H\u00ecnh h\u1ecdc - Ch\u01b0\u01a1ng 3 - B\u00e0i 3 : \u0110\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng<\/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-bai-3-duong-tha\u0309ng-va-ma\u0323t-pha\u0309ng-song-song\/\" \/>\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 3 - B\u00e0i 3 : \u0110\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng\" \/>\n<meta property=\"og:description\" content=\"B\u00e0i 1 (trang 104 SGK H\u00ecnh h\u1ecdc 11):\u00a0Cho m\u1eb7t ph\u1eb3ng (\u03b1) v\u00e0 hai \u0111\u01b0\u1eddng th\u1eb3ng a, b. 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B\u00e0i 1 (trang 104 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho m\u1eb7t ph\u1eb3ng (\u03b1) v\u00e0 hai \u0111\u01b0\u1eddng th\u1eb3ng a, b. C\u00e1c m\u1ec7nh \u0111\u1ec1 sau \u0111\u00e2y \u0111\u00fang hay sai?<\/p>\n

b) \u0110i\u1ec1u n\u00e0y ch\u01b0a \u0111\u1ee7 \u0111\u1ec3 b \u22a5(\u03b1)<\/p>\n

a^{‘<\/sup>\u00a0v\u00e0 b^{‘<\/sup>\u00a0c\u00f3 th\u1ec3 c\u1eaft nhau n\u00ean a v\u00e0 b c\u00f3 th\u1ec3 ch\u00e9o nhau<\/p>\n}}

d) a \u22a5(\u03b1) v\u00e0 b \u22a5a th\u00ec b c\u00f3 th\u1ec3 n\u1eb1m trong mp(\u03b1)<\/p>\n

B\u00e0i 2 (trang 104 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho t\u1ee9 di\u1ec7n ABCD c\u00f3 hai m\u1eb7t ABC v\u00e0 BCD l\u00e0 hai tam gi\u00e1c c\u00e2n c\u00f3 chung \u0111\u00e1y BC. G\u1ecdi I l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh BC.<\/p>\n

a) Ch\u1ee9ng minh r\u1eb1ng BC vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng (ADI)<\/p>\n

b) G\u1ecdi AH l\u00e0 \u0111\u01b0\u1eddng cao c\u1ee7a tam gi\u00e1c ADI, ch\u1ee9ng minh r\u1eb1ng AH vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng (BCD).<\/p>\n

B\u00e0i 3 (trang 104 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho h\u00ecnh ch\u00f3p S.ABCD c\u00f3 \u0111\u00e1y l\u00e0 h\u00ecnh thoi ABCD t\u00e2m O v\u00e0 c\u00f3 SA = SB = SC = SD. Ch\u1ee9ng minh r\u1eb1ng:<\/p>\n

a) \u0110\u01b0\u1eddng th\u1eb3ng SO vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng (ABCD)<\/p>\n

b) \u0110\u01b0\u1eddng th\u1eb3ng AC vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng (SBD) v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng BD vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng (SAC).<\/p>\n

B\u00e0i 4 (trang 105 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho t\u1ee9 di\u1ec7n OABC c\u00f3 ba c\u1ea1nh OA, OB v\u00e0 OC \u0111\u00f4i m\u1ed9t vu\u00f4ng g\u00f3c. G\u1ecdi H l\u00e0 ch\u00e2n \u0111\u01b0\u1eddng vu\u00f4ng g\u00f3c h\u1ea1 t\u1eeb O t\u1edbi m\u1eb7t ph\u1eb3ng (ABC). Ch\u1ee9ng minh r\u1eb1ng :<\/p>\n

B\u00e0i 5 (trang 105 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Tr\u00ean m\u1eb7t ph\u1eb3ng (\u03b1) cho h\u00ecnh b\u00ecnh h\u00e0nh ABCD t\u00e2m O. G\u1ecdi S l\u00e0 m\u1ed9t \u0111i\u1ec3m n\u1eb1m ngo\u00e0i m\u1eb7t ph\u1eb3ng (\u03b1) sao cho SA = SC, SB = SD. Ch\u1ee9ng minh r\u1eb1ng:<\/p>\n

\n
a) SO \u22a5(\u03b1)<\/p>\n
b) N\u1ebfu trong m\u1eb7t ph\u1eb3ng (SAB) k\u1ebb SH vu\u00f4ng g\u00f3c v\u1edbi AB t\u1ea1i H th\u00ec AB vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng (SOH).<\/p>\n
L\u1eddi gi\u1ea3i:<\/b><\/p>\n
$\"\"$ <\/p>\n
$\"\"$ <\/p>\n
B\u00e0i 6 (trang 105 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho h\u00ecnh ch\u00f3p S.ABCD c\u00f3 \u0111\u00e1y l\u00e0 h\u00ecnh thoi ABCD v\u00e0 c\u00f3 c\u1ea1nh SA vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng (ABCD). G\u1ecdi I v\u00e0 K l\u00e0 hai \u0111i\u1ec3m l\u1ea7n l\u01b0\u1ee3t l\u1ea5y tr\u00ean hai c\u1ea1nh SB v\u00e0 SD sao cho SI\/SB = SK\/SD . Ch\u1ee9ng minh:<\/p>\n
a) BD \u22a5 SC<\/p>\n
b) IK \u22a5mp(SAC)<\/p>\n
L\u1eddi gi\u1ea3i:<\/b><\/p>\n
$\"\"$ <\/p>\n
$\"\"$ <\/p>\n
B\u00e0i 7 (trang 105 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho t\u1ee9 di\u1ec7n SABC c\u00f3 SA vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng (ABC) v\u00e0 tam gi\u00e1c ABC vu<\/p>\n
Ch\u1ee9ng minh r\u1eb1ng:<\/p>\n
a) BC \u22a5 (SAB), AM \u22a5 (SBC)<\/p>\n
b) SB \u22a5 AN<\/p>\n
L\u1eddi gi\u1ea3i:<\/b><\/p>\n
$\"\"$ <\/p>\n
$\"\"$ <\/p>\n
B\u00e0i 8 (trang 105 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho \u0111i\u1ec3m S kh\u00f4ng thu\u1ed9c m\u1eb7t ph\u1eb3ng (\u03b1) c\u00f3 h\u00ecnh chi\u1ebfu tr\u00ean (\u03b1) l\u00e0 \u0111i\u1ec3m H. V\u1edbi \u0111i\u1ec3m M b\u1ea5t k\u00ec tr\u00ean (\u03b1) v\u00e0 kh\u00f4ng tr\u00f9ng v\u1edbi H, ta g\u1ecdi SM l\u00e0 \u0111\u01b0\u1eddng xi\u00ean v\u00e0 \u0111o\u1ea1n HM l\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a \u0111\u01b0\u1eddng xi\u00ean \u0111\u00f3.<\/p>\n
Ch\u1ee9ng minh r\u1eb1ng:<\/p>\n
a) Hai \u0111\u01b0\u1eddng xi\u00ean b\u1eb1ng nhau khi v\u00e0 ch\u1ec9 khi hai h\u00ecnh chi\u1ebfu c\u1ee7a ch\u00fang b\u1eb1ng nhau;<\/p>\n
b) V\u1edbi hai \u0111\u01b0\u1eddng xi\u00ean cho tr\u01b0\u1edbc, \u0111\u01b0\u1eddng xi\u00ean n\u00e0o l\u1edbn h\u01a1n th\u00ec c\u00f3 h\u00ecnh chi\u1ebfu l\u1edbn h\u01a1n v\u00e0 ng\u01b0\u1ee3c l\u1ea1i, \u0111\u01b0\u1eddng xi\u00ean n\u00e0o c\u00f3 h\u00ecnh chi\u1ebfu l\u1edbn h\u01a1n th\u00ec l\u1edbn h\u01a1n.<\/p>\n
L\u1eddi gi\u1ea3i:<\/b><\/p>\n
$\"\"$ <\/p>\n
a) Gi\u1ea3 s\u1eed ta c\u00f3 hai \u0111\u01b0\u1eddng xi\u00ean SA, SB v\u00e0 c\u00e1c h\u00ecnh chi\u1ebfu HA, HB c\u1ee7a ch\u00fang tr\u00ean mp(\u03b1)<\/p>\n
Gi\u1ea3 s\u1eed HA = HB<\/p>\n
V\u00ec SH \u22a5 mp(\u03b1) n\u00ean SH \u22a5 HA v\u00e0 SH \u22a5 SB v\u00e0 c\u00e1c tam gi\u00e1c SHA, SHB l\u00e0 c\u00e1c tam gi\u00e1c vu\u00f4ng. Hai tam gi\u00e1c vu\u00f4ng SHA, SHB c\u00f3 canh SH chung v\u00e0 HA = HB n\u00ean :<\/p>\n
\u0394SHA = \u0394SHB SA = SB<\/p>\n
Ng\u01b0\u1ee3c l\u1ea1i n\u1ebfu SA = SB th\u00ec \u0394SHA = \u0394SHB \u21d2 HA = HB<\/p>\n
K\u1ebft qu\u1ea3, ta c\u00f3 HA = HB SA= SB (\u0111pcm)<\/p>\n
b) Gi\u1ea3 s\u1eed c\u00f3 hai \u0111\u01b0\u1eddng xi\u00ean SA, SC v\u00e0 c\u00e1c h\u00ecnh chi\u1ebfu HA, HC c\u1ee7a ch\u00fang tr\u00ean mp(\u03b1) v\u1edbi gi\u1ea3 thi\u1ebft HC > HA.<\/p>\n
Tr\u00ean \u0111o\u1ea1n HC, l\u1ea5y \u0111i\u1ec3m B^{‘<\/sup>\u00a0sao cho HA^{‘<\/sup>\u00a0= HA \u21d2 HC > HA^{‘<\/sup>. Nh\u01b0 v\u1eady, theo k\u1ebft qu\u1ea3 c\u00e2u a) ta c\u00f3 SA^{‘<\/sup>\u00a0= SA. Ta c\u00f3 trong c\u00e1c tam gi\u00e1c vu\u00f4ng SHB^{‘<\/sup>, SHC th\u00ec :<\/p>\n}}}}}
SC^{2<\/sup>= SH^{2<\/sup>\u00a0+ HC^{2<\/sup><\/p>\n}}}
SA^{2<\/sup>\u00a0= SH^{2<\/sup>\u00a0+ HA^{2<\/sup><\/p>\n}}}
V\u00ec HC > HA^{‘<\/sup>\u00a0n\u00ean SC^{2<\/sup>\u00a0> SA^{2<\/sup>\u00a0\u21d2 SC > SA<\/p>\n}}}
Suy ra SC > SA<\/p>\n
Nh\u01b0 v\u1eady HC > HA \u21d2 SC > SA<\/p>\n
L\u00ed lu\u1eadn t\u01b0\u01a1ng t\u1ef1, ta c\u00f3 : SC > SA \u21d2 HC > HA<\/p>\n
K\u1ebft qu\u1ea3 : HC > HA \u21d4 SC > SA<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
B\u00e0i 1 (trang 104 SGK H\u00ecnh h\u1ecdc 11):\u00a0Cho m\u1eb7t ph\u1eb3ng (\u03b1) v\u00e0 hai \u0111\u01b0\u1eddng th\u1eb3ng a, b. C\u00e1c m\u1ec7nh \u0111\u1ec1 sau \u0111\u00e2y \u0111\u00fang hay sai? a) N\u1ebfu a \/\/ (\u03b1), b \u22a5(\u03b1) th\u00ec a \u22a5b. b) N\u1ebfu a \/\/ (\u03b1), b \u22a5a th\u00ec b \u22a5(\u03b1). c) N\u1ebfu a \/\/ (\u03b1), b \/\/ (\u03b1) th\u00ec b […]<\/p>\n","protected":false},"author":3,"featured_media":29435,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"tdm_status":"","tdm_grid_status":""},"categories":[1318],"tags":[1464,1463],"yoast_head":"\nH\u00ecnh h\u1ecdc - Ch\u01b0\u01a1ng 3 - B\u00e0i 3 : \u0110\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng<\/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-bai-3-duong-tha\u0309ng-va-ma\u0323t-pha\u0309ng-song-song\/\" \/>\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 3 - B\u00e0i 3 : \u0110\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng\" \/>\n<meta property=\"og:description\" content=\"B\u00e0i 1 (trang 104 SGK H\u00ecnh h\u1ecdc 11):\u00a0Cho m\u1eb7t ph\u1eb3ng (\u03b1) v\u00e0 hai \u0111\u01b0\u1eddng th\u1eb3ng a, b. 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