ee7a 3 c\u1ea1nh c\u00f9ng xu\u1ea5t ph\u00e1t t\u1ea1i m\u1ed9t \u0111\u1ec9nh.<\/p>\n

B\u00e0i 8 (trang 15 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao):<\/b><\/p>\n

Cho h\u00ecnh h\u1ed9p l\u1eadp Ph\u01b0\u01a1ng ABCD.A\u2019B\u2019C\u2019D\u2019. ch\u1ee9ng minh r\u1eb1ng:<\/p>\n

a) Cho c\u00e1c h\u00ecnh ch\u00f3p A.A\u2019B\u2019C\u2019D\u2019 v\u00e0 h\u00ecnh ch\u00f3p C\u2019.ABCD b\u1eb1ng nhau.<\/p>\n

b) H\u00ecnh l\u0103ng tr\u1ee5 ABC.A\u2019B\u2019C\u2019 v\u00e0 AA\u2019D\u2019.BB\u2019C\u2019 b\u1eb1ng nhau.<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

<\/div>\n

\"\"<\/p>\n

a) C\u00e1ch 1: Do ABCD.A\u2019B\u2019C\u2019D\u2019 l\u00e0 h\u00ecnh l\u1eadp Ph\u01b0\u01a1ng n\u00ean ph\u1ebfp \u0111\u1ed1i x\u1ee9ng qua m\u1eb7t ph\u1eb3ng trung tr\u1ef1c c\u1ee7a AA\u2019 bi\u1ebfn h\u00ecnh ch\u00f3p A.A\u2019B\u2019C\u2019D\u2019 th\u00e0nh h\u00ecnh ch\u00f3pA\u2019.ABCD v\u00e0 ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua (BB\u2019DD\u2019) bi\u1ebfn h\u00ecnh ch\u00f3p A\u2019.ABCD th\u00e0nh h\u00ecnh ch\u00f3p A.A\u2019B\u2019C\u2019D\u2019 v\u00e0 C\u2019.ABCD b\u1eb1ng nhau (v\u00ec ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua m\u1eb7t ph\u1eb3ng ph\u00e9p d\u1eddi h\u00ecnh)<\/p>\n

C\u00e1ch 2: cho \u0111i\u1ec3m O c\u1ed1 \u0111\u1ecbnh. Ph\u00e9p bi\u1ebfn h\u00ecnh bi\u1ebfn m\u1ed7i \u0111i\u1ec3m M trong kh\u00f4ng gian th\u00e0nh \u0111i\u1ec3m M\u2019 sao cho (OM’) \u20d7=- (OM) \u20d7 g\u1ecdi l\u00e0 ph\u00e9p \u0111\u1ed1i x\u1ee9ng t\u00e2m O. d\u1ec5 ch\u1ee9ng minh \u0111\u01b0\u1ee3c ph\u00e9p \u0111\u1edbi x\u1ee9ng t\u00e2m l\u00e0 m\u1ed9t ph\u00e9p d\u1eddi h\u00ecnh.<\/p>\n

G\u1ecdi O l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AC\u2019 th\u00ec O c\u0169ng l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u00e1c \u0111\u01b0\u1eddng ch\u00e9p BD\u2019, A\u2019C, B\u2019D n\u00ean ph\u00e9p \u0111\u1ed1i x\u1ee9ng t\u00e2m O bi\u1ebfn A, A\u2019, B\u2019, C\u2019, D\u2019 l\u1ea7n l\u01b0\u1ee3t th\u00e0nh C\u2019, C, D, A, B. v\u1eady c\u00e1c h\u00ecnh ch\u00f3p A.A\u2019B\u2019C\u2019D\u2019 v\u00e0 C\u2019.ABCD b\u1eb1ng nhau (do ph\u00e9p \u0111\u1ed1i x\u1ee9ng t\u00e2m l\u00e0 ph\u00e9p d\u1eddi h\u00ecnh).<\/p>\n

b) X\u00e9t ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua m\u1eb7t ph\u1eb3ng (ADC\u2019B\u2019)<\/p>\n

Ta c\u00f3:<\/p>\n

A->A’;B->A,C->D,A’->B,B’->B; C’->C’<\/p>\n

Do \u0111\u00f3 l\u0103ng tr\u1ee5 ABC.A\u2019B\u2019C\u2019 -> l\u0103ng tr\u1ee5 AA\u2019D\u2019.BB\u2019C\u2019<\/p>\n

V\u00ec v\u1eady hai l\u0103ng tr\u1ee5 ABC.A\u2019B\u2019C\u2019 v\u00e0 AA\u2019D\u2019.BB\u2019C\u2019<\/p>\n

B\u00e0i 9 (trang 15 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao):<\/b><\/p>\n

Ch\u1ee9ng minh r\u1eb1ng c\u00e1c ph\u00e9p t\u1ecbnh ti\u1ebfn, \u0111\u1ed1i x\u1ee9ng tr\u1ee5c, \u0111\u1ed1i x\u1ee9ng t\u00e2m l\u00e0 nh\u1eefng ph\u00e9p d\u1eddi h\u00ecnh.<\/p>\n

\"\"<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

\u2022 Ph\u00e9p t\u1ecbnh ti\u1ebfn l\u00e0 ph\u00e9p d\u1eddi h\u00ecnh.<\/p>\n

N\u1ebfu ph\u00e9p t\u00ednh ti\u1ebfn\u00a0v\u2192<\/i>\u00a0bi\u1ebfn hai \u0111i\u1ec3m M, N l\u1ea7n l\u01b0\u1ee3t th\u00e0nh M\u2019, N\u2019 th\u00ec<\/p>\n

\"\"<\/p>\n

Suy ra M\u2019N\u2019 = MN hay ph\u00e9p t\u00ednh ti\u1ebfn l\u00e0 m\u1ed9t ph\u00e9p d\u1eddi h\u00ecnh.<\/p>\n

\u2022 Ph\u00e9p \u0111\u1ed1i x\u1ee9ng tr\u1ee5c l\u00e0 ph\u00e9p d\u1eddi h\u00ecnh.<\/p>\n

\"\"<\/p>\n

C\u00e1ch 1. G\u1ecdi \u0110d<\/sub>\u00a0l\u00e0 ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua \u0111\u01b0\u1eddng th\u1eb3ng d<\/p>\n

Gi\u1ea3 s\u1eed I l\u00e0 trung \u0111i\u1ec3m MN\u2019, J l\u00e0 trung \u0111i\u1ec3m c\u1ee7a NM\u2019<\/p>\n

Suy ra I, J \u2208 d<\/p>\n

Ta c\u00f3:<\/p>\n

\"\"<\/p>\n

T\u1eeb (1), (2), (3) suy ra MN2<\/sup>=M;N’2<\/sup>=>MN=M’N’<\/p>\n

=> V\u1eady ph\u00e9p \u0111\u1ed1i x\u1ee9ng tr\u1ee5c l\u00e0 ph\u00e9p d\u1eddi h\u00ecnh.<\/p>\n

\"\"<\/p>\n

C\u00e1ch 2. Gi\u1ea3 s\u1eed ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua \u0111\u01b0\u1eddng th\u1eb3ng d bi\u1ebfn M th\u00e0nh M\u2019, N th\u00e0nh N\u2019<\/p>\n

G\u1ecdi (P) l\u00e0 m\u1eb7t ph\u1eb3ng ch\u1ee9a NM\u2019 v\u00e0 (P) \/\/ MM\u2019<\/p>\n

M1<\/sub>,M1<\/sub>‘ l\u1ea7n l\u01b0\u1ee3t l\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a M, M\u2019 tr\u00ean (P); O = \u2229(P). Ta c\u00f3 d \u22a5 (P) n\u00ean O \u0111\u1ed3ng th\u1eddi l\u00e0 trung \u0111i\u1ec3m c\u1ee7a M1<\/sub>\u00a0M1<\/sub>‘ v\u00e0 NN’. V\u1eady ph\u00e9p \u0111\u1ed1i x\u1ee9ng t\u00e2m O bi\u1ebfn M1<\/sub>th\u00e0nh M1<\/sub>‘, N th\u00e0nh N\u2019 n\u00ean M1<\/sub>\u00a0M1<\/sub>‘ n\u00ean M1<\/sub>\u00a0N=M1<\/sub>‘N’.<\/p>\n

M\u1eb7t kh\u00e1c M1<\/sub>\u00a0N,M1<\/sub>‘N’ l\u1ea7n l\u01b0\u1ee3t l\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a MN, M\u2019N\u2019 tr\u00ean (P), MM\u2019 \/\/ (P) n\u00ean MN = M\u2019N\u2019.<\/p>\n

V\u1eady ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua \u0111\u01b0\u1eddng th\u1eb3ng l\u00e0 ph\u00e9p d\u1eddi h\u00ecnh.<\/p>\n

\"\"<\/p>\n

\u2022 Ph\u00e9p \u0111\u1ed1i x\u1ee9ng t\u00e2m l\u00e0 ph\u00e9p d\u1eddi h\u00ecnh.<\/p>\n

N\u1ebfu ph\u00e9p \u0111\u1ed1i x\u1ee9ng t\u00e2m O bi\u1ebfn hai \u0111i\u1ec3m M, N l\u1ea7n l\u01b0\u1ee3t th\u00e0nh M\u2019, N\u2019 th\u00ec<\/p>\n

\"\"<\/p>\n

V\u1eady ph\u00e9p \u0111\u1ed1i x\u1ee9ng t\u00e2m l\u00e0 ph\u00e9p d\u1eddi h\u00ecnh.<\/p>\n

B\u00e0i 10 (trang 15 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao):<\/b><\/p>\n

Ch\u1ee9ng minh r\u1eb1ng:<\/p>\n

a) H\u1ee3p th\u00e0nh c\u1ee7a hai ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua m\u1eb7t ph\u1eb3ng song song (P) v\u00e0 (Q) l\u00e0 m\u1ed9t ph\u00e9p h\u1ee3p t\u1ecbnh ti\u1ebfn.<\/p>\n

b) H\u1ee3p th\u00e0nh c\u1ee7a hai ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua m\u1eb7t ph\u1eb3ng (P) v\u00e0 (Q) vu\u00f4ng g\u00f3c v\u1edbi nhau l\u00e0 m\u1ed9t ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua \u0111\u01b0\u1eddng th\u1eb3ng.<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

<\/div>\n

\"\"<\/p>\n

a) L\u1ea5y \u0111i\u1ec3m M b\u1ea5t k\u00ec trong kh\u00f4ng gian<\/p>\n

Gi\u1ea3 s\u1eed ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua (P) bi\u1ebfn M th\u00e0nh M1<\/sub>\u00a0v\u00e0 ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua (P) bi\u1ebfn M1<\/sub>\u00a0th\u00e0nh M\u2019.<\/p>\n

G\u1ecdi I, J l\u00e0 trung \u0111i\u1ec3m c\u1ee7a MM1<\/sub>, M1<\/sub>\u00a0M’ (suy ra I \u2208 (P), J \u2208(Q) IJ \u22a5 (P))<\/p>\n

Ta c\u00f3:<\/p>\n

\"\"<\/p>\n

Ch\u00fa \u00fd r\u1eb1ng:\u00a0IJ\u2192<\/i>\u00a0c\u00f3 ph\u01b0\u01a1ng vu\u00f4ng g\u00f3c v\u1edbi (P) \u0111\u1ed9 d\u00e0i b\u1eb1ng kho\u1ea3ng c\u00e1ch gi\u1eefa (P) v\u00e0 (Q)) h\u01b0\u1eddng t\u1eeb (P) \u0111\u1ebfn (Q)).<\/p>\n

N\u1ebfu \u0111\u1eb7t 2IJ\u2192<\/i>=\u00a0v\u2192<\/i>\u00a0th\u00ecv\u2192<\/i>\u00a0c\u00f3 Ph\u01b0\u01a1ng, h\u01b0\u1edbng v\u00e0 \u0111\u1ed9 d\u00e0i kh\u00f4ng \u0111\u1ed5i. khi \u0111\u00f3 ph\u00e9p t\u1ecbnh ti\u1ebfn theo\u00a0X\u2192<\/i>\u00a0bi\u1ebfn M th\u00e0nh M\u2019. V\u1eady h\u1ee3p th\u00e0nh 2 ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua hai m\u1eb7t ph\u1eb3ng song song l\u00e0 m\u1ed9t ph\u00e9p t\u1ecbnh ti\u1ebfn.<\/p>\n

\"Gi\u1ea3i<\/p>\n

c) G\u1ecdi d = (P) \u2229 (Q). M l\u00e0 m\u1ed9t bi\u1ebfn b\u1ea5t k\u00ec. Gi\u1ea3 s\u1eed ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua (P) bi\u1ebfn M th\u00e0nh M\u2019 v\u00e0 ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua (Q) bi\u1ebfn M\u2019 th\u00e0nh M\u2019\u2019.<\/p>\n

I \u2208 (P) v\u00e0 I \u2208 (Q)<\/p>\n

I \u2208 d m\u00e0 d \u22a5 MM\u2019\u2019 (do d <=> (Q). v\u1eady d l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a MM\u2019\u2019.<\/p>\n

Tr\u01b0\u1eddng h\u1ee3p M \u2208 (Q) nh\u01b0ng M \u2208 d t\u01b0\u01a1ng t\u1ef1.<\/p>\n

Tr\u01b0\u1eddng h\u1ee3p 3. N\u1ebfu M \u2208(P) v\u00e0 M \u2208(Q)t th\u00ec M, M\u2019, M\u2019\u2019 ph\u00e2n bi\u1ec7t. v\u00ec I = (P)\u2229 (Q) m\u00e0 (P), (Q) l\u1ea7n l\u01b0\u1ee3t l\u00e0 m\u1eb7t ph\u1eb3ng trung tr\u1ef1c c\u1ee7a MM\u2019, M\u2019M\u2019\u2019 n\u00ean d \u22a5 (MM\u2019M\u2019\u2019) => d \u22a5 MM” (*).<\/p>\n

M\u1eb7t kh\u00e1c, g\u1ecdi I l\u00e0 trung \u0111i\u1ec3m c\u1ee7a MM\u2019\u2019, do \u0394MM\u2019M\u2019\u2019 vu\u00f4ng t\u1ea1i M\u2019 n\u00ean M = IM\u2019 = IM\u2019\u2019 => I \u0111\u1ed3ng th\u1eddi thu\u1ed9c m\u1eb7t ph\u1eb3ng trung tr\u1ef1c c\u1ee7a MM\u2019 v\u00e0 M\u2019M\u2019\u2019 hay I \u2208(P) v\u00e0 I \u2208(Q)=>I \u2208d (**)<\/p>\n

T\u1eeb (*), (**) ta c\u00f3 d l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n MM\u2019\u2019 (3)<\/p>\n

K\u1ebft lu\u1eadn: t\u1eeb (1), (2), (3). Ta th\u1ea5y: n\u1ebfu th\u1ef1c hi\u1ec7n li\u00ean ti\u1ebfp hai ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua hai m\u1eb7t ph\u1eb3ng vu\u00f4ng g\u00f3c (P) v\u00e0 (Q) th\u00ec m\u1ed7i \u0111i\u1ec3m M \u2208 d (v\u1edbi d \u2208(P)\u2229 (Q) bi\u1ebfn th\u00e0nh ch\u00ednh n\u00f3, m\u1ed7i \u0111i\u1ec3m M \u2208d bi\u1ebfn th\u00e0nh M\u2019\u2019 sao cho d l\u00e0 trung tr\u1ef1c c\u1ee7a MM\u2019\u2019. \u0110\u00f3 ch\u00ednh l\u00e0 ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua \u0111\u01b0\u1eddng th\u1eb3ng d.<\/p>\n

<\/div>\n","protected":false},"excerpt":{"rendered":"

B\u00e0i 6 (trang 15 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao): G\u1ecdi \u0110 l\u00e0 ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua mp (P) v\u00e0 a l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng n\u00e0o \u0111\u00f3. Gi\u1ea3 s\u1eed \u0110 bi\u1ebfn a th\u00e0nh \u0111\u01b0\u1eddng th\u1eb3ng a\u2019. tr\u01b0\u1eddng h\u1ee3p n\u00e0o th\u00ec: a) a tr\u00f9ng a\u2019 \u00a0\u00a0\u00a0 b) a song song v\u1edbi a\u2019 c) a c\u1eaft a\u2019 […]<\/p>\n","protected":false},"author":3,"featured_media":22465,"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":"\nH\u00ecnh h\u1ecdc - Ch\u01b0\u01a1ng 1 - B\u00e0i 2: Ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua m\u1eb7t ph\u1eb3ng v\u00e0 s\u1ef1 b\u1eb1ng nhau c\u1ee7a c\u00e1c kh\u1ed1i \u0111a di\u1ec7n<\/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-2-phep-doi-xung-qua-mat-phang-va-su-bang-nhau-cua-cac-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 2: Ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua m\u1eb7t ph\u1eb3ng v\u00e0 s\u1ef1 b\u1eb1ng nhau c\u1ee7a c\u00e1c kh\u1ed1i \u0111a di\u1ec7n\" \/>\n<meta property=\"og:description\" content=\"B\u00e0i 6 (trang 15 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao): G\u1ecdi \u0110 l\u00e0 ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua mp (P) v\u00e0 a l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng n\u00e0o \u0111\u00f3. Gi\u1ea3 s\u1eed \u0110 bi\u1ebfn a th\u00e0nh \u0111\u01b0\u1eddng th\u1eb3ng a\u2019. tr\u01b0\u1eddng h\u1ee3p n\u00e0o th\u00ec: a) a tr\u00f9ng a\u2019 \u00a0\u00a0\u00a0 b) a song song v\u1edbi a\u2019 c) a c\u1eaft a\u2019 […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-1-bai-2-phep-doi-xung-qua-mat-phang-va-su-bang-nhau-cua-cac-khoi-da-dien\/\" \/>\n<meta property=\"og:site_name\" content=\"Lop12.edu.vn - C\u1ed9ng \u0111\u1ed3ng h\u1ecdc sinh l\u1edbp 12 l\u1edbn nh\u1ea5t t\u1ea1i Vi\u1ec7t Nam\" \/>\n<meta property=\"article:published_time\" content=\"2018-03-19T11:13:54+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-219.png\" \/>\n\t<meta property=\"og:image:width\" content=\"378\" \/>\n\t<meta property=\"og:image:height\" content=\"213\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"H\u00e0 Trang\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"H\u00e0 Trang\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"12 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-1-bai-2-phep-doi-xung-qua-mat-phang-va-su-bang-nhau-cua-cac-khoi-da-dien\/\",\"url\":\"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-1-bai-2-phep-doi-xung-qua-mat-phang-va-su-bang-nhau-cua-cac-khoi-da-dien\/\",\"name\":\"H\u00ecnh h\u1ecdc - Ch\u01b0\u01a1ng 1 - B\u00e0i 2: Ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua m\u1eb7t ph\u1eb3ng v\u00e0 s\u1ef1 b\u1eb1ng nhau c\u1ee7a c\u00e1c kh\u1ed1i \u0111a di\u1ec7n\",\"isPartOf\":{\"@id\":\"https:\/\/lop12.edu.vn\/#website\"},\"datePublished\":\"2018-03-19T11:13:54+00:00\",\"dateModified\":\"2018-03-19T11:13:54+00:00\",\"author\":{\"@id\":\"https:\/\/lop12.edu.vn\/#\/schema\/person\/2da855e5d06b553ac0065157cc261a45\"},\"breadcrumb\":{\"@id\":\"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-1-bai-2-phep-doi-xung-qua-mat-phang-va-su-bang-nhau-cua-cac-khoi-da-dien\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-1-bai-2-phep-doi-xung-qua-mat-phang-va-su-bang-nhau-cua-cac-khoi-da-dien\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-1-bai-2-phep-doi-xung-qua-mat-phang-va-su-bang-nhau-cua-cac-khoi-da-dien\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/lop12.edu.vn\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"H\u00ecnh h\u1ecdc – Ch\u01b0\u01a1ng 1 – B\u00e0i 2: Ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua m\u1eb7t ph\u1eb3ng v\u00e0 s\u1ef1 b\u1eb1ng nhau c\u1ee7a c\u00e1c kh\u1ed1i \u0111a di\u1ec7n\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/lop12.edu.vn\/#website\",\"url\":\"https:\/\/lop12.edu.vn\/\",\"name\":\"Lop12.edu.vn - C\u1ed9ng \u0111\u1ed3ng h\u1ecdc sinh l\u1edbp 12\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/lop12.edu.vn\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/lop12.edu.vn\/#\/schema\/person\/2da855e5d06b553ac0065157cc261a45\",\"name\":\"H\u00e0 Trang\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/lop12.edu.vn\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/545a8100db1147f314111301d261dc33?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/545a8100db1147f314111301d261dc33?s=96&d=mm&r=g\",\"caption\":\"H\u00e0 Trang\"},\"url\":\"https:\/\/lop12.edu.vn\/author\/trangvth2\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"H\u00ecnh h\u1ecdc - Ch\u01b0\u01a1ng 1 - B\u00e0i 2: Ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua m\u1eb7t ph\u1eb3ng v\u00e0 s\u1ef1 b\u1eb1ng nhau c\u1ee7a c\u00e1c kh\u1ed1i \u0111a di\u1ec7n","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-1-bai-2-phep-doi-xung-qua-mat-phang-va-su-bang-nhau-cua-cac-khoi-da-dien\/","og_locale":"en_US","og_type":"article","og_title":"H\u00ecnh h\u1ecdc - Ch\u01b0\u01a1ng 1 - B\u00e0i 2: Ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua m\u1eb7t ph\u1eb3ng v\u00e0 s\u1ef1 b\u1eb1ng nhau c\u1ee7a c\u00e1c kh\u1ed1i \u0111a di\u1ec7n","og_description":"B\u00e0i 6 (trang 15 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao): G\u1ecdi \u0110 l\u00e0 ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua mp (P) v\u00e0 a l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng n\u00e0o \u0111\u00f3. Gi\u1ea3 s\u1eed \u0110 bi\u1ebfn a th\u00e0nh \u0111\u01b0\u1eddng th\u1eb3ng a\u2019. tr\u01b0\u1eddng h\u1ee3p n\u00e0o th\u00ec: a) a tr\u00f9ng a\u2019 \u00a0\u00a0\u00a0 b) a song song v\u1edbi a\u2019 c) a c\u1eaft a\u2019 […]","og_url":"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-1-bai-2-phep-doi-xung-qua-mat-phang-va-su-bang-nhau-cua-cac-khoi-da-dien\/","og_site_name":"Lop12.edu.vn - C\u1ed9ng \u0111\u1ed3ng h\u1ecdc sinh l\u1edbp 12 l\u1edbn nh\u1ea5t t\u1ea1i Vi\u1ec7t Nam","article_published_time":"2018-03-19T11:13:54+00:00","og_image":[{"width":378,"height":213,"url":"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-219.png","type":"image\/png"}],"author":"H\u00e0 Trang","twitter_card":"summary_large_image","twitter_misc":{"Written by":"H\u00e0 Trang","Est. reading time":"12 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-1-bai-2-phep-doi-xung-qua-mat-phang-va-su-bang-nhau-cua-cac-khoi-da-dien\/","url":"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-1-bai-2-phep-doi-xung-qua-mat-phang-va-su-bang-nhau-cua-cac-khoi-da-dien\/","name":"H\u00ecnh h\u1ecdc - Ch\u01b0\u01a1ng 1 - B\u00e0i 2: Ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua m\u1eb7t ph\u1eb3ng v\u00e0 s\u1ef1 b\u1eb1ng nhau c\u1ee7a c\u00e1c kh\u1ed1i \u0111a di\u1ec7n","isPartOf":{"@id":"https:\/\/lop12.edu.vn\/#website"},"datePublished":"2018-03-19T11:13:54+00:00","dateModified":"2018-03-19T11:13:54+00:00","author":{"@id":"https:\/\/lop12.edu.vn\/#\/schema\/person\/2da855e5d06b553ac0065157cc261a45"},"breadcrumb":{"@id":"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-1-bai-2-phep-doi-xung-qua-mat-phang-va-su-bang-nhau-cua-cac-khoi-da-dien\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/lop12.edu.vn\/hinh-hoc-chuong-1-bai-2-phep-doi-xung-qua-mat-phang-va-su-bang-nhau-cua-cac-khoi-da-dien\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-1-bai-2-phep-doi-xung-qua-mat-phang-va-su-bang-nhau-cua-cac-khoi-da-dien\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/lop12.edu.vn\/"},{"@type":"ListItem","position":2,"name":"H\u00ecnh h\u1ecdc – Ch\u01b0\u01a1ng 1 – B\u00e0i 2: Ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua m\u1eb7t ph\u1eb3ng v\u00e0 s\u1ef1 b\u1eb1ng nhau c\u1ee7a c\u00e1c kh\u1ed1i \u0111a di\u1ec7n"}]},{"@type":"WebSite","@id":"https:\/\/lop12.edu.vn\/#website","url":"https:\/\/lop12.edu.vn\/","name":"Lop12.edu.vn - C\u1ed9ng \u0111\u1ed3ng h\u1ecdc sinh l\u1edbp 12","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/lop12.edu.vn\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/lop12.edu.vn\/#\/schema\/person\/2da855e5d06b553ac0065157cc261a45","name":"H\u00e0 Trang","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/lop12.edu.vn\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/545a8100db1147f314111301d261dc33?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/545a8100db1147f314111301d261dc33?s=96&d=mm&r=g","caption":"H\u00e0 Trang"},"url":"https:\/\/lop12.edu.vn\/author\/trangvth2\/"}]}},"_links":{"self":[{"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/posts\/22464"}],"collection":[{"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/comments?post=22464"}],"version-history":[{"count":1,"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/posts\/22464\/revisions"}],"predecessor-version":[{"id":22478,"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/posts\/22464\/revisions\/22478"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/media\/22465"}],"wp:attachment":[{"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/media?parent=22464"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/categories?post=22464"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/tags?post=22464"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}