Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn<\/p>\n\n\n\n
Hi\u1ec7n nay, trong ch\u01b0\u01a1ng tr\u00ecnh Trung h\u1ecdc c\u01a1 s\u1edf v\u00e0 trung h\u1ecdc ph\u1ed5 th\u00f4ng, c\u00e1c ph\u00e9p bi\u1ebfn h\u00ecnh trong h\u00ecnh h\u1ecdc ph\u1eb3ng v\u00e0 h\u00ecnh h\u1ecdc kh\u00f4ng gian chi\u1ebfm m\u1ed9t dung l\u01b0\u1ee3ng kh\u00f4ng h\u1ec1 nh\u1ecf. Trong \u0111\u00f3, ph\u1ea3i k\u1ec3 \u0111\u1ebfn ph\u00e9p \u0111\u1ed1i x\u1ee9ng tr\u1ee5c. B\u00e0i vi\u1ebft sau \u0111\u00e2y Vietlearn s\u1ebd c\u00f9ng c\u00e1c em \u00f4n luy\u1ec7n l\u1ea1i ki\u1ebfn th\u1ee9c c\u1ee7a n\u1ed9i dung n\u00e0y theo To\u00e1n 8 v\u00e0 \u00e1p d\u1ee5ng cho t\u1eebng b\u00e0i th\u1ef1c h\u00e0nh nh\u00e9.<\/p>\n\n\n\n
T\u00f3m t\u1eaft l\u00fd thuy\u1ebft<\/p>\n\n\n\n
Tr\u01b0\u1edbc ti\u00ean, ch\u00fang ta s\u1ebd t\u00ecm hi\u1ec3u chung v\u1ec1 ph\u00e9p \u0111\u1ed1i x\u1ee9ng tr\u1ee5c tr\u01b0\u1edbc khi \u0111i v\u00e0o t\u1eebng b\u00e0i th\u1ef1c h\u00e0nh nh\u00e9.<\/p>\n\n\n\n
Kh\u00e1i ni\u1ec7m v\u1ec1 ph\u00e9p \u0111\u1ed1i x\u1ee9ng tr\u1ee5c<\/p>\n\n\n\n
Sau n\u00e0y khi h\u1ecdc \u1edf nh\u1eefng l\u1edbp cao h\u01a1n, c\u00e1c em s\u1ebd bi\u1ebft \u0111\u01b0\u1ee3c \u0111\u1ed1i x\u1ee9ng tr\u1ee5c l\u00e0 m\u1ed9t trong nh\u1eefng n\u1ed9i dung c\u1ee7a ph\u00e9p bi\u1ebfn h\u00ecnh.<\/p>\n\n\n\n
Ph\u00e9p \u0111\u1ed1i x\u1ee9ng tr\u1ee5c \u0111\u01b0\u1ee3c \u0111\u1ecbnh ngh\u0129a nh\u01b0 sau: Ph\u00e9p bi\u1ebfn h\u00ecnh cho ph\u00e9p bi\u1ebfn m\u1ed7i \u0111i\u1ec3m M thu\u1ed9c \u0111\u01b0\u1eddng th\u1eb3ng d th\u00e0nh ch\u00ednh n\u00f3, cho ph\u00e9p bi\u1ebfn m\u1ed7i \u0111i\u1ec3m M kh\u00f4ng thu\u1ed9c \u0111\u01b0\u1eddng th\u1eb3ng d th\u00e0nh \u0111i\u1ec3m M\u2019 sao cho d l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng MM\u2019. \u0110\u00f3 \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 ph\u00e9p \u0111\u1ed1i x\u1ee9ng tr\u1ee5c d hay ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua \u0111\u01b0\u1eddng th\u1eb3ng d.<\/p>\n\n\n\n
C\u00f3 th\u1ec3 nh\u00ecn th\u1ea5y r\u00f5 r\u00e0ng b\u1eb1ng h\u00ecnh \u1ea3nh sau:<\/p>\n\n\n\n
V\u00ed d\u1ee5 minh h\u1ecda cho ph\u00e9p \u0111\u1ed1i x\u1ee9ng tr\u1ee5c<\/p>\n\n\n\n
C\u00f3 th\u1ec3 nh\u00ecn th\u1ea5y r\u00f5 \u0111\u1ecbnh ngh\u0129a l\u1ea1i tr\u00ean \u0111\u01b0\u1ee3c m\u00f4 t\u1ea3 r\u1ea5t r\u00f5 \u1edf trong h\u00ecnh v\u00ed d\u1ee5 minh h\u1ecda n\u00e0y. M \u0111\u1ed1i x\u1ee9ng v\u1edbi M\u2019 qua \u0111\u01b0\u1eddng th\u1eb3ng d.<\/p>\n\n\n\n
Trong kh\u00e1i ni\u1ec7m n\u00e0y, \u0111\u01b0\u1eddng th\u1eb3ng d \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 tr\u1ee5c \u0111\u1ed1i x\u1ee9ng. v\u00e0 ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua \u0111\u01b0\u1eddng th\u1eb3ng n\u00e0y \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 \u0110d (ph\u00e9p \u0111\u1ed1i x\u1ee9ng tr\u1ee5c d).<\/p>\n\n\n\n
M\u1ed9t s\u1ed1 t\u00ednh ch\u1ea5t c\u1ee7a ph\u00e9p \u0111\u1ed1i x\u1ee9ng tr\u1ee5c l\u1edbp 8<\/p>\n\n\n\n
Trong n\u1ed9i dung b\u00e0i h\u1ecdc, n\u1ed9i dung v\u1ec1 t\u00ednh ch\u1ea5t c\u00e1c em c\u1ea7n ph\u1ea3i nh\u1edb, b\u1edfi n\u00f3 \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng trong r\u1ea5t nhi\u1ec1u c\u00e1c b\u00e0i to\u00e1n th\u1ef1c h\u00e0nh sau n\u00e0y. C\u00f3 c\u00e1c t\u00ednh ch\u1ea5t sau c\u1ee7a \u0111\u1ed1i x\u1ee9ng tr\u1ee5c, c\u00e1c em ghi ch\u00e9p v\u00e0o nh\u00e9:<\/p>\n\n\n\n
T\u00ednh ch\u1ea5t 1: Ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua \u0111\u01b0\u1eddng th\u1eb3ng b\u1ea3o to\u00e0n kho\u1ea3ng c\u00e1ch gi\u1eefa hai \u0111i\u1ec3m b\u1ea5t k\u1ef3. T\u1ee9c l\u00e0, th\u00f4ng qua tr\u1ee5c \u0111\u1ed1i x\u1ee9ng, \u0111i\u1ec3m M v\u00e0 \u0111i\u1ec3m M\u2019 c\u00f3 kho\u1ea3ng c\u00e1ch b\u1eb1ng nhau ho\u1eb7c h\u00ecnh A s\u1ebd gi\u1ed1ng h\u00ecnh A\u2019 t\u1eeb k\u00edch th\u01b0\u1edbc, h\u00ecnh d\u00e1ng cho \u0111\u1ebfn di\u1ec7n t\u00edch, chu vi.<\/p>\n\n\n\n
T\u00ednh ch\u1ea5t 2: Ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua \u0111\u01b0\u1eddng th\u1eb3ng gi\u00fap:<\/p>\n\n\n\n
Bi\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng th\u00e0nh \u0111\u01b0\u1eddng th\u1eb3ng,<\/p>\n\n\n\n
Bi\u1ebfn \u0111o\u1ea1n th\u1eb3ng th\u00e0nh \u0111o\u1ea1n th\u1eb3ng b\u1eb1ng n\u00f3,<\/p>\n\n\n\n
Bi\u1ebfn tam gi\u00e1c th\u00e0nh tam gi\u00e1c b\u1eb1ng n\u00f3,<\/p>\n\n\n\n
Bi\u1ebfn \u0111\u01b0\u1eddng tr\u00f2n th\u00e0nh \u0111\u01b0\u1eddng tr\u00f2n c\u00f3 c\u00f9ng b\u00e1n k\u00ednh,<\/p>\n\n\n\n
Bi\u1ebfn m\u1ed9t tia th\u00e0nh tia,<\/p>\n\n\n\n
Bi\u1ebfn m\u1ed9t g\u00f3c th\u00e0nh g\u00f3c.<\/p>\n\n\n\n
N\u00f3i c\u00e1ch kh\u00e1ch, n\u00f3 s\u1ebd bi\u1ebfn c\u00e1c h\u00ecnh d\u00e1ng h\u00ecnh h\u1ecdc th\u00e0nh m\u1ed9t tia, \u0111\u01b0\u1eddng th\u1eb3ng, h\u00ecnh h\u1ecdc y h\u1ec7t n\u00f3 m\u00e0 kh\u00f4ng l\u00e0m bi\u1ebfn d\u1ea1ng b\u1ea5t k\u1ef3 m\u1ed9t h\u00ecnh h\u1ecdc n\u00e0o.<\/p>\n\n\n\n
Hai \u0111i\u1ec3m \u0111\u1ed1i x\u1ee9ng qua m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng<\/p>\n\n\n\n
B\u00ean c\u1ea1nh c\u00e1c l\u00fd thuy\u1ebft v\u1ec1 kh\u00e1i ni\u1ec7m c\u0169ng nh\u01b0 t\u00ednh ch\u1ea5t, to\u00e1n 8 \u0111\u1ed1i x\u1ee9ng tr\u1ee5c c\u0169ng \u0111\u01b0a ra c\u00e1c kh\u00e1i ni\u1ec7m v\u00e0 \u0111\u1eb7c tr\u01b0ng c\u1ee7a hai h\u00ecnh \u0111\u1ed1i x\u1ee9ng qua m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 h\u00ecnh c\u00f3 tr\u1ee5c \u0111\u1ed1i x\u1ee9ng.<\/p>\n\n\n\n
V\u1ec1 hai \u0111i\u1ec3m \u0111\u1ed1i x\u1ee9ng qua m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng, kh\u00e1i ni\u1ec7m n\u00e0y \u0111\u01b0\u1ee3c \u0111\u1ecbnh ngh\u0129a nh\u01b0 sau: Hai \u0111i\u1ec3m \u0111\u1ed1i x\u1ee9ng v\u1edbi nhau qua \u0111\u01b0\u1eddng th\u1eb3ng d n\u1ebfu d l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng n\u1ed1i hai \u0111i\u1ec3m \u0111\u00f3. V\u1edbi t\u00ednh ch\u1ea5t n\u00e0y c\u0169ng c\u1ea7n \u0111\u1eb7t ra \u0111i\u1ec1u ki\u1ec7n l\u00e0: N\u1ebfu \u0111i\u1ec3m B n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng th\u1eb3ng d th\u00ec \u0111i\u1ec3m \u0111\u1ed1i x\u1ee9ng v\u1edbi B qua \u0111\u01b0\u1eddng d c\u0169ng l\u00e0 \u0111i\u1ec3m B.<\/p>\n\n\n\n
Hai h\u00ecnh \u0111\u1ed1i x\u1ee9ng qua m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng<\/p>\n\n\n\n
Hai h\u00ecnh \u0111\u1ed1i x\u1ee9ng qua m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng d n\u1ebfu m\u1ed7i \u0111i\u1ec3m thu\u1ed9c h\u00ecnh n\u00e0y \u0111\u1ed1i x\u1ee9ng qua d v\u1edbi m\u1ed9t \u0111i\u1ec3m thu\u1ed9c h\u00ecnh kia v\u00e0 ng\u01b0\u1ee3c l\u1ea1i. T\u1ee9c l\u00e0 n\u1ebfu hai h\u00ecnh \u0111\u1ed1i x\u1ee9ng nhau qua d th\u00ec b\u1eaft bu\u1ed9c c\u00e1c \u0111i\u1ec3m \u1edf h\u00ecnh n\u00e0y ph\u1ea3i \u0111\u1ed1i x\u1ee9ng t\u01b0\u01a1ng \u1ee9ng v\u1edbi \u0111i\u1ec3m c\u1ee7a h\u00ecnh kia qua \u0111\u01b0\u1eddng th\u1eb3ng.<\/p>\n\n\n\n
H\u00ecnh \u1ea3nh hai h\u00ecnh \u0111\u1ed1i x\u1ee9ng qua m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng<\/p>\n\n\n\n
Nh\u01b0 v\u1eady, t\u1eeb kh\u00e1i ni\u1ec7m n\u00e0y, c\u00f3 th\u1ec3 th\u1ea5y c\u00e1c \u0111o\u1ea1n th\u1eb3ng (g\u00f3c, tam gi\u00e1c) khi \u0111\u1ed1i x\u1ee9ng nhau qua \u0111\u01b0\u1eddng th\u1eb3ng th\u00ec ch\u00fang s\u1ebd b\u1eb1ng nhau.<\/p>\n\n\n\n
Tr\u1ee5c \u0111\u1ed1i x\u1ee9ng qua m\u1ed9t h\u00ecnh<\/p>\n\n\n\n
Nh\u01b0 v\u1eady, n\u1ebfu tr\u1ee5c \u0111\u1ed1i x\u1ee9ng qua m\u1ed9t h\u00ecnh th\u00ec s\u1ebd \u0111\u01b0\u1ee3c \u0111\u1ecbnh ngh\u0129a nh\u01b0 th\u1ebf n\u00e0o v\u00e0 c\u00f3 t\u00ednh ch\u1ea5t ra sao? Tr\u01b0\u1edbc ti\u00ean, n\u1ebfu \u0111\u01b0\u1eddng th\u1eb3ng d l\u00e0 tr\u1ee5c \u0111\u1ed1i x\u1ee9ng c\u1ee7a h\u00ecnh c\u1ee7a h\u00ecnh F n\u1ebfu \u0111i\u1ec3m \u0111\u1ed1i x\u1ee9ng qua d c\u1ee7a m\u1ed7i \u0111i\u1ec3m thu\u1ed9c h\u00ecnh F c\u0169ng thu\u1ed9c h\u00ecnh F.<\/p>\n\n\n\n
C\u00f3 m\u1ed9t tr\u01b0\u1eddng h\u1ee3p \u0111i\u1ec3n h\u00ecnh c\u1ee7a tr\u1ee5c \u0111\u1ed1i x\u1ee9ng qua m\u1ed9t h\u00ecnh ch\u00ednh l\u00e0 h\u00ecnh thang c\u00e2n s\u1ebd nh\u1eadn \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua trung \u0111i\u1ec3m hai \u0111\u00e1y l\u00e0m tr\u1ee5c \u0111\u1ed1i x\u1ee9ng. \u0110\u00e2y l\u00e0 t\u00ednh ch\u1ea5t b\u1ea5t di b\u1ea5t d\u1ecbch.<\/p>\n\n\n\n
\u0110\u1ed1i x\u1ee9ng t\u00e2m<\/p><\/blockquote>\n\n\n\n
C\u00e1c d\u1ea1ng to\u00e1n c\u1ee7a ph\u00e9p \u0111\u1ed1i x\u1ee9ng tr\u1ee5c<\/p>\n\n\n\n
C\u00f9ng xem c\u00f3 c\u00e1c d\u1ea1ng to\u00e1n n\u00e0o cho nh\u1eefng b\u00e0i nh\u01b0 th\u1ebf n\u00e0y nh\u00e9.<\/p>\n\n\n\n
X\u00e1c \u0111\u1ecbnh \u1ea3nh c\u1ee7a m\u1ed9t h\u00ecnh<\/p>\n\n\n\n
V\u1edbi nh\u1eefng b\u00e0i to\u00e1n nh\u01b0 th\u1ebf n\u00e0y, ph\u01b0\u01a1ng ph\u00e1p s\u1eed d\u1ee5ng \u0111\u1ec3 gi\u1ea3i ch\u00ednh l\u00e0 d\u00f9ng \u0111\u1ecbnh ngh\u0129a ph\u00e9p \u0111\u1ed1i qua \u0111\u01b0\u1eddng th\u1eb3ng, ho\u1eb7c d\u00f9ng bi\u1ec3u th\u1ee9c t\u1ecda \u0111\u1ed9 bi\u1ec3u th\u1ee9c t\u1ecda \u0111\u1ed9 c\u1ee7a ph\u00e9p \u0111\u1ed1i qua \u0111\u01b0\u1eddng th\u1eb3ng m\u00e0 tr\u1ee5c \u0111\u1ed1i x\u1ee9ng l\u00e0 c\u00e1c tr\u1ee5c t\u1ecda \u0111\u1ed9 Ox, Oy. Ngo\u00e0i ra, b\u1ea1n c\u0169ng ho\u00e0n to\u00e0n c\u00f3 th\u1ec3 d\u00f9ng bi\u1ec3u th\u1ee9c vect\u01a1.<\/p>\n\n\n\n
B\u00e0i t\u1eadp v\u00ed d\u1ee5 v\u1ec1 x\u00e1c \u0111\u1ecbnh \u1ea3nh c\u1ee7a m\u1ed9t h\u00ecnh<\/p>\n\n\n\n
C\u00e1c b\u00e0i to\u00e1n d\u1ef1ng h\u00ecnh<\/p>\n\n\n\n
B\u00ean c\u1ea1nh x\u00e1c \u0111\u1ecbnh \u1ea3nh c\u1ee7a m\u1ed9t h\u00ecnh, m\u1ed9t b\u00e0i to\u00e1n c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng ph\u00e9p bi\u1ebfn h\u00ecnh n\u00e0y \u0111\u1ec3 gi\u1ea3i n\u1eefa ch\u00ednh l\u00e0 b\u00e0i to\u00e1n d\u1ef1ng h\u00ecnh. V\u1edbi b\u00e0i to\u00e1n d\u1ef1ng h\u00ecnh, ch\u00fang ta c\u1ea7n x\u00e1c \u0111\u1ecbnh n\u00f3 l\u00e0 \u1ea3nh c\u1ee7a m\u1ed9t \u0111i\u1ec3m \u0111\u00e3 bi\u1ebft qua ph\u00e9p \u0111\u1ed1i qua \u0111\u01b0\u1eddng th\u1eb3ng. Ho\u1eb7c c\u00f3 th\u1ec3 xem M l\u00e0 giao \u0111i\u1ec3m c\u1ee7a m\u1ed9t \u0111\u01b0\u1eddng c\u1ed1 \u0111\u1ecbnh v\u00e0 m\u1ed9t \u1ea3nh c\u1ee7a \u0111\u01b0\u1eddng \u0111\u00e3 bi\u1ebft qua ph\u00e9p \u0111\u1ed1i x\u1ee9ng n\u00e0y.<\/p>\n\n\n\n
T\u00f3m l\u1ea1i, ch\u00fang ta v\u1eeba t\u00ecm hi\u1ec3u qua v\u1ec1 ph\u00e9p \u0111\u1ed1i x\u1ee9ng tr\u1ee5c t\u1eeb l\u00fd thuy\u1ebft chung cho \u0111\u1ebfn c\u00e1c b\u00e0i to\u00e1n c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng ph\u00e9p bi\u1ebfn h\u00ecnh n\u00e0y \u0111\u1ec3 \u00e1p d\u1ee5ng gi\u1ea3i. Quan tr\u1ecdng c\u1ee7a n\u1ed9i dung b\u00e0i h\u1ecdc l\u00e0 c\u00e1c em c\u1ea7n hi\u1ec3u \u0111\u1ecbnh ngh\u0129a, t\u00ednh ch\u1ea5t c\u1ee7a n\u00f3 \u0111\u1ec3 v\u1eadn d\u1ee5ng th\u00e0nh c\u00f4ng trong b\u00e0i.<\/p>\n\n\n\n
<\/p>\n\n\n\n
\u0110\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c, c\u1ee7a h\u00ecnh<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn Hi\u1ec7n nay, trong ch\u01b0\u01a1ng tr\u00ecnh Trung h\u1ecdc c\u01a1 s\u1edf v\u00e0 trung h\u1ecdc ph\u1ed5 th\u00f4ng, c\u00e1c ph\u00e9p bi\u1ebfn h\u00ecnh trong h\u00ecnh h\u1ecdc ph\u1eb3ng v\u00e0 h\u00ecnh h\u1ecdc kh\u00f4ng gian chi\u1ebfm m\u1ed9t dung l\u01b0\u1ee3ng kh\u00f4ng h\u1ec1 nh\u1ecf. Trong \u0111\u00f3, ph\u1ea3i k\u1ec3 \u0111\u1ebfn ph\u00e9p \u0111\u1ed1i x\u1ee9ng tr\u1ee5c. B\u00e0i vi\u1ebft sau \u0111\u00e2y Vietlearn s\u1ebd […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_disable_autopaging":false},"categories":[9],"tags":[],"class_list":["post-1093","post","type-post","status-publish","format-standard","hentry","category-toan-hoc"],"_links":{"self":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/1093","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/comments?post=1093"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/1093\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=1093"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=1093"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=1093"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}