{"id":2085,"date":"2025-05-16T17:25:26","date_gmt":"2025-05-16T17:25:26","guid":{"rendered":"https:\/\/daotaotructuyentiengtrung.edu.vn\/index.php\/2025\/05\/16\/1700-tinh-chat-duong-cao-trong-tam-giac-vuong-ung-dung-va-cach-tinh\/"},"modified":"2025-05-16T17:25:26","modified_gmt":"2025-05-16T17:25:26","slug":"1700-tinh-chat-duong-cao-trong-tam-giac-vuong-ung-dung-va-cach-tinh","status":"publish","type":"post","link":"https:\/\/daotaotructuyentiengtrung.edu.vn\/index.php\/2025\/05\/16\/1700-tinh-chat-duong-cao-trong-tam-giac-vuong-ung-dung-va-cach-tinh\/","title":{"rendered":"T\u00ednh Ch\u1ea5t \u0110\u01b0\u1eddng Cao Trong Tam Gi\u00e1c Vu\u00f4ng: \u1ee8ng D\u1ee5ng V\u00e0 C\u00e1ch T\u00ednh?"},"content":{"rendered":"

T\u00ednh Ch\u1ea5t \u0111\u01b0\u1eddng Cao Trong Tam Gi\u00e1c Vu\u00f4ng<\/a><\/u> \u0111\u00f3ng vai tr\u00f2 quan tr\u1ecdng trong h\u00ecnh h\u1ecdc v\u00e0 c\u00f3 nhi\u1ec1u \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf. Xe T\u1ea3i M\u1ef9 \u0110\u00ecnh (XETAIMYDINH.EDU.VN) s\u1ebd cung c\u1ea5p cho b\u1ea1n c\u00e1i nh\u00ecn s\u00e2u s\u1eafc v\u1ec1 t\u00ednh ch\u1ea5t n\u00e0y, c\u00f9ng v\u1edbi c\u00e1c v\u00ed d\u1ee5 minh h\u1ecda v\u00e0 c\u00f4ng th\u1ee9c t\u00ednh to\u00e1n chi ti\u1ebft \u0111\u1ec3 b\u1ea1n d\u1ec5 d\u00e0ng \u00e1p d\u1ee5ng. B\u00e0i vi\u1ebft n\u00e0y c\u0169ng s\u1ebd \u0111\u1ec1 c\u1eadp \u0111\u1ebfn c\u00e1c \u1ee9ng d\u1ee5ng c\u1ee7a \u0111\u01b0\u1eddng cao trong tam gi\u00e1c vu\u00f4ng v\u00e0 c\u00e1c kh\u00e1i ni\u1ec7m li\u00ean quan kh\u00e1c nh\u01b0 \u0111\u1ecbnh l\u00fd Pitago v\u00e0 h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c vu\u00f4ng, gi\u00fap b\u1ea1n n\u1eafm v\u1eefng ki\u1ebfn th\u1ee9c m\u1ed9t c\u00e1ch to\u00e0n di\u1ec7n.<\/span><\/p>\n

1. \u0110\u01b0\u1eddng Cao Trong Tam Gi\u00e1c Vu\u00f4ng L\u00e0 G\u00ec?<\/strong><\/h2>\n

\u0110\u01b0\u1eddng cao trong tam gi\u00e1c vu\u00f4ng l\u00e0 \u0111o\u1ea1n th\u1eb3ng k\u1ebb t\u1eeb \u0111\u1ec9nh g\u00f3c vu\u00f4ng xu\u1ed1ng c\u1ea1nh huy\u1ec1n v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi c\u1ea1nh huy\u1ec1n \u0111\u00f3. \u0110\u01b0\u1eddng cao n\u00e0y chia tam gi\u00e1c vu\u00f4ng ban \u0111\u1ea7u th\u00e0nh hai tam gi\u00e1c vu\u00f4ng nh\u1ecf \u0111\u1ed3ng d\u1ea1ng v\u1edbi tam gi\u00e1c vu\u00f4ng ban \u0111\u1ea7u v\u00e0 \u0111\u1ed3ng d\u1ea1ng v\u1edbi nhau.<\/span><\/p>\n

1.1. \u0110\u1ecbnh Ngh\u0129a \u0110\u01b0\u1eddng Cao Trong Tam Gi\u00e1c Vu\u00f4ng<\/strong><\/h3>\n

\u0110\u01b0\u1eddng cao trong tam gi\u00e1c vu\u00f4ng, c\u00f2n \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111\u01b0\u1eddng cao \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n, l\u00e0 \u0111o\u1ea1n th\u1eb3ng k\u1ebb t\u1eeb \u0111\u1ec9nh g\u00f3c vu\u00f4ng (\u0111\u1ec9nh c\u00f3 g\u00f3c 90 \u0111\u1ed9) xu\u1ed1ng c\u1ea1nh huy\u1ec1n (c\u1ea1nh \u0111\u1ed1i di\u1ec7n g\u00f3c vu\u00f4ng). \u0110\u01b0\u1eddng cao n\u00e0y ph\u1ea3i vu\u00f4ng g\u00f3c v\u1edbi c\u1ea1nh huy\u1ec1n. Theo \u0111\u1ecbnh ngh\u0129a c\u1ee7a Wikipedia, \u0111\u01b0\u1eddng cao l\u00e0 m\u1ed9t \u0111o\u1ea1n th\u1eb3ng n\u1ed1i t\u1eeb m\u1ed9t \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng ch\u1ee9a c\u1ea1nh \u0111\u1ed1i di\u1ec7n, sao cho \u0111o\u1ea1n th\u1eb3ng n\u00e0y vu\u00f4ng g\u00f3c v\u1edbi c\u1ea1nh \u0111\u1ed1i di\u1ec7n.<\/span><\/p>\n

1.2. T\u00ednh Ch\u1ea5t Quan Tr\u1ecdng C\u1ee7a \u0110\u01b0\u1eddng Cao Trong Tam Gi\u00e1c Vu\u00f4ng<\/strong><\/h3>\n

\u0110\u01b0\u1eddng cao trong tam gi\u00e1c vu\u00f4ng s\u1edf h\u1eefu nh\u1eefng t\u00ednh ch\u1ea5t \u0111\u1eb7c bi\u1ec7t quan tr\u1ecdng, \u0111\u01b0\u1ee3c \u1ee9ng d\u1ee5ng r\u1ed9ng r\u00e3i trong gi\u1ea3i to\u00e1n v\u00e0 c\u00e1c b\u00e0i to\u00e1n th\u1ef1c t\u1ebf:<\/span><\/p>\n

    \n
  1. <\/span>Chia Tam Gi\u00e1c Vu\u00f4ng Th\u00e0nh Hai Tam Gi\u00e1c Vu\u00f4ng Nh\u1ecf \u0110\u1ed3ng D\u1ea1ng:<\/strong> \u0110\u01b0\u1eddng cao chia tam gi\u00e1c vu\u00f4ng l\u1edbn th\u00e0nh hai tam gi\u00e1c vu\u00f4ng nh\u1ecf h\u01a1n. Hai tam gi\u00e1c vu\u00f4ng nh\u1ecf n\u00e0y \u0111\u1ed3ng d\u1ea1ng v\u1edbi nhau v\u00e0 \u0111\u1ed3ng d\u1ea1ng v\u1edbi tam gi\u00e1c vu\u00f4ng l\u1edbn ban \u0111\u1ea7u.<\/span><\/li>\n
  2. <\/span>H\u1ec7 Th\u1ee9c L\u01b0\u1ee3ng Li\u00ean Quan \u0110\u1ebfn \u0110\u01b0\u1eddng Cao:<\/strong> \u0110\u01b0\u1eddng cao tham gia v\u00e0o c\u00e1c h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng quan tr\u1ecdng trong tam gi\u00e1c vu\u00f4ng, gi\u00fap thi\u1ebft l\u1eadp m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c c\u1ea1nh v\u00e0 g\u00f3c c\u1ee7a tam gi\u00e1c.<\/span><\/li>\n
  3. <\/span>Li\u00ean H\u1ec7 V\u1edbi \u0110\u1ecbnh L\u00fd Pitago:<\/strong> \u0110\u01b0\u1eddng cao c\u00f3 m\u1ed1i li\u00ean h\u1ec7 m\u1eadt thi\u1ebft v\u1edbi \u0111\u1ecbnh l\u00fd Pitago, m\u1ed9t trong nh\u1eefng \u0111\u1ecbnh l\u00fd c\u01a1 b\u1ea3n nh\u1ea5t c\u1ee7a h\u00ecnh h\u1ecdc.<\/span><\/li>\n<\/ol>\n

    1.3. \u0110\u01b0\u1eddng Cao So V\u1edbi \u0110\u01b0\u1eddng Trung Tuy\u1ebfn, \u0110\u01b0\u1eddng Ph\u00e2n Gi\u00e1c V\u00e0 \u0110\u01b0\u1eddng Trung Tr\u1ef1c<\/strong><\/h3>\n

    \u0110\u1ec3 hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 \u0111\u01b0\u1eddng cao, ch\u00fang ta h\u00e3y so s\u00e1nh n\u00f3 v\u1edbi c\u00e1c lo\u1ea1i \u0111\u01b0\u1eddng kh\u00e1c trong tam gi\u00e1c:<\/span><\/p>\n\n\n\n\n\n\n\n
    Lo\u1ea1i \u0110\u01b0\u1eddng\u0110\u1ecbnh Ngh\u0129aT\u00ednh Ch\u1ea5t<\/span><\/td>\n<\/tr>\n
    \u0110\u01b0\u1eddng Cao<\/span><\/td>\n\u0110o\u1ea1n th\u1eb3ng k\u1ebb t\u1eeb \u0111\u1ec9nh xu\u1ed1ng c\u1ea1nh \u0111\u1ed1i di\u1ec7n v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi c\u1ea1nh \u0111\u00f3.<\/span><\/td>\nChia tam gi\u00e1c th\u00e0nh hai tam gi\u00e1c nh\u1ecf h\u01a1n, c\u00f3 h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng \u0111\u1eb7c bi\u1ec7t.<\/span><\/td>\n<\/tr>\n
    \u0110\u01b0\u1eddng Trung Tuy\u1ebfn<\/span><\/td>\n\u0110o\u1ea1n th\u1eb3ng n\u1ed1i \u0111\u1ec9nh v\u1edbi trung \u0111i\u1ec3m c\u1ea1nh \u0111\u1ed1i di\u1ec7n.<\/span><\/td>\nChia c\u1ea1nh \u0111\u1ed1i di\u1ec7n th\u00e0nh hai ph\u1ea7n b\u1eb1ng nhau, tr\u1ecdng t\u00e2m l\u00e0 giao \u0111i\u1ec3m c\u1ee7a ba \u0111\u01b0\u1eddng trung tuy\u1ebfn.<\/span><\/td>\n<\/tr>\n
    \u0110\u01b0\u1eddng Ph\u00e2n Gi\u00e1c<\/span><\/td>\n\u0110o\u1ea1n th\u1eb3ng chia m\u1ed9t g\u00f3c c\u1ee7a tam gi\u00e1c th\u00e0nh hai g\u00f3c b\u1eb1ng nhau.<\/span><\/td>\nC\u00e1c \u0111i\u1ec3m tr\u00ean \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u00e1ch \u0111\u1ec1u hai c\u1ea1nh c\u1ee7a g\u00f3c \u0111\u00f3, t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp l\u00e0 giao \u0111i\u1ec3m c\u1ee7a ba \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c.<\/span><\/td>\n<\/tr>\n
    \u0110\u01b0\u1eddng Trung Tr\u1ef1c<\/span><\/td>\n\u0110\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi m\u1ed9t c\u1ea1nh t\u1ea1i trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh \u0111\u00f3.<\/span><\/td>\nM\u1ecdi \u0111i\u1ec3m tr\u00ean \u0111\u01b0\u1eddng trung tr\u1ef1c c\u00e1ch \u0111\u1ec1u hai \u0111\u1ea7u m\u00fat c\u1ee7a c\u1ea1nh \u0111\u00f3, t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp l\u00e0 giao \u0111i\u1ec3m c\u1ee7a ba \u0111\u01b0\u1eddng trung tr\u1ef1c.<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    2. C\u00e1c H\u1ec7 Th\u1ee9c L\u01b0\u1ee3ng Li\u00ean Quan \u0110\u1ebfn \u0110\u01b0\u1eddng Cao Trong Tam Gi\u00e1c Vu\u00f4ng<\/strong><\/h2>\n

    Trong tam gi\u00e1c vu\u00f4ng, \u0111\u01b0\u1eddng cao \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n t\u1ea1o ra c\u00e1c h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng v\u00f4 c\u00f9ng quan tr\u1ecdng, gi\u00fap gi\u1ea3i quy\u1ebft nhi\u1ec1u b\u00e0i to\u00e1n h\u00ecnh h\u1ecdc ph\u1ee9c t\u1ea1p.<\/span><\/p>\n

    2.1. H\u1ec7 Th\u1ee9c V\u1ec1 B\u00ecnh Ph\u01b0\u01a1ng \u0110\u01b0\u1eddng Cao<\/strong><\/h3>\n

    Trong m\u1ed9t tam gi\u00e1c vu\u00f4ng, b\u00ecnh ph\u01b0\u01a1ng \u0111\u01b0\u1eddng cao \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n b\u1eb1ng t\u00edch c\u1ee7a hai h\u00ecnh chi\u1ebfu c\u1ee7a hai c\u1ea1nh g\u00f3c vu\u00f4ng tr\u00ean c\u1ea1nh huy\u1ec1n.<\/span><\/p>\n

    C\u00f4ng th\u1ee9c:<\/strong><\/p>\n

    N\u1ebfu tam gi\u00e1c ABC vu\u00f4ng t\u1ea1i A, \u0111\u01b0\u1eddng cao AH, ta c\u00f3:<\/span><\/p>\n

    AH\u00b2 = BH * CH<\/p>\n

    2.2. H\u1ec7 Th\u1ee9c V\u1ec1 T\u00edch C\u1ee7a C\u1ea1nh G\u00f3c Vu\u00f4ng V\u00e0 \u0110\u01b0\u1eddng Cao<\/strong><\/h3>\n

    T\u00edch c\u1ee7a c\u1ea1nh g\u00f3c vu\u00f4ng v\u00e0 \u0111\u01b0\u1eddng cao t\u01b0\u01a1ng \u1ee9ng b\u1eb1ng t\u00edch c\u1ee7a hai c\u1ea1nh g\u00f3c vu\u00f4ng.<\/span><\/p>\n

    C\u00f4ng th\u1ee9c:<\/strong><\/p>\n

    AB * AC = AH * BC<\/p>\n

    2.3. H\u1ec7 Th\u1ee9c V\u1ec1 Ngh\u1ecbch \u0110\u1ea3o B\u00ecnh Ph\u01b0\u01a1ng \u0110\u01b0\u1eddng Cao<\/strong><\/h3>\n

    Ngh\u1ecbch \u0111\u1ea3o c\u1ee7a b\u00ecnh ph\u01b0\u01a1ng \u0111\u01b0\u1eddng cao b\u1eb1ng t\u1ed5ng c\u00e1c ngh\u1ecbch \u0111\u1ea3o c\u1ee7a b\u00ecnh ph\u01b0\u01a1ng hai c\u1ea1nh g\u00f3c vu\u00f4ng.<\/span><\/p>\n

    C\u00f4ng th\u1ee9c:<\/strong><\/p>\n

    1\/AH\u00b2 = 1\/AB\u00b2 + 1\/AC\u00b2<\/p>\n

    2.4. \u1ee8ng D\u1ee5ng C\u1ee7a C\u00e1c H\u1ec7 Th\u1ee9c L\u01b0\u1ee3ng<\/strong><\/h3>\n

    C\u00e1c h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng n\u00e0y kh\u00f4ng ch\u1ec9 gi\u00fap gi\u1ea3i c\u00e1c b\u00e0i to\u00e1n h\u00ecnh h\u1ecdc trong s\u00e1ch gi\u00e1o khoa m\u00e0 c\u00f2n c\u00f3 \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf trong c\u00e1c l\u0129nh v\u1ef1c nh\u01b0 x\u00e2y d\u1ef1ng, thi\u1ebft k\u1ebf v\u00e0 \u0111o \u0111\u1ea1c. V\u00ed d\u1ee5, trong x\u00e2y d\u1ef1ng, ng\u01b0\u1eddi ta c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng c\u00e1c h\u1ec7 th\u1ee9c n\u00e0y \u0111\u1ec3 t\u00ednh to\u00e1n chi\u1ec1u cao c\u1ee7a m\u1ed9t c\u00f4ng tr\u00ecnh ho\u1eb7c kho\u1ea3ng c\u00e1ch gi\u1eefa c\u00e1c \u0111i\u1ec3m m\u00e0 kh\u00f4ng c\u1ea7n ph\u1ea3i \u0111o tr\u1ef1c ti\u1ebfp. Theo t\u1ea1p ch\u00ed X\u00e2y d\u1ef1ng Vi\u1ec7t Nam, vi\u1ec7c \u00e1p d\u1ee5ng c\u00e1c h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng gi\u00fap ti\u1ebft ki\u1ec7m th\u1eddi gian v\u00e0 chi ph\u00ed trong qu\u00e1 tr\u00ecnh thi c\u00f4ng.<\/span><\/p>\n

    3. C\u00e1ch T\u00ednh \u0110\u01b0\u1eddng Cao Trong Tam Gi\u00e1c Vu\u00f4ng<\/strong><\/h2>\n

    C\u00f3 nhi\u1ec1u ph\u01b0\u01a1ng ph\u00e1p \u0111\u1ec3 t\u00ednh \u0111\u01b0\u1eddng cao trong tam gi\u00e1c vu\u00f4ng, t\u00f9y thu\u1ed9c v\u00e0o th\u00f4ng tin \u0111\u00e3 bi\u1ebft.<\/span><\/p>\n

    3.1. T\u00ednh \u0110\u01b0\u1eddng Cao Khi Bi\u1ebft \u0110\u1ed9 D\u00e0i Hai C\u1ea1nh G\u00f3c Vu\u00f4ng<\/strong><\/h3>\n

    N\u1ebfu bi\u1ebft \u0111\u1ed9 d\u00e0i hai c\u1ea1nh g\u00f3c vu\u00f4ng (AB v\u00e0 AC), ta c\u00f3 th\u1ec3 t\u00ednh \u0111\u01b0\u1eddng cao AH b\u1eb1ng c\u00f4ng th\u1ee9c:<\/span><\/p>\n

    AH = (AB * AC) \/ BC<\/p>\n

    Trong \u0111\u00f3 BC l\u00e0 c\u1ea1nh huy\u1ec1n, \u0111\u01b0\u1ee3c t\u00ednh theo \u0111\u1ecbnh l\u00fd Pitago:<\/span><\/p>\n

    BC = \u221a(AB\u00b2 + AC\u00b2)<\/p>\n

    V\u00ed d\u1ee5:<\/strong><\/p>\n

    Cho tam gi\u00e1c ABC vu\u00f4ng t\u1ea1i A, AB = 3cm, AC = 4cm. T\u00ednh \u0111\u01b0\u1eddng cao AH.<\/span><\/p>\n

      \n
    1. <\/span>T\u00ednh c\u1ea1nh huy\u1ec1n BC:<\/span><\/li>\n
    2. <\/span>BC = \u221a(3\u00b2 + 4\u00b2) = \u221a25 = 5cm<\/li>\n
    3. <\/span>T\u00ednh \u0111\u01b0\u1eddng cao AH:<\/span><\/li>\n
    4. <\/span>AH = (3 * 4) \/ 5 = 2.4cm<\/li>\n<\/ol>\n

      3.2. T\u00ednh \u0110\u01b0\u1eddng Cao Khi Bi\u1ebft Di\u1ec7n T\u00edch V\u00e0 C\u1ea1nh Huy\u1ec1n<\/strong><\/h3>\n

      N\u1ebfu bi\u1ebft di\u1ec7n t\u00edch (S) c\u1ee7a tam gi\u00e1c vu\u00f4ng v\u00e0 \u0111\u1ed9 d\u00e0i c\u1ea1nh huy\u1ec1n (BC), ta c\u00f3 th\u1ec3 t\u00ednh \u0111\u01b0\u1eddng cao AH b\u1eb1ng c\u00f4ng th\u1ee9c:<\/span><\/p>\n

      AH = (2 * S) \/ BC<\/p>\n

      V\u00ed d\u1ee5:<\/strong><\/p>\n

      Cho tam gi\u00e1c ABC vu\u00f4ng t\u1ea1i A, di\u1ec7n t\u00edch S = 6cm\u00b2, c\u1ea1nh huy\u1ec1n BC = 5cm. T\u00ednh \u0111\u01b0\u1eddng cao AH.<\/span><\/p>\n

      AH = (2 * 6) \/ 5 = 2.4cm<\/p>\n

      3.3. S\u1eed D\u1ee5ng \u0110\u1ecbnh L\u00fd Pitago \u0110\u1ec3 T\u00ednh \u0110\u01b0\u1eddng Cao<\/strong><\/h3>\n

      Trong tam gi\u00e1c vu\u00f4ng ABC, \u0111\u01b0\u1eddng cao AH chia c\u1ea1nh huy\u1ec1n BC th\u00e0nh hai \u0111o\u1ea1n BH v\u00e0 CH. Ta c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00fd Pitago \u0111\u1ec3 t\u00ednh AH n\u1ebfu bi\u1ebft \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh kh\u00e1c.<\/span><\/p>\n

      C\u00e1c b\u01b0\u1edbc th\u1ef1c hi\u1ec7n:<\/strong><\/p>\n

        \n
      1. <\/span>T\u00ednh BH ho\u1eb7c CH (n\u1ebfu bi\u1ebft m\u1ed9t trong hai).<\/span><\/li>\n
      2. <\/span>\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pitago cho tam gi\u00e1c ABH ho\u1eb7c ACH \u0111\u1ec3 t\u00ednh AH.<\/span><\/li>\n<\/ol>\n

        V\u00ed d\u1ee5:<\/strong><\/p>\n

        Cho tam gi\u00e1c ABC vu\u00f4ng t\u1ea1i A, AB = 3cm, BC = 5cm, BH = 1.8cm. T\u00ednh \u0111\u01b0\u1eddng cao AH.<\/span><\/p>\n

          \n
        1. <\/span>\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pitago cho tam gi\u00e1c ABH:<\/span><\/li>\n
        2. <\/span>AH\u00b2 = AB\u00b2 – BH\u00b2 = 3\u00b2 – 1.8\u00b2 = 9 – 3.24 = 5.76<\/li>\n
        3. <\/span>T\u00ednh \u0111\u01b0\u1eddng cao AH:<\/span><\/li>\n
        4. <\/span>AH = \u221a5.76 = 2.4cm<\/li>\n<\/ol>\n

          4. C\u00e1c D\u1ea1ng B\u00e0i T\u1eadp Th\u01b0\u1eddng G\u1eb7p V\u1ec1 \u0110\u01b0\u1eddng Cao Trong Tam Gi\u00e1c Vu\u00f4ng<\/strong><\/h2>\n

          \u0110\u1ec3 n\u1eafm v\u1eefng ki\u1ebfn th\u1ee9c v\u1ec1 \u0111\u01b0\u1eddng cao trong tam gi\u00e1c vu\u00f4ng, ch\u00fang ta h\u00e3y c\u00f9ng nhau gi\u1ea3i m\u1ed9t s\u1ed1 d\u1ea1ng b\u00e0i t\u1eadp th\u01b0\u1eddng g\u1eb7p.<\/span><\/p>\n

          4.1. B\u00e0i T\u1eadp Ch\u1ee9ng Minh C\u00e1c H\u1ec7 Th\u1ee9c L\u01b0\u1ee3ng<\/strong><\/h3>\n

          \u0110\u1ec1 b\u00e0i:<\/strong> Cho tam gi\u00e1c ABC vu\u00f4ng t\u1ea1i A, \u0111\u01b0\u1eddng cao AH. Ch\u1ee9ng minh r\u1eb1ng <\/span>AH\u00b2 = BH * CH.<\/span><\/p>\n

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

            \n
          1. <\/span>X\u00e9t tam gi\u00e1c ABH v\u00e0 tam gi\u00e1c CAH, ta c\u00f3:<\/span><\/li>\n
          2. <\/span>G\u00f3c AHB = G\u00f3c CHA = 90\u00b0<\/span><\/li>\n
          3. <\/span>G\u00f3c BAH = G\u00f3c ACH (c\u00f9ng ph\u1ee5 v\u1edbi g\u00f3c ABC)<\/span><\/li>\n
          4. <\/span>V\u1eady tam gi\u00e1c ABH \u0111\u1ed3ng d\u1ea1ng v\u1edbi tam gi\u00e1c CAH (g.g).<\/span><\/li>\n
          5. <\/span>Suy ra t\u1ec9 l\u1ec7: <\/span>AH\/CH = BH\/AH<\/li>\n
          6. <\/span>T\u1eeb \u0111\u00f3, ta c\u00f3: <\/span>AH\u00b2 = BH * CH (\u0111i\u1ec1u ph\u1ea3i ch\u1ee9ng minh).<\/span><\/li>\n<\/ol>\n

            4.2. B\u00e0i T\u1eadp T\u00ednh \u0110\u1ed9 D\u00e0i \u0110\u01b0\u1eddng Cao<\/strong><\/h3>\n

            \u0110\u1ec1 b\u00e0i:<\/strong> Cho tam gi\u00e1c ABC vu\u00f4ng t\u1ea1i A, AB = 6cm, AC = 8cm. T\u00ednh \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng cao AH.<\/span><\/p>\n

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

              \n
            1. <\/span>T\u00ednh c\u1ea1nh huy\u1ec1n BC theo \u0111\u1ecbnh l\u00fd Pitago:<\/span><\/li>\n
            2. <\/span>BC = \u221a(AB\u00b2 + AC\u00b2) = \u221a(6\u00b2 + 8\u00b2) = \u221a100 = 10cm<\/li>\n
            3. <\/span>T\u00ednh \u0111\u01b0\u1eddng cao AH theo c\u00f4ng th\u1ee9c:<\/span><\/li>\n
            4. <\/span>AH = (AB * AC) \/ BC = (6 * 8) \/ 10 = 4.8cm<\/li>\n<\/ol>\n

              4.3. B\u00e0i T\u1eadp V\u1eadn D\u1ee5ng C\u00e1c H\u1ec7 Th\u1ee9c L\u01b0\u1ee3ng \u0110\u1ec3 Gi\u1ea3i To\u00e1n<\/strong><\/h3>\n

              \u0110\u1ec1 b\u00e0i:<\/strong> Cho tam gi\u00e1c ABC vu\u00f4ng t\u1ea1i A, \u0111\u01b0\u1eddng cao AH = 4cm, BH = 3cm. T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh CH v\u00e0 AC.<\/span><\/p>\n

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

                \n
              1. <\/span>\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng <\/span>AH\u00b2 = BH * CH, ta c\u00f3:<\/span><\/li>\n
              2. <\/span>4\u00b2 = 3 * CH<\/li>\n
              3. <\/span>CH = 16 \/ 3 cm<\/li>\n
              4. <\/span>\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pitago cho tam gi\u00e1c ACH:<\/span><\/li>\n
              5. <\/span>AC\u00b2 = AH\u00b2 + CH\u00b2 = 4\u00b2 + (16\/3)\u00b2 = 16 + 256\/9 = 400\/9<\/li>\n
              6. <\/span>AC = \u221a(400\/9) = 20\/3 cm<\/li>\n<\/ol>\n

                5. \u1ee8ng D\u1ee5ng Th\u1ef1c T\u1ebf C\u1ee7a \u0110\u01b0\u1eddng Cao Trong Tam Gi\u00e1c Vu\u00f4ng<\/strong><\/h2>\n

                Kh\u00f4ng ch\u1ec9 l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m h\u00ecnh h\u1ecdc tr\u1eebu t\u01b0\u1ee3ng, \u0111\u01b0\u1eddng cao trong tam gi\u00e1c vu\u00f4ng c\u00f2n c\u00f3 nhi\u1ec1u \u1ee9ng d\u1ee5ng thi\u1ebft th\u1ef1c trong \u0111\u1eddi s\u1ed1ng v\u00e0 k\u1ef9 thu\u1eadt.<\/span><\/p>\n

                5.1. Trong X\u00e2y D\u1ef1ng V\u00e0 Thi\u1ebft K\u1ebf<\/strong><\/h3>\n

                Trong x\u00e2y d\u1ef1ng, \u0111\u01b0\u1eddng cao \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u00ednh to\u00e1n chi\u1ec1u cao c\u1ee7a c\u00e1c c\u00f4ng tr\u00ecnh, \u0111\u1ed9 d\u1ed1c c\u1ee7a m\u00e1i nh\u00e0, ho\u1eb7c kho\u1ea3ng c\u00e1ch gi\u1eefa c\u00e1c \u0111i\u1ec3m tr\u00ean b\u1ea3n v\u1ebd. V\u00ed d\u1ee5, khi x\u00e2y d\u1ef1ng m\u1ed9t m\u00e1i nh\u00e0, k\u1ef9 s\u01b0 c\u1ea7n t\u00ednh to\u00e1n \u0111\u1ed9 d\u1ed1c sao cho ph\u00f9 h\u1ee3p v\u1edbi \u0111i\u1ec1u ki\u1ec7n th\u1eddi ti\u1ebft v\u00e0 \u0111\u1ea3m b\u1ea3o tho\u00e1t n\u01b0\u1edbc t\u1ed1t. \u0110\u01b0\u1eddng cao trong tam gi\u00e1c vu\u00f4ng gi\u00fap x\u00e1c \u0111\u1ecbnh \u0111\u1ed9 d\u1ed1c n\u00e0y m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c.<\/span><\/p>\n

                5.2. Trong \u0110o \u0110\u1ea1c V\u00e0 Tr\u1eafc \u0110\u1ecba<\/strong><\/h3>\n

                Trong \u0111o \u0111\u1ea1c v\u00e0 tr\u1eafc \u0111\u1ecba, \u0111\u01b0\u1eddng cao \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh \u0111\u1ed9 cao c\u1ee7a \u0111\u1ecba h\u00ecnh, t\u00ednh to\u00e1n kho\u1ea3ng c\u00e1ch gi\u1eefa c\u00e1c \u0111i\u1ec3m tr\u00ean b\u1ea3n \u0111\u1ed3, ho\u1eb7c x\u00e1c \u0111\u1ecbnh v\u1ecb tr\u00ed c\u1ee7a c\u00e1c c\u00f4ng tr\u00ecnh. Theo T\u1ed5ng c\u1ee5c Th\u1ed1ng k\u00ea, vi\u1ec7c s\u1eed d\u1ee5ng c\u00e1c ph\u01b0\u01a1ng ph\u00e1p \u0111o \u0111\u1ea1c d\u1ef1a tr\u00ean h\u00ecnh h\u1ecdc gi\u00fap t\u0103ng \u0111\u1ed9 ch\u00ednh x\u00e1c v\u00e0 hi\u1ec7u qu\u1ea3 trong c\u00f4ng t\u00e1c qu\u1ea3n l\u00fd \u0111\u1ea5t \u0111ai v\u00e0 quy ho\u1ea1ch \u0111\u00f4 th\u1ecb.<\/span><\/p>\n

                5.3. Trong Thi\u1ebft K\u1ebf C\u01a1 Kh\u00ed<\/strong><\/h3>\n

                Trong thi\u1ebft k\u1ebf c\u01a1 kh\u00ed, \u0111\u01b0\u1eddng cao \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u00ednh to\u00e1n k\u00edch th\u01b0\u1edbc v\u00e0 v\u1ecb tr\u00ed c\u1ee7a c\u00e1c b\u1ed9 ph\u1eadn m\u00e1y m\u00f3c, \u0111\u1ea3m b\u1ea3o ch\u00fang ho\u1ea1t \u0111\u1ed9ng ch\u00ednh x\u00e1c v\u00e0 hi\u1ec7u qu\u1ea3. V\u00ed d\u1ee5, khi thi\u1ebft k\u1ebf m\u1ed9t h\u1ec7 th\u1ed1ng treo cho xe t\u1ea3i, k\u1ef9 s\u01b0 c\u1ea7n t\u00ednh to\u00e1n \u0111\u1ed9 d\u00e0i v\u00e0 g\u00f3c nghi\u00eang c\u1ee7a c\u00e1c thanh ch\u1ed1ng \u0111\u1ec3 \u0111\u1ea3m b\u1ea3o xe v\u1eadn h\u00e0nh \u1ed5n \u0111\u1ecbnh v\u00e0 an to\u00e0n.<\/span><\/p>\n

                6. M\u1ed1i Li\u00ean H\u1ec7 Gi\u1eefa \u0110\u01b0\u1eddng Cao V\u00e0 C\u00e1c Kh\u00e1i Ni\u1ec7m H\u00ecnh H\u1ecdc Kh\u00e1c<\/strong><\/h2>\n

                \u0110\u01b0\u1eddng cao trong tam gi\u00e1c vu\u00f4ng kh\u00f4ng t\u1ed3n t\u1ea1i \u0111\u1ed9c l\u1eadp m\u00e0 c\u00f3 m\u1ed1i li\u00ean h\u1ec7 ch\u1eb7t ch\u1ebd v\u1edbi c\u00e1c kh\u00e1i ni\u1ec7m h\u00ecnh h\u1ecdc kh\u00e1c.<\/span><\/p>\n

                6.1. \u0110\u1ecbnh L\u00fd Pitago<\/strong><\/h3>\n

                \u0110\u1ecbnh l\u00fd Pitago l\u00e0 m\u1ed9t trong nh\u1eefng \u0111\u1ecbnh l\u00fd c\u01a1 b\u1ea3n nh\u1ea5t c\u1ee7a h\u00ecnh h\u1ecdc, ph\u00e1t bi\u1ec3u r\u1eb1ng trong m\u1ed9t tam gi\u00e1c vu\u00f4ng, b\u00ecnh ph\u01b0\u01a1ng c\u1ea1nh huy\u1ec1n b\u1eb1ng t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng hai c\u1ea1nh g\u00f3c vu\u00f4ng. \u0110\u01b0\u1eddng cao trong tam gi\u00e1c vu\u00f4ng c\u00f3 m\u1ed1i li\u00ean h\u1ec7 m\u1eadt thi\u1ebft v\u1edbi \u0111\u1ecbnh l\u00fd Pitago, v\u00ec n\u00f3 gi\u00fap chia tam gi\u00e1c vu\u00f4ng th\u00e0nh hai tam gi\u00e1c vu\u00f4ng nh\u1ecf, m\u1ed7i tam gi\u00e1c \u0111\u1ec1u tu\u00e2n theo \u0111\u1ecbnh l\u00fd Pitago.<\/span><\/p>\n

                C\u00f4ng th\u1ee9c:<\/strong><\/p>\n

                BC\u00b2 = AB\u00b2 + AC\u00b2<\/p>\n

                6.2. C\u00e1c H\u00e0m L\u01b0\u1ee3ng Gi\u00e1c<\/strong><\/h3>\n

                C\u00e1c h\u00e0m l\u01b0\u1ee3ng gi\u00e1c nh\u01b0 sin, cos, tan c\u0169ng c\u00f3 m\u1ed1i li\u00ean h\u1ec7 v\u1edbi \u0111\u01b0\u1eddng cao trong tam gi\u00e1c vu\u00f4ng. V\u00ed d\u1ee5, sin c\u1ee7a m\u1ed9t g\u00f3c trong tam gi\u00e1c vu\u00f4ng b\u1eb1ng t\u1ec9 s\u1ed1 gi\u1eefa c\u1ea1nh \u0111\u1ed1i v\u00e0 c\u1ea1nh huy\u1ec1n. \u0110\u01b0\u1eddng cao c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u00ednh to\u00e1n c\u00e1c t\u1ec9 s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c n\u00e0y.<\/span><\/p>\n

                C\u00f4ng th\u1ee9c:<\/strong><\/p>\n

                  \n
                1. <\/span>sin(B) = AC \/ BC<\/li>\n
                2. <\/span>cos(B) = AB \/ BC<\/li>\n
                3. <\/span>tan(B) = AC \/ AB<\/li>\n<\/ol>\n

                  6.3. Di\u1ec7n T\u00edch Tam Gi\u00e1c Vu\u00f4ng<\/strong><\/h3>\n

                  Di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c vu\u00f4ng c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng nhi\u1ec1u c\u00e1ch, trong \u0111\u00f3 c\u00f3 c\u00e1ch s\u1eed d\u1ee5ng \u0111\u01b0\u1eddng cao. Di\u1ec7n t\u00edch tam gi\u00e1c vu\u00f4ng b\u1eb1ng n\u1eeda t\u00edch c\u1ee7a c\u1ea1nh huy\u1ec1n v\u00e0 \u0111\u01b0\u1eddng cao t\u01b0\u01a1ng \u1ee9ng.<\/span><\/p>\n

                  C\u00f4ng th\u1ee9c:<\/strong><\/p>\n

                  S = (1\/2) * BC * AH<\/p>\n

                  7. C\u00e1c Lo\u1ea1i Tam Gi\u00e1c \u0110\u1eb7c Bi\u1ec7t V\u00e0 \u0110\u01b0\u1eddng Cao<\/strong><\/h2>\n

                  \u0110\u01b0\u1eddng cao trong c\u00e1c lo\u1ea1i tam gi\u00e1c \u0111\u1eb7c bi\u1ec7t (tam gi\u00e1c \u0111\u1ec1u, tam gi\u00e1c c\u00e2n) c\u00f3 nh\u1eefng t\u00ednh ch\u1ea5t ri\u00eang bi\u1ec7t.<\/span><\/p>\n

                  7.1. \u0110\u01b0\u1eddng Cao Trong Tam Gi\u00e1c \u0110\u1ec1u<\/strong><\/h3>\n

                  Trong tam gi\u00e1c \u0111\u1ec1u, ba \u0111\u01b0\u1eddng cao c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng nhau v\u00e0 \u0111\u1ed3ng th\u1eddi l\u00e0 \u0111\u01b0\u1eddng trung tuy\u1ebfn, \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c v\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c. \u0110\u01b0\u1eddng cao trong tam gi\u00e1c \u0111\u1ec1u chia tam gi\u00e1c th\u00e0nh hai tam gi\u00e1c vu\u00f4ng b\u1eb1ng nhau.<\/span><\/p>\n

                  C\u00f4ng th\u1ee9c t\u00ednh \u0111\u01b0\u1eddng cao:<\/strong><\/p>\n

                  N\u1ebfu c\u1ea1nh c\u1ee7a tam gi\u00e1c \u0111\u1ec1u l\u00e0 a, th\u00ec \u0111\u01b0\u1eddng cao h l\u00e0:<\/span><\/p>\n

                  h = (a\u221a3) \/ 2<\/p>\n

                  Alt: \u0110\u01b0\u1eddng cao trong tam gi\u00e1c \u0111\u1ec1u, minh h\u1ecda t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng cao.<\/em><\/p>\n

                  7.2. \u0110\u01b0\u1eddng Cao Trong Tam Gi\u00e1c C\u00e2n<\/strong><\/h3>\n

                  Trong tam gi\u00e1c c\u00e2n, \u0111\u01b0\u1eddng cao xu\u1ea5t ph\u00e1t t\u1eeb \u0111\u1ec9nh c\u00e2n \u0111\u1ed3ng th\u1eddi l\u00e0 \u0111\u01b0\u1eddng trung tuy\u1ebfn, \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c v\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c. \u0110\u01b0\u1eddng cao n\u00e0y chia tam gi\u00e1c c\u00e2n th\u00e0nh hai tam gi\u00e1c vu\u00f4ng b\u1eb1ng nhau.<\/span><\/p>\n

                  T\u00ednh ch\u1ea5t:<\/strong><\/p>\n

                    \n
                  1. <\/span>\u0110\u01b0\u1eddng cao \u1ee9ng v\u1edbi c\u1ea1nh \u0111\u00e1y l\u00e0 \u0111\u01b0\u1eddng trung tuy\u1ebfn, \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c v\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a tam gi\u00e1c.<\/span><\/li>\n
                  2. <\/span>Hai \u0111\u01b0\u1eddng cao \u1ee9ng v\u1edbi hai c\u1ea1nh b\u00ean c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng nhau.<\/span><\/li>\n<\/ol>\n

                    7.3. \u0110\u01b0\u1eddng Cao Trong Tam Gi\u00e1c Vu\u00f4ng C\u00e2n<\/strong><\/h3>\n

                    Tam gi\u00e1c vu\u00f4ng c\u00e2n l\u00e0 tam gi\u00e1c v\u1eeba vu\u00f4ng v\u1eeba c\u00e2n. Trong tam gi\u00e1c vu\u00f4ng c\u00e2n, hai c\u1ea1nh g\u00f3c vu\u00f4ng b\u1eb1ng nhau v\u00e0 \u0111\u01b0\u1eddng cao \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n \u0111\u1ed3ng th\u1eddi l\u00e0 \u0111\u01b0\u1eddng trung tuy\u1ebfn.<\/span><\/p>\n

                    T\u00ednh ch\u1ea5t:<\/strong><\/p>\n

                      \n
                    1. <\/span>\u0110\u01b0\u1eddng cao \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n b\u1eb1ng n\u1eeda c\u1ea1nh huy\u1ec1n.<\/span><\/li>\n
                    2. <\/span>\u0110\u01b0\u1eddng cao \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n chia tam gi\u00e1c vu\u00f4ng c\u00e2n th\u00e0nh hai tam gi\u00e1c vu\u00f4ng c\u00e2n nh\u1ecf b\u1eb1ng nhau.<\/span><\/li>\n<\/ol>\n

                      8. C\u00e1c B\u00e0i To\u00e1n N\u00e2ng Cao V\u1ec1 \u0110\u01b0\u1eddng Cao Trong Tam Gi\u00e1c Vu\u00f4ng<\/strong><\/h2>\n

                      \u0110\u1ec3 th\u1eed th\u00e1ch kh\u1ea3 n\u0103ng gi\u1ea3i to\u00e1n, ch\u00fang ta h\u00e3y c\u00f9ng nhau gi\u1ea3i m\u1ed9t s\u1ed1 b\u00e0i to\u00e1n n\u00e2ng cao v\u1ec1 \u0111\u01b0\u1eddng cao trong tam gi\u00e1c vu\u00f4ng.<\/span><\/p>\n

                      8.1. B\u00e0i To\u00e1n Ch\u1ee9ng Minh Ba \u0110i\u1ec3m Th\u1eb3ng H\u00e0ng<\/strong><\/h3>\n

                      \u0110\u1ec1 b\u00e0i:<\/strong> Cho tam gi\u00e1c ABC vu\u00f4ng t\u1ea1i A, \u0111\u01b0\u1eddng cao AH. G\u1ecdi D v\u00e0 E l\u1ea7n l\u01b0\u1ee3t l\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a H tr\u00ean AB v\u00e0 AC. Ch\u1ee9ng minh r\u1eb1ng ba \u0111i\u1ec3m A, D, E th\u1eb3ng h\u00e0ng.<\/span><\/p>\n

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

                        \n
                      1. <\/span>V\u00ec D l\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a H tr\u00ean AB, n\u00ean HD vu\u00f4ng g\u00f3c v\u1edbi AB.<\/span><\/li>\n
                      2. <\/span>V\u00ec E l\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a H tr\u00ean AC, n\u00ean HE vu\u00f4ng g\u00f3c v\u1edbi AC.<\/span><\/li>\n
                      3. <\/span>X\u00e9t t\u1ee9 gi\u00e1c ADHE, ta c\u00f3:<\/span><\/li>\n
                      4. <\/span>G\u00f3c DAH + G\u00f3c ADH + G\u00f3c DHE + G\u00f3c HEA = 360\u00b0<\/span><\/li>\n
                      5. <\/span>90\u00b0 + 90\u00b0 + G\u00f3c DHE + 90\u00b0 = 360\u00b0<\/span><\/li>\n
                      6. <\/span>G\u00f3c DHE = 90\u00b0<\/span><\/li>\n
                      7. <\/span>V\u1eady t\u1ee9 gi\u00e1c ADHE l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt.<\/span><\/li>\n
                      8. <\/span>Suy ra, g\u00f3c ADE = g\u00f3c AHE (c\u00f9ng ph\u1ee5 v\u1edbi g\u00f3c HAD).<\/span><\/li>\n
                      9. <\/span>M\u00e0 g\u00f3c AHE = g\u00f3c ACB (c\u00f9ng ph\u1ee5 v\u1edbi g\u00f3c HAC).<\/span><\/li>\n
                      10. <\/span>Do \u0111\u00f3, g\u00f3c ADE = g\u00f3c ACB.<\/span><\/li>\n
                      11. <\/span>V\u1eady ba \u0111i\u1ec3m A, D, E th\u1eb3ng h\u00e0ng (v\u00ec g\u00f3c ADE v\u00e0 g\u00f3c ACB l\u00e0 hai g\u00f3c so le trong b\u1eb1ng nhau).<\/span><\/li>\n<\/ol>\n

                        8.2. B\u00e0i To\u00e1n T\u00ecm Gi\u00e1 Tr\u1ecb L\u1edbn Nh\u1ea5t, Nh\u1ecf Nh\u1ea5t<\/strong><\/h3>\n

                        \u0110\u1ec1 b\u00e0i:<\/strong> Cho tam gi\u00e1c ABC vu\u00f4ng t\u1ea1i A c\u00f3 BC c\u1ed1 \u0111\u1ecbnh. T\u00ecm v\u1ecb tr\u00ed \u0111i\u1ec3m A \u0111\u1ec3 \u0111\u01b0\u1eddng cao AH c\u00f3 \u0111\u1ed9 d\u00e0i l\u1edbn nh\u1ea5t.<\/span><\/p>\n

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

                          \n
                        1. <\/span>Ta c\u00f3 c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c ABC: <\/span>S = (1\/2) * BC * AH.<\/span><\/li>\n
                        2. <\/span>V\u00ec BC c\u1ed1 \u0111\u1ecbnh, n\u00ean \u0111\u1ec3 AH l\u1edbn nh\u1ea5t th\u00ec di\u1ec7n t\u00edch S ph\u1ea3i l\u1edbn nh\u1ea5t.<\/span><\/li>\n
                        3. <\/span>Di\u1ec7n t\u00edch S l\u1edbn nh\u1ea5t khi tam gi\u00e1c ABC vu\u00f4ng c\u00e2n t\u1ea1i A (khi \u0111\u00f3 AH l\u00e0 \u0111\u01b0\u1eddng trung tuy\u1ebfn v\u00e0 b\u1eb1ng n\u1eeda c\u1ea1nh huy\u1ec1n).<\/span><\/li>\n
                        4. <\/span>V\u1eady v\u1ecb tr\u00ed \u0111i\u1ec3m A \u0111\u1ec3 \u0111\u01b0\u1eddng cao AH c\u00f3 \u0111\u1ed9 d\u00e0i l\u1edbn nh\u1ea5t l\u00e0 khi tam gi\u00e1c ABC vu\u00f4ng c\u00e2n t\u1ea1i A.<\/span><\/li>\n<\/ol>\n

                          8.3. B\u00e0i To\u00e1n S\u1eed D\u1ee5ng T\u00ednh Ch\u1ea5t Ti\u1ebfp Tuy\u1ebfn<\/strong><\/h3>\n

                          \u0110\u1ec1 b\u00e0i:<\/strong> Cho tam gi\u00e1c ABC vu\u00f4ng t\u1ea1i A, \u0111\u01b0\u1eddng cao AH. V\u1ebd \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m A b\u00e1n k\u00ednh AH. Ch\u1ee9ng minh r\u1eb1ng \u0111\u01b0\u1eddng th\u1eb3ng BC l\u00e0 ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n n\u00e0y.<\/span><\/p>\n

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

                            \n
                          1. <\/span>X\u00e9t \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m A b\u00e1n k\u00ednh AH.<\/span><\/li>\n
                          2. <\/span>Ta c\u00f3 AH vu\u00f4ng g\u00f3c v\u1edbi BC t\u1ea1i H.<\/span><\/li>\n
                          3. <\/span>Theo \u0111\u1ecbnh ngh\u0129a, n\u1ebfu m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi b\u00e1n k\u00ednh c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1i m\u1ed9t \u0111i\u1ec3m tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n th\u00ec \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u00f3 l\u00e0 ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n.<\/span><\/li>\n
                          4. <\/span>V\u1eady \u0111\u01b0\u1eddng th\u1eb3ng BC l\u00e0 ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m A b\u00e1n k\u00ednh AH.<\/span><\/li>\n<\/ol>\n

                            9. C\u00e1c L\u1ed7i Th\u01b0\u1eddng G\u1eb7p Khi Gi\u1ea3i B\u00e0i T\u1eadp V\u1ec1 \u0110\u01b0\u1eddng Cao<\/strong><\/h2>\n

                            Trong qu\u00e1 tr\u00ecnh gi\u1ea3i b\u00e0i t\u1eadp v\u1ec1 \u0111\u01b0\u1eddng cao, h\u1ecdc sinh th\u01b0\u1eddng m\u1eafc ph\u1ea3i m\u1ed9t s\u1ed1 l\u1ed7i sai c\u01a1 b\u1ea3n.<\/span><\/p>\n

                            9.1. Nh\u1ea7m L\u1eabn Gi\u1eefa C\u00e1c H\u1ec7 Th\u1ee9c L\u01b0\u1ee3ng<\/strong><\/h3>\n

                            M\u1ed9t trong nh\u1eefng l\u1ed7i ph\u1ed5 bi\u1ebfn nh\u1ea5t l\u00e0 nh\u1ea7m l\u1eabn gi\u1eefa c\u00e1c h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng. \u0110\u1ec3 tr\u00e1nh l\u1ed7i n\u00e0y, c\u1ea7n n\u1eafm v\u1eefng v\u00e0 ph\u00e2n bi\u1ec7t r\u00f5 c\u00e1c h\u1ec7 th\u1ee9c, c\u0169ng nh\u01b0 \u0111i\u1ec1u ki\u1ec7n \u00e1p d\u1ee5ng c\u1ee7a ch\u00fang.<\/span><\/p>\n

                            V\u00ed d\u1ee5:<\/strong><\/p>\n

                              \n
                            1. <\/span>Nh\u1ea7m l\u1eabn gi\u1eefa <\/span>AH\u00b2 = BH * CH v\u00e0 <\/span>1\/AH\u00b2 = 1\/AB\u00b2 + 1\/AC\u00b2.<\/span><\/li>\n
                            2. <\/span>Kh\u00f4ng nh\u1edb r\u00f5 h\u1ec7 th\u1ee9c n\u00e0o \u00e1p d\u1ee5ng cho c\u1ea1nh g\u00f3c vu\u00f4ng, h\u1ec7 th\u1ee9c n\u00e0o \u00e1p d\u1ee5ng cho c\u1ea1nh huy\u1ec1n.<\/span><\/li>\n<\/ol>\n

                              9.2. Sai L\u1ea7m Trong T\u00ednh To\u00e1n<\/strong><\/h3>\n

                              C\u00e1c sai s\u00f3t trong t\u00ednh to\u00e1n c\u0169ng th\u01b0\u1eddng d\u1eabn \u0111\u1ebfn k\u1ebft qu\u1ea3 sai. \u0110\u1ec3 tr\u00e1nh l\u1ed7i n\u00e0y, c\u1ea7n c\u1ea9n th\u1eadn trong t\u1eebng b\u01b0\u1edbc t\u00ednh to\u00e1n, ki\u1ec3m tra l\u1ea1i k\u1ebft qu\u1ea3 v\u00e0 s\u1eed d\u1ee5ng m\u00e1y t\u00ednh h\u1ed7 tr\u1ee3 khi c\u1ea7n thi\u1ebft.<\/span><\/p>\n

                              V\u00ed d\u1ee5:<\/strong><\/p>\n

                                \n
                              1. <\/span>T\u00ednh sai c\u0103n b\u1eadc hai, b\u00ecnh ph\u01b0\u01a1ng.<\/span><\/li>\n
                              2. <\/span>T\u00ednh sai c\u00e1c ph\u00e9p c\u1ed9ng, tr\u1eeb, nh\u00e2n, chia.<\/span><\/li>\n<\/ol>\n

                                9.3. Kh\u00f4ng V\u1ebd H\u00ecnh Ho\u1eb7c V\u1ebd H\u00ecnh Sai<\/strong><\/h3>\n

                                Vi\u1ec7c kh\u00f4ng v\u1ebd h\u00ecnh ho\u1eb7c v\u1ebd h\u00ecnh sai c\u0169ng l\u00e0 m\u1ed9t nguy\u00ean nh\u00e2n d\u1eabn \u0111\u1ebfn vi\u1ec7c gi\u1ea3i b\u00e0i t\u1eadp sai. H\u00ecnh v\u1ebd gi\u00fap h\u00ecnh dung b\u00e0i to\u00e1n v\u00e0 x\u00e1c \u0111\u1ecbnh c\u00e1c y\u1ebfu t\u1ed1 li\u00ean quan.<\/span><\/p>\n

                                L\u1eddi khuy\u00ean:<\/strong><\/p>\n

                                  \n
                                1. <\/span>Lu\u00f4n v\u1ebd h\u00ecnh tr\u01b0\u1edbc khi b\u1eaft \u0111\u1ea7u gi\u1ea3i b\u00e0i t\u1eadp.<\/span><\/li>\n
                                2. <\/span>V\u1ebd h\u00ecnh ch\u00ednh x\u00e1c, t\u1ec9 l\u1ec7 t\u01b0\u01a1ng \u0111\u1ed1i.<\/span><\/li>\n
                                3. <\/span>Ghi ch\u00fa \u0111\u1ea7y \u0111\u1ee7 c\u00e1c th\u00f4ng tin \u0111\u00e3 bi\u1ebft tr\u00ean h\u00ecnh v\u1ebd.<\/span><\/li>\n<\/ol>\n

                                  10. C\u00e2u H\u1ecfi Th\u01b0\u1eddng G\u1eb7p (FAQ) V\u1ec1 \u0110\u01b0\u1eddng Cao Trong Tam Gi\u00e1c Vu\u00f4ng<\/strong><\/h2>\n

                                  D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p v\u1ec1 \u0111\u01b0\u1eddng cao trong tam gi\u00e1c vu\u00f4ng, c\u00f9ng v\u1edbi c\u00e2u tr\u1ea3 l\u1eddi chi ti\u1ebft.<\/span><\/p>\n

                                  10.1. \u0110\u01b0\u1eddng cao trong tam gi\u00e1c vu\u00f4ng l\u00e0 g\u00ec?<\/strong><\/h3>\n

                                  \u0110\u01b0\u1eddng cao trong tam gi\u00e1c vu\u00f4ng l\u00e0 \u0111o\u1ea1n th\u1eb3ng k\u1ebb t\u1eeb \u0111\u1ec9nh g\u00f3c vu\u00f4ng xu\u1ed1ng c\u1ea1nh huy\u1ec1n v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi c\u1ea1nh huy\u1ec1n \u0111\u00f3.<\/span><\/p>\n

                                  10.2. C\u00f3 bao nhi\u00eau \u0111\u01b0\u1eddng cao trong m\u1ed9t tam gi\u00e1c vu\u00f4ng?<\/strong><\/h3>\n

                                  M\u1ed9t tam gi\u00e1c vu\u00f4ng c\u00f3 ba \u0111\u01b0\u1eddng cao, nh\u01b0ng \u0111\u01b0\u1eddng cao \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n c\u00f3 vai tr\u00f2 \u0111\u1eb7c bi\u1ec7t quan tr\u1ecdng.<\/span><\/p>\n

                                  10.3. \u0110\u01b0\u1eddng cao trong tam gi\u00e1c vu\u00f4ng c\u00f3 nh\u1eefng t\u00ednh ch\u1ea5t g\u00ec?<\/strong><\/h3>\n

                                  \u0110\u01b0\u1eddng cao chia tam gi\u00e1c vu\u00f4ng th\u00e0nh hai tam gi\u00e1c vu\u00f4ng nh\u1ecf \u0111\u1ed3ng d\u1ea1ng v\u1edbi tam gi\u00e1c vu\u00f4ng ban \u0111\u1ea7u v\u00e0 \u0111\u1ed3ng d\u1ea1ng v\u1edbi nhau.<\/span><\/p>\n

                                  10.4. L\u00e0m th\u1ebf n\u00e0o \u0111\u1ec3 t\u00ednh \u0111\u01b0\u1eddng cao trong tam gi\u00e1c vu\u00f4ng khi bi\u1ebft \u0111\u1ed9 d\u00e0i hai c\u1ea1nh g\u00f3c vu\u00f4ng?<\/strong><\/h3>\n

                                  S\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c: <\/span>AH = (AB * AC) \/ BC, trong \u0111\u00f3 BC l\u00e0 c\u1ea1nh huy\u1ec1n.<\/span><\/p>\n

                                  10.5. \u0110\u1ecbnh l\u00fd Pitago c\u00f3 li\u00ean quan g\u00ec \u0111\u1ebfn \u0111\u01b0\u1eddng cao trong tam gi\u00e1c vu\u00f4ng?<\/strong><\/h3>\n

                                  \u0110\u1ecbnh l\u00fd Pitago gi\u00fap t\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh huy\u1ec1n, t\u1eeb \u0111\u00f3 t\u00ednh \u0111\u01b0\u1ee3c \u0111\u01b0\u1eddng cao.<\/span><\/p>\n

                                  10.6. C\u00e1c h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c vu\u00f4ng l\u00e0 g\u00ec?<\/strong><\/h3>\n

                                  C\u00e1c h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng bao g\u1ed3m: <\/span>AH\u00b2 = BH * CH, <\/span>AB * AC = AH * BC, <\/span>1\/AH\u00b2 = 1\/AB\u00b2 + 1\/AC\u00b2.<\/span><\/p>\n

                                  10.7. \u0110\u01b0\u1eddng cao trong tam gi\u00e1c vu\u00f4ng c\u00f3 \u1ee9ng d\u1ee5ng g\u00ec trong th\u1ef1c t\u1ebf?<\/strong><\/h3>\n

                                  \u0110\u01b0\u1eddng cao \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong x\u00e2y d\u1ef1ng, \u0111o \u0111\u1ea1c, thi\u1ebft k\u1ebf c\u01a1 kh\u00ed v\u00e0 nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c.<\/span><\/p>\n

                                  10.8. Trong tam gi\u00e1c vu\u00f4ng c\u00e2n, \u0111\u01b0\u1eddng cao c\u00f3 t\u00ednh ch\u1ea5t g\u00ec \u0111\u1eb7c bi\u1ec7t?<\/strong><\/h3>\n

                                  \u0110\u01b0\u1eddng cao \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n b\u1eb1ng n\u1eeda c\u1ea1nh huy\u1ec1n v\u00e0 chia tam gi\u00e1c vu\u00f4ng c\u00e2n th\u00e0nh hai tam gi\u00e1c vu\u00f4ng c\u00e2n nh\u1ecf b\u1eb1ng nhau.<\/span><\/p>\n

                                  10.9. T\u1ea1i sao c\u1ea7n n\u1eafm v\u1eefng ki\u1ebfn th\u1ee9c v\u1ec1 \u0111\u01b0\u1eddng cao trong tam gi\u00e1c vu\u00f4ng?<\/strong><\/h3>\n

                                  Ki\u1ebfn th\u1ee9c v\u1ec1 \u0111\u01b0\u1eddng cao gi\u00fap gi\u1ea3i quy\u1ebft nhi\u1ec1u b\u00e0i to\u00e1n h\u00ecnh h\u1ecdc v\u00e0 c\u00f3 \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf trong nhi\u1ec1u l\u0129nh v\u1ef1c.<\/span><\/p>\n

                                  10.10. L\u00e0m th\u1ebf n\u00e0o \u0111\u1ec3 tr\u00e1nh nh\u1eefng l\u1ed7i sai khi gi\u1ea3i b\u00e0i t\u1eadp v\u1ec1 \u0111\u01b0\u1eddng cao?<\/strong><\/h3>\n

                                  N\u1eafm v\u1eefng c\u00e1c h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng, c\u1ea9n th\u1eadn trong t\u00ednh to\u00e1n v\u00e0 v\u1ebd h\u00ecnh ch\u00ednh x\u00e1c.<\/span><\/p>\n

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                                  T\u00ednh Ch\u1ea5t \u0111\u01b0\u1eddng Cao Trong Tam Gi\u00e1c Vu\u00f4ng \u0111\u00f3ng vai tr\u00f2 quan tr\u1ecdng trong h\u00ecnh h\u1ecdc v\u00e0 c\u00f3 nhi\u1ec1u \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf. Xe T\u1ea3i M\u1ef9 \u0110\u00ecnh (XETAIMYDINH.EDU.VN) s\u1ebd cung c\u1ea5p cho b\u1ea1n c\u00e1i nh\u00ecn s\u00e2u s\u1eafc v\u1ec1 t\u00ednh ch\u1ea5t n\u00e0y, c\u00f9ng v\u1edbi c\u00e1c v\u00ed d\u1ee5 minh h\u1ecda v\u00e0 c\u00f4ng th\u1ee9c t\u00ednh to\u00e1n chi ti\u1ebft \u0111\u1ec3 […]\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-2085","post","type-post","status-publish","format-standard","hentry","category-khong-phan-loai"],"_links":{"self":[{"href":"https:\/\/daotaotructuyentiengtrung.edu.vn\/index.php\/wp-json\/wp\/v2\/posts\/2085","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/daotaotructuyentiengtrung.edu.vn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/daotaotructuyentiengtrung.edu.vn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/daotaotructuyentiengtrung.edu.vn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/daotaotructuyentiengtrung.edu.vn\/index.php\/wp-json\/wp\/v2\/comments?post=2085"}],"version-history":[{"count":0,"href":"https:\/\/daotaotructuyentiengtrung.edu.vn\/index.php\/wp-json\/wp\/v2\/posts\/2085\/revisions"}],"wp:attachment":[{"href":"https:\/\/daotaotructuyentiengtrung.edu.vn\/index.php\/wp-json\/wp\/v2\/media?parent=2085"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/daotaotructuyentiengtrung.edu.vn\/index.php\/wp-json\/wp\/v2\/categories?post=2085"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/daotaotructuyentiengtrung.edu.vn\/index.php\/wp-json\/wp\/v2\/tags?post=2085"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}