Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn<\/p>\n\n\n\n
Toa\u0301n 7 la\u0300 m\u00f4\u0323t trong nh\u01b0\u0303ng n\u00ea\u0300n mo\u0301ng c\u01a1 ba\u0309n \u0111\u00ea\u0309 pha\u0301t tri\u00ea\u0309n kha\u0309 n\u0103ng t\u01b0 duy va\u0300 la\u0300m ba\u0300i t\u00e2\u0323p xuy\u00ean su\u00f4\u0301t c\u00e2\u0301p 2 va\u0300 c\u00e2\u0301p 3. Chi\u0301nh vi\u0300 v\u00e2\u0323y, no\u0301 bao g\u00f4\u0300m nh\u01b0\u0303ng ki\u00ea\u0301n th\u01b0\u0301c \u0111\u01b0\u01a1\u0323c cho la\u0300 c\u0103n ba\u0309n ma\u0300 t\u00e2\u0301t ca\u0309 mo\u0323i ng\u01b0\u01a1\u0300i \u0111\u00ea\u0300u c\u00e2\u0300n pha\u0309i n\u0103\u0301m \u0111\u01b0\u01a1\u0323c. \u01a0\u0309 chuy\u00ean mu\u0323c l\u00e2\u0300n na\u0300y, chu\u0301ng ta se\u0303 cu\u0300ng \u0111i ti\u0300m hi\u00ea\u0309u v\u00ea\u0300 t\u00ednh ch\u1ea5t ba \u0111\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a tam gi\u00e1c. Ha\u0303y cu\u0300ng toppy \u0111i tra\u0309 l\u01a1\u0300i nh\u01b0\u0303ng c\u00e2u ho\u0309i li\u00ean quan t\u01a1\u0301i chu\u0309 \u0111\u00ea\u0300 na\u0300y nhe\u0301.<\/p>\n\n\n\n
Kha\u0301i ni\u00ea\u0323m \u0111\u01b0\u01a1\u0300ng trung tuy\u00ea\u0301n cu\u0309a tam gia\u0301c<\/p>\n\n\n\n
\u0110\u01b0\u01a1\u0300ng trung tuy\u00ea\u0301n cu\u0309a m\u00f4\u0323t tam \u0111\u01b0\u01a1\u0323c \u0111i\u0323nh nghi\u0303a la\u0300 \u0111oa\u0323n th\u0103\u0309ng n\u00f4\u0301i t\u01b0\u0300 m\u00f4\u0323t \u0111i\u0309nh cu\u0309a tam gia\u0301c \u0111\u00ea\u0301n trung \u0111i\u00ea\u0309m cu\u0309a ca\u0323nh \u0111\u00f4\u0301i di\u00ea\u0323n. Chi\u0301nh vi\u0300 v\u00e2\u0323y, v\u01a1\u0301i m\u00f4\u0303i tam gia\u0301c b\u00e2\u0301t ky\u0300, chu\u0301ng ta se\u0303 co\u0301 \u0111\u01b0\u01a1\u0323c 3 \u0111\u01b0\u01a1\u0300ng trung tuy\u00ea\u0301n t\u01a1\u0301i t\u01b0\u0300 3 \u0111i\u0309nh.<\/p>\n\n\n\n
Vi\u0301 du: Gia\u0309 s\u01b0\u0309 tam gia\u0301c ABC co\u0301 \u0111i\u00ea\u0309m E la\u0300 trung \u0111i\u00ea\u0309m cu\u0309a ca\u0323nh BC. N\u00f4\u0301i E vs A ta \u0111\u01b0\u01a1\u0323c \u0111\u01b0\u01a1\u0300ng trung tuy\u00ea\u0301n AE \u01b0\u0301ng v\u01a1\u0301i ca\u0323nh BC ho\u0103\u0323c \u01b0\u0301ng v\u01a1\u0301i \u0111i\u0309nh A. N\u00ea\u0301u trung \u0111i\u00ea\u0309m cu\u0309a 2 ca\u0323nh AC va\u0300 AB co\u0300n la\u0323i l\u00e2\u0300n l\u01b0\u01a1\u0323t la\u0300 F vs I thi\u0300 ta co\u0301 \u0111\u01b0\u01a1\u0323c 2 \u0111\u01b0\u01a1\u0300ng trung tuy\u00ea\u0301n co\u0300n la\u0323i la\u0300 BF va\u0300 CI.<\/p>\n\n\n\n
T\u00ednh ch\u1ea5t ba \u0111\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a tam gi\u00e1c<\/p>\n\n\n\n
M\u00f4\u0303i loa\u0323i \u0111\u01b0\u01a1\u0300ng trong m\u00f4\u0323t tam gia\u0301c \u0111\u00ea\u0300u th\u00ea\u0309 hi\u00ea\u0323n s\u01b0\u0323 \u0111\u0103\u0323c tr\u01b0ng ri\u00eang bi\u00ea\u0323t cu\u0309a mi\u0300nh th\u00f4ng qua nh\u01b0\u0303ng ti\u0301nh ch\u00e2\u0301t. \u0110\u01b0\u01a1ng nhi\u00ean, \u0111\u01b0\u01a1\u0300ng trung tuy\u00ea\u0301n cu\u0303ng kh\u00f4ng pha\u0309i la\u0300 tr\u01b0\u01a1\u0300ng h\u01a1\u0323p ngoa\u0323i l\u00ea\u0323.<\/p>\n\n\n\n
Chu\u0301ng ta co\u0301 \u0111i\u0323nh ly\u0301 v\u00ea\u0300 t\u00ednh ch\u1ea5t ba \u0111\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a tam gi\u00e1c nh\u01b0 sau: 3 \u0111\u01b0\u01a1\u0300ng trung tuy\u00ea\u0301n cu\u0309a tam gia\u0301c cu\u0300ng \u0111i qua 1 \u0111i\u00ea\u0309m. \u0110i\u00ea\u0309m na\u0300y ca\u0301ch ca\u0301c \u0111i\u0309nh cu\u0309a tam gia\u0301c m\u00f4\u0323t \u0111oa\u0323n b\u0103\u0300ng 2\/3 \u0111\u00f4\u0323 da\u0300i cu\u0309a chi\u0301nh ca\u0301c \u0111\u01b0\u01a1\u0300ng trung tuy\u00ea\u0301n \u0111i qua \u0111i\u0309nh \u0111o\u0301. Giao \u0111i\u00ea\u0309m na\u0300y \u0111\u01b0\u01a1\u0323c go\u0323i la\u0300 tro\u0323ng t\u00e2m.<\/p>\n\n\n\n
Vi\u0301 du\u0323: Tam gia\u0301c ABC co\u0301 trung \u0111i\u00ea\u0309m cu\u0309a 3 ca\u0323nh: AB, AC, BC l\u00e2\u0300n l\u01b0\u01a1\u0323t la\u0300 E, F, I. 3 \u0111\u01b0\u01a1\u0300ng trung tuy\u00ea\u0301n CE, BF va\u0300 AI c\u0103\u0301t nhau ta\u0323i 1 \u0111i\u00ea\u0309m \u0111\u0103\u0323t t\u00ean la\u0300 G. G chi\u0301nh la\u0300 tro\u0323ng t\u00e2m cu\u0309a tam gia\u0301c ABC. Trong \u0111o\u0301: EG\/EC = FG\/FB = IG\/IB = 2\/3.<\/p>\n\n\n\n
Ba\u0300i t\u00e2\u0323p tr\u0103\u0301c nghi\u00ea\u0323m v\u00ea\u0300 t\u00ednh ch\u1ea5t ba \u0111\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a tam gi\u00e1c<\/p>\n\n\n\n
C\u00e2u 1: Cho\u0323n \u0111a\u0301p a\u0301n \u0111u\u0301ng v\u1ec1 t\u00ednh ch\u1ea5t ba \u0111\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a tam gi\u00e1c<\/p>\n\n\n\n
M\u00f4\u0323t tam gia\u0301c co\u0301 3 \u0111\u01b0\u01a1\u0300ng trung tuy\u00ea\u0301n.<\/p>\n\n\n\n
M\u00f4\u0323t tam gia\u0301c co\u0301 2 \u0111\u01b0\u01a1\u0300ng trung tuy\u00ea\u0301n.<\/p>\n\n\n\n
M\u00f4\u0323t tam gia\u0301c co\u0301 2 tro\u0323ng t\u00e2m.<\/p>\n\n\n\n
Ca\u0301c \u0111\u01b0\u01a1\u0300ng trung tuy\u00ea\u0301n kh\u00f4ng c\u0103\u0301t nhau.<\/p>\n\n\n\n
M\u00f4\u0323t tam gia\u0301c co\u0301 3 \u0111\u01b0\u01a1\u0300ng trung tuy\u00ea\u0301n.<\/p>\n\n\n\n
Cho\u0323n A.<\/p>\n\n\n\n
C\u00e2u 2: D\u1ef1a v\u00e0o t\u00ednh ch\u1ea5t ba \u0111\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a tam gi\u00e1c, giao \u0111i\u00ea\u0309m cu\u0309a 3 \u0111\u01b0\u01a1\u0300ng trung tuy\u00ea\u0301n go\u0323i la\u0300 gi\u0300?<\/p>\n\n\n\n
Tr\u01b0\u0323c t\u00e2m<\/p>\n\n\n\n
Tro\u0323ng t\u00e2m<\/p>\n\n\n\n
T\u00e2m \u0111\u01b0\u01a1\u0300ng tro\u0300n n\u00f4\u0323i ti\u00ea\u0301p<\/p>\n\n\n\n
1 \u0111i\u00ea\u0309m b\u00e2\u0301t ky\u0300<\/p>\n\n\n\n
Giao \u0111i\u00ea\u0309m cu\u0309a 3 \u0111\u01b0\u01a1\u0300ng trung tuy\u00ea\u0301n trong m\u00f4\u0323t tam gia\u0301c la\u0300 tro\u0323ng t\u00e2m.<\/p>\n\n\n\n
Giao \u0111i\u00ea\u0309m cu\u0309a 3 \u0111\u01b0\u01a1\u0300ng trung tuy\u00ea\u0301n la\u0300 gi\u0300?<\/p>\n\n\n\n
Cho\u0323n B.<\/p>\n\n\n\n
C\u00e2u 3: Tro\u0323ng t\u00e2m ca\u0301ch m\u00f4\u0303i \u0111i\u0309nh m\u00f4\u0323t khoa\u0309ng b\u0103\u0300ng?<\/p>\n\n\n\n
1\/3 \u0111\u00f4\u0323 da\u0300i \u0111\u01b0\u01a1\u0300ng trung tuy\u00ea\u0301n \u01b0\u0301ng v\u01a1\u0301i \u0111i\u0309nh \u0111o\u0301.<\/p>\n\n\n\n
1\/4 \u0111\u00f4\u0323 da\u0300i \u0111\u01b0\u01a1\u0300ng trung tuy\u00ea\u0301n \u01b0\u0301ng v\u01a1\u0301i \u0111i\u0309nh \u0111o\u0301.<\/p>\n\n\n\n
2\/3 \u0111\u00f4\u0323 da\u0300i \u0111\u01b0\u01a1\u0300ng trung tuy\u00ea\u0301n \u01b0\u0301ng v\u01a1\u0301i \u0111i\u0309nh \u0111o\u0301.<\/p>\n\n\n\n
2\/5 \u0111\u00f4\u0323 da\u0300i \u0111\u01b0\u01a1\u0300ng trung tuy\u00ea\u0301n \u01b0\u0301ng v\u01a1\u0301i \u0111i\u0309nh \u0111o\u0301.<\/p>\n\n\n\n
Tro\u0323ng t\u00e2m ca\u0301ch m\u00f4\u0303i \u0111i\u0309nh m\u00f4\u0323t khoa\u0309ng b\u0103\u0300ng 2\/3 \u0111\u00f4\u0323 da\u0300i \u0111\u01b0\u01a1\u0300ng trung tuy\u00ea\u0301n \u01b0\u0301ng v\u01a1\u0301i \u0111i\u0309nh \u0111o\u0301.<\/p>\n\n\n\n
Cho\u0323n C.<\/p>\n\n\n\n
C\u00e2u 4: Tam gia\u0301c ABC co\u0301 G la\u0300 tro\u0323ng t\u00e2m cu\u0309a tam gia\u0301c. Go\u0323i E la\u0300 trung \u0111i\u00ea\u0309m cu\u0309a BC. IG b\u0103\u0300ng?<\/p>\n\n\n\n
2\/3 AE<\/p>\n\n\n\n
1\/3 AE<\/p>\n\n\n\n
1\/3 AB<\/p>\n\n\n\n
1\/4 AC<\/p>\n\n\n\n
G la\u0300 tro\u0323ng t\u00e2m suy ra EG = 2\/3 AE. Do \u0111o\u0301 IG= AE \u2013 2\/3AE = 1\/3AE.<\/p>\n\n\n\n
C\u00e2u 5: Cho G la\u0300 tro\u0323ng t\u00e2m tam gia\u0301c MNE. O la\u0300 trung \u0111i\u00ea\u0309m cu\u0309a NE. Kh\u0103\u0309ng \u0111i\u0323nh na\u0300o sau \u0111\u00e2y \u0111u\u0301ng?<\/p>\n\n\n\n
MG\/MO = 2\/3<\/p>\n\n\n\n
MG\/MO = 1\/3<\/p>\n\n\n\n
MG\/GO = 1\/3<\/p>\n\n\n\n
MG\/MO= 1<\/p>\n\n\n\n
G la\u0300 tro\u0323ng t\u00e2m cu\u0309a tam gia\u0301c va\u0300 O la\u0300 trung \u0111i\u00ea\u0309m cu\u0309a NE. Theo ti\u0301nh ch\u00e2\u0301t tro\u0323ng t\u00e2m ta co\u0301: MG\/MO = 2\/3.<\/p>\n\n\n\n
Cho\u0323n A.<\/p>\n\n\n\n
C\u00e2u 6: Cho tam gia\u0301c ABC co\u0301 2 \u0111\u01b0\u01a1\u0300ng trung tuy\u00ea\u0301n AE va\u0300 BF c\u0103\u0301t nhau ta\u0323i I. Cho 2 \u0111i\u00ea\u0309m M va\u0300 N l\u00e2\u0300n l\u01b0\u01a1\u0323t la\u0300 trung \u0111i\u00ea\u0309m IA va\u0300 IB. Kh\u0103\u0309ng \u0111i\u0323nh na\u0300o sau \u0111\u00e2y \u0111u\u0301ng:<\/p>\n\n\n\n
IN = IM<\/p>\n\n\n\n
IE = IB<\/p>\n\n\n\n
AI = BI<\/p>\n\n\n\n
IN = IF<\/p>\n\n\n\n
I la\u0300 giao \u0111i\u00ea\u0309m cu\u0309a 2 \u0111\u01b0\u01a1\u0300ng trung tuy\u00ea\u0301n n\u00ean I la\u0300 tro\u0323ng t\u00e2m. Suy ra IB = 2\/3BF => IF = 1\/2IB. La\u0323i co\u0301 N la\u0300 trung \u0111i\u00ea\u0309m cu\u0309a IB suy ra IN = 1\/2IB. V\u00e2\u0323y IN = IF.<\/p>\n\n\n\n
C\u00e2u 7: Cho tam gia\u0301c vu\u00f4ng ABC vu\u00f4ng ta\u0323i A. Co\u0301 F la\u0300 trung \u0111i\u00ea\u0309m cu\u0309a ca\u0323nh BC. \u0110\u00f4\u0323 da\u0300i AF b\u0103\u0300ng?<\/p>\n\n\n\n
AF = 1\/2BC<\/p>\n\n\n\n
AF = 1\/2AB<\/p>\n\n\n\n
AF = 1\/2AC<\/p>\n\n\n\n
AF = 1\/3BC<\/p>\n\n\n\n
Trong tam gia\u0301c vu\u00f4ng, \u0111\u01b0\u01a1\u0300ng trung tuy\u00ea\u0301n \u01b0\u0301ng v\u01a1\u0301i ca\u0323nh huy\u00ea\u0300n co\u0301 \u0111\u00f4\u0323 da\u0300i b\u0103\u0300ng n\u01b0\u0309a ca\u0323nh huy\u00ea\u0300n. Tam gia\u0301c ABC vu\u00f4ng ta\u0323i A suy ra BC la\u0300 ca\u0323nh huy\u00ea\u0300n. F la\u0300 trung \u0111i\u00ea\u0309m cu\u0309a BC => AF = 1\/2BC.<\/p>\n\n\n\n
T\u00ednh ch\u1ea5t 3 \u0111\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a tam gi\u00e1c<\/p>\n\n\n\n
Cho\u0323n B.<\/p>\n\n\n\n
C\u00e2u 9: Tam gia\u0301c ABC la\u0300 tam gia\u0301c \u0111\u00ea\u0300u. G la\u0300 tro\u0323ng t\u00e2m cu\u0309a tam gia\u0301c thi\u0300 G \u0111\u00f4\u0300ng th\u01a1\u0300i la\u0300 gi\u0300?<\/p>\n\n\n\n
Tr\u01b0\u0323c t\u00e2m<\/p>\n\n\n\n
T\u00e2m \u0111\u01b0\u01a1\u0300ng tro\u0300n n\u00f4\u0323i ti\u00ea\u0301p<\/p>\n\n\n\n
T\u00e2m \u0111\u01b0\u01a1\u0300ng tro\u0300n ngoa\u0323i ti\u00ea\u0301p<\/p>\n\n\n\n
Ca\u0309 3 \u0111a\u0301p a\u0301n tr\u00ean<\/p>\n\n\n\n
Trong tam gia\u0301c \u0111\u00ea\u0300u, tro\u0323ng t\u00e2m la\u0300 tr\u01b0\u0323c t\u00e2m, t\u00e2m \u0111\u01b0\u01a1\u0300ng tro\u0300n n\u00f4\u0323i ti\u00ea\u0301p, t\u00e2m \u0111\u01b0\u01a1\u0300ng tro\u0300n ngoa\u0323i ti\u00ea\u0301p.<\/p>\n\n\n\n
Cho\u0323n D.<\/p>\n\n\n\n
Tr\u00ean \u0111\u00e2y la\u0300 toa\u0300n b\u00f4\u0323 nh\u01b0\u0303ng ki\u00ea\u0301n th\u01b0\u0301c v\u00ea\u0300 t\u00ednh ch\u1ea5t ba \u0111\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a tam gi\u00e1c. D\u01b0\u0323a va\u0300o nh\u01b0\u0303ng vi\u0301 du\u0323 k\u00ea\u0309 tr\u00ean, Vietlearn hy vo\u0323ng co\u0301 th\u00ea\u0309 \u0111em la\u0323i cho ba\u0323n nh\u01b0\u0303ng thay \u0111\u00f4\u0309i v\u00ea\u0300 k\u00ea\u0301t qua\u0309 ho\u0323c t\u00e2\u0323p. \u0110\u00ea\u0309 la\u0300m chu\u0309 b\u00f4\u0323 m\u00f4n toa\u0301n hi\u0300nh ho\u0323c, ha\u0303y cu\u0300ng \u0111\u00f4\u0300ng ha\u0300nh v\u01a1\u0301i Vietlearn \u01a1\u0309 nh\u01b0\u0303ng ba\u0300i vi\u00ea\u0301t ti\u00ea\u0301p theo.<\/p>\n\n\n\n
<\/p><\/blockquote>\n\n\n\n
T\u00ednh ch\u1ea5t tia ph\u00e2n gi\u00e1c c\u1ee7a m\u1ed9t g\u00f3c \u2013 Gia\u0309i ma\u0303 toa\u0301n hi\u0300nh ho\u0323c 7<\/p>\n\n\n\n
T\u00ednh ch\u1ea5t ba \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn Toa\u0301n 7 la\u0300 m\u00f4\u0323t trong nh\u01b0\u0303ng n\u00ea\u0300n mo\u0301ng c\u01a1 ba\u0309n \u0111\u00ea\u0309 pha\u0301t tri\u00ea\u0309n kha\u0309 n\u0103ng t\u01b0 duy va\u0300 la\u0300m ba\u0300i t\u00e2\u0323p xuy\u00ean su\u00f4\u0301t c\u00e2\u0301p 2 va\u0300 c\u00e2\u0301p 3. Chi\u0301nh vi\u0300 v\u00e2\u0323y, no\u0301 bao g\u00f4\u0300m nh\u01b0\u0303ng ki\u00ea\u0301n th\u01b0\u0301c \u0111\u01b0\u01a1\u0323c cho la\u0300 c\u0103n ba\u0309n ma\u0300 t\u00e2\u0301t ca\u0309 mo\u0323i ng\u01b0\u01a1\u0300i \u0111\u00ea\u0300u c\u00e2\u0300n […]<\/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-943","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\/943","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=943"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/943\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=943"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=943"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=943"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}