<\/span><\/h3>\n\u0110\u1ed3ng quy l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m trong h\u00ecnh h\u1ecdc, n\u00f3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 ch\u1ec9 s\u1ef1 t\u01b0\u01a1ng \u0111\u1ed3ng ho\u1eb7c tr\u00f9ng h\u1ee3p gi\u1eefa c\u00e1c h\u00ecnh h\u1ecdc. Khi hai hay nhi\u1ec1u \u0111\u1ed1i t\u01b0\u1ee3ng c\u00f3 c\u00f9ng m\u1ed9t thu\u1ed9c t\u00ednh ho\u1eb7c \u0111\u1eb7c \u0111i\u1ec3m, ta n\u00f3i ch\u00fang \u0111\u1ed3ng quy v\u1edbi nhau. Trong to\u00e1n h\u1ecdc, \u0111\u1ed3ng quy th\u01b0\u1eddng \u00e1p d\u1ee5ng cho c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng, tam gi\u00e1c, t\u1ee9 di\u1ec7n v\u00e0 c\u00e1c h\u00ecnh kh\u00e1c.<\/p>\n
Khi hai \u0111\u01b0\u1eddng th\u1eb3ng song song c\u1eaft qua m\u1ed9t \u0111\u01b0\u1eddng th\u1ee9 ba, ch\u00fang \u0111\u01b0\u1ee3c coi l\u00e0 \u0111\u1ed3ng quy. \u0110\u1ed1i v\u1edbi tam gi\u00e1c, khi c\u00f3 ba \u0111i\u1ec3m tr\u00ean c\u00e1c c\u1ea1nh c\u1ee7a tam gi\u00e1c sao cho c\u00e1c \u0111o\u1ea1n th\u1eb3ng n\u1ed1i c\u00e1c \u0111i\u1ec3m n\u00e0y l\u1ea1i giao nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t, ta n\u00f3i tam gi\u00e1c n\u00e0y c\u00f3 trung t\u00e2m v\u00e0 c\u00e1c \u0111o\u1ea1n th\u1eb3ng n\u00e0y c\u1eaft nhau t\u1ea1i trung t\u00e2m c\u1ee7a tam gi\u00e1c. T\u01b0\u01a1ng t\u1ef1, khi c\u00f3 b\u1ed1n \u0111i\u1ec3m tr\u00ean m\u1ed9t t\u1ee9 di\u1ec7n sao cho c\u00e1c \u0111o\u1ea1n th\u1eb3ng n\u1ed1i c\u00e1c \u0111i\u1ec3m n\u00e0y l\u1ea1i giao nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t, ta n\u00f3i t\u1ee9 di\u1ec7n n\u00e0y c\u00f3 trung t\u00e2m v\u00e0 c\u00e1c \u0111o\u1ea1n th\u1eb3ng n\u00e0y c\u1eaft nhau t\u1ea1i trung t\u00e2m c\u1ee7a t\u1ee9 di\u1ec7n.<\/p>\n
<\/span>2. T\u00ednh ch\u1ea5t c\u1ee7a \u0111\u1ed3ng quy trong to\u00e1n h\u1ecdc.<\/span><\/h3>\nC\u00f3 m\u1ed9t s\u1ed1 t\u00ednh ch\u1ea5t c\u01a1 b\u1ea3n c\u1ee7a \u0111\u1ed3ng quy trong to\u00e1n h\u1ecdc:<\/p>\n
\n- \u0110\u01b0\u1eddng th\u1eb3ng \u0111\u1ed3ng quy l\u00e0 c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 c\u00f9ng m\u1ed9t h\u01b0\u1edbng v\u00e0 kh\u00f4ng bao gi\u1edd giao nhau.<\/li>\n
- Tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng l\u00e0 c\u00e1c tam gi\u00e1c c\u00f3 c\u00e1c g\u00f3c t\u01b0\u01a1ng \u1ee9ng b\u1eb1ng nhau v\u00e0 t\u1ec9 l\u1ec7 c\u00e1c c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng b\u1eb1ng nhau.<\/li>\n
- Hai tam gi\u00e1c vu\u00f4ng \u0111\u1ed3ng d\u1ea1ng khi c\u00f3 m\u1ed9t g\u00f3c vu\u00f4ng v\u00e0 hai g\u00f3c kh\u00e1c t\u01b0\u01a1ng \u1ee9ng b\u1eb1ng nhau.<\/li>\n
- Trong tam gi\u00e1c, ba trung tuy\u1ebfn c\u1eaft nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t, \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 trung \u0111i\u1ec3m. \u0110i\u1ec3m n\u00e0y chia ba trung tuy\u1ebfn th\u00e0nh c\u00e1c ph\u1ea7n b\u1eb1ng nhau.<\/li>\n<\/ul>\n
C\u00e1c t\u00ednh ch\u1ea5t n\u00e0y \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 ch\u1ee9ng minh c\u00e1c ph\u00e9p bi\u1ebfn \u0111\u1ed5i h\u00ecnh h\u1ecdc, t\u00ednh to\u00e1n di\u1ec7n t\u00edch v\u00e0 chu vi, v\u00e0 x\u00e2y d\u1ef1ng c\u00e1c c\u00f4ng th\u1ee9c trong to\u00e1n h\u1ecdc.<\/p>\n
<\/span>1. \u0110\u1ed3ng quy l\u00e0 g\u00ec?<\/span><\/h2>\n<\/span>Kh\u00e1i ni\u1ec7m \u0111\u1ed3ng quy<\/span><\/h3>\n\u0110\u1ed3ng quy l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m trong to\u00e1n h\u1ecdc, \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 ch\u1ec9 s\u1ef1 t\u01b0\u01a1ng \u0111\u1ed3ng gi\u1eefa c\u00e1c h\u00ecnh h\u1ecdc ho\u1eb7c c\u00e1c ph\u1ea7n t\u1eed trong kh\u00f4ng gian. Khi hai hay nhi\u1ec1u h\u00ecnh h\u1ecdc c\u00f3 c\u00e1c thu\u1ed9c t\u00ednh t\u01b0\u01a1ng t\u1ef1 nhau, ta n\u00f3i ch\u00fang \u0111\u1ed3ng quy v\u1edbi nhau.<\/p>\n
<\/span>V\u00ed d\u1ee5 v\u1ec1 \u0111\u1ed3ng quy<\/span><\/h3>\nM\u1ed9t v\u00ed d\u1ee5 c\u01a1 b\u1ea3n v\u1ec1 \u0111\u1ed3ng quy l\u00e0 khi hai tam gi\u00e1c c\u00f3 c\u00f9ng ba g\u00f3c b\u1eb1ng nhau, ta n\u00f3i ch\u00fang \u0111\u1ed3ng quy. \u0110i\u1ec1u n\u00e0y c\u00f3 ngh\u0129a r\u1eb1ng c\u00e1c g\u00f3c c\u1ee7a hai tam gi\u00e1c n\u00e0y c\u00f3 c\u00f9ng k\u00edch th\u01b0\u1edbc v\u00e0 t\u01b0\u01a1ng \u1ee9ng v\u1edbi nhau.<\/p>\n
<\/span>2. T\u00ednh ch\u1ea5t c\u1ee7a \u0111\u1ed3ng quy trong to\u00e1n h\u1ecdc.<\/span><\/h2>\n<\/span>T\u00ednh ch\u1ea5t 1: C\u00e1c h\u00ecnh h\u1ecdc \u0111\u1ed3ng quy c\u00f3 c\u00f9ng k\u00edch th\u01b0\u1edbc<\/span><\/h3>\nKhi hai hay nhi\u1ec1u h\u00ecnh h\u1ecdc \u0111\u1ed3ng quy v\u1edbi nhau, ch\u00fang c\u00f3 c\u00f9ng k\u00edch th\u01b0\u1edbc v\u00e0 t\u1ec9 l\u1ec7 v\u1edbi nhau. \u0110i\u1ec1u n\u00e0y cho ph\u00e9p ta \u00e1p d\u1ee5ng c\u00e1c c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch, chu vi, th\u1ec3 t\u00edch v\u00e0 c\u00e1c t\u00ednh ch\u1ea5t kh\u00e1c c\u1ee7a m\u1ed9t h\u00ecnh h\u1ecdc l\u00ean c\u00e1c h\u00ecnh h\u1ecdc \u0111\u1ed3ng quy.<\/p>\n
<\/span>T\u00ednh ch\u1ea5t 2: \u0110\u1ed3ng quy l\u00e0 m\u1ed9t quan h\u1ec7 t\u01b0\u01a1ng \u0111\u01b0\u01a1ng<\/span><\/h3>\nQuan h\u1ec7 \u0111\u1ed3ng quy l\u00e0 m\u1ed9t quan h\u1ec7 t\u01b0\u01a1ng \u0111\u01b0\u01a1ng trong to\u00e1n h\u1ecdc. \u0110i\u1ec1u n\u00e0y c\u00f3 ngh\u0129a r\u1eb1ng n\u1ebfu hai h\u00ecnh h\u1ecdc A v\u00e0 B \u0111\u1ed3ng quy v\u1edbi nhau, th\u00ec A c\u0169ng \u0111\u1ed3ng quy v\u1edbi B. Quan h\u1ec7 \u0111\u1ed3ng quy c\u0169ng th\u1ecfa m\u00e3n t\u00ednh ch\u1ea5t ph\u1ea3n x\u1ea1, \u0111\u1ed1i x\u1ee9ng v\u00e0 b\u1eafc c\u1ea7u.<\/p>\n
<\/span>3. C\u00e1ch ch\u1ee9ng minh \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u1ed3ng quy.<\/span><\/h2>\n<\/span>C\u00e1ch ch\u1ee9ng minh 1: S\u1eed d\u1ee5ng g\u00f3c b\u1eb1ng nhau<\/span><\/h3>\n\u0110\u1ec3 ch\u1ee9ng minh hai \u0111i\u1ec3m thu\u1ed9c v\u00e0o c\u00f9ng m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng, ta c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng t\u00ednh ch\u1ea5t g\u00f3c b\u1eb1nh nhau. N\u1ebfu hai g\u00f3c t\u1ea1i hai \u0111i\u1ec3m kh\u00e1c nhau tr\u00ean hai \u0111\u01b0\u1eddng th\u1eb3ng kh\u00e1c nhau b\u1eb1nh nhau, ta c\u00f3 th\u1ec3 k\u1ebft lu\u1eadn r\u1eb1ng hai \u0111i\u1ec3m n\u00e0y thu\u1ed9c v\u00e0o c\u00f9ng m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng.<\/p>\n
C\u00e1ch ch\u1ee9ng minh 2: S\u1eed d\u1ee5n<\/p>\n4. Hai tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng v\u00e0 c\u00e1ch ch\u1ee9ng minh.<\/h2>\n4.1 \u0110\u1ecbnh ngh\u0129a tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng<\/h3>\n
Tam gi\u00e1c ABD v\u00e0 tam gi\u00e1c ACE \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111\u1ed3ng d\u1ea1ng n\u1ebfu c\u00f3 m\u1ed9t ph\u00e9p \u00e1nh x\u1ea1 bi\u1ebfn \u0111\u1ed5i AB th\u00e0nh AC, AD th\u00e0nh AE sao cho t\u1ec9 l\u1ec7 c\u00e1c c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng b\u1eb1ng nhau.<\/p>\n
C\u1ee5 th\u1ec3, ta c\u00f3:<\/p>\n
\n- C\u1ea1nh AB t\u01b0\u01a1ng \u1ee9ng v\u1edbi c\u1ea1nh AC;<\/li>\n
- C\u1ea1nh AD t\u01b0\u01a1ng \u1ee9ng v\u1edbi c\u1ea1nh AE;<\/li>\n
- C\u1ea1nh BD t\u01b0\u01a1ng \u1ee9ng v\u1edbi c\u1ea1nh CE.<\/li>\n<\/ul>\n
<\/span>4.2 C\u00e1ch ch\u1ee9ng minh hai tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng<\/span><\/h3>\nC\u00f3 m\u1ed9t s\u1ed1 ph\u01b0\u01a1ng ph\u00e1p \u0111\u1ec3 ch\u1ee9ng minh hai tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng:<\/p>\n
\n- Ph\u01b0\u01a1ng ph\u00e1p SSS (Side-Side-Side):<\/strong> Ch\u1ec9 c\u1ea7n bi\u1ebft r\u1eb1ng ba c\u1eb7p c\u1ea1nh c\u1ee7a hai tam gi\u00e1c t\u01b0\u01a1ng \u1ee9ng b\u1eb1ng nhau, ta c\u00f3 th\u1ec3 k\u1ebft lu\u1eadn r\u1eb1ng hai tam gi\u00e1c \u0111\u00f3 l\u00e0 \u0111\u1ed3ng d\u1ea1n
\n<\/span>5. T\u00ednh ch\u1ea5t c\u1ee7a 3 \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u1ed3ng quy trong tam gi\u00e1c.<\/span><\/h2>\n<\/span>T\u00ednh ch\u1ea5t 1: \u0110\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a m\u1ed9t c\u1ea1nh tam gi\u00e1c \u0111i qua tr\u1ecdng t\u00e2m v\u00e0 t\u00e2m ngo\u1ea1i ti\u1ebfp<\/span><\/h3>\nTrong tam gi\u00e1c ABC, g\u1ecdi G l\u00e0 tr\u1ecdng t\u00e2m v\u00e0 O l\u00e0 t\u00e2m ngo\u1ea1i ti\u1ebfp. Khi \u0111\u00f3, \u0111\u01b0\u1eddng th\u1eb3ng AG l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a c\u1ea1nh BC.<\/p>\n
<\/span>T\u00ednh ch\u1ea5t 2: \u0110\u01b0\u1eddng cao c\u1ee7a tam gi\u00e1c \u0111i qua tr\u1ecdng t\u00e2m v\u00e0 t\u00e2m n\u1ed9i ti\u1ebfp vu\u00f4ng g\u00f3c v\u1edbi nhau<\/span><\/h3>\nTrong tam gi\u00e1c ABC, g\u1ecdi G l\u00e0 tr\u1ecdng t\u00e2m v\u00e0 I l\u00e0 t\u00e2m n\u1ed9i ti\u1ebfp. Khi \u0111\u00f3, \u0111\u01b0\u1eddng th\u1eb3ng GI l\u00e0 \u0111\u01b0\u1eddng cao c\u1ee7a tam gi\u00e1c ABC v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi nhau.<\/p>\n
<\/span>V\u00ed d\u1ee5:<\/span><\/h4>\n\n- X\u00e9t tam gi\u00e1c ABC c\u00f3 c\u00e1c \u0111\u1ec9nh A(2, 4), B(6, 8) v\u00e0 C(10, 6). T\u00ecm to\u1ea1 \u0111\u1ed9 c\u1ee7a tr\u1ecdng t\u00e2m G.<\/li>\n
- X\u00e9t tam gi\u00e1c ABC c\u00f3 c\u00e1c \u0111\u1ec9nh A(1, 2), B(-1, -4) v\u00e0 C(5, -6). T\u00ecm to\u1ea1 \u0111\u1ed9 c\u1ee7a t\u00e2m ngo\u1ea1i ti\u1ebfp O.<\/li>\n<\/ul>\n
<\/span>6. Tr\u1ef1c t\u00e2m, tr\u1ecdng t\u00e2m, t\u00e2m ngo\u1ea1i ti\u1ebfp, t\u00e2m n\u1ed9i ti\u1ebfp v\u00e0 t\u00e2m b\u00e0ng ti\u1ebfp trong tam gi\u00e1c.<\/span><\/h2>\n<\/span>Tr\u1ef1c t\u00e2m:<\/span><\/h3>\nTr\u1ef1c t\u00e2m c\u1ee7a m\u1ed9t tam gi\u00e1c l\u00e0 giao \u0111i\u1ec3m c\u1ee7a ba \u0111\u01b0\u1eddng tr\u1ef1c vu\u00f4ng g\u00f3c v\u1edbi c\u00e1c c\u1ea1nh c\u1ee7a tam gi\u00e1c.<\/p>\n
<\/span>Tr\u1ecdng t\u00e2m:<\/span><\/h3>\nTr\u1ecdng t\u00e2m c\u1ee7a m\u1ed9t tam gi\u00e1c l\u00e0 giao \u0111i\u1ec3m c\u1ee7a ba \u0111\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a tam gi\u00e1c.<\/p>\n
<\/span>T\u00e2m ngo\u1ea1i ti\u1ebfp:<\/span><\/h3>\nT\u00e2m ngo\u1ea1i ti\u1ebfp c\u1ee7a m\u1ed9t tam gi\u00e1c l\u00e0 t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c, t\u1ee9c l\u00e0 t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n \u0111i qua ba \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c.<\/p>\n
<\/span>V\u00ed d\u1ee5:<\/span><\/h4>\n\n- X\u00e9t tam gi\u00e1c ABC c\u00f3 c\u00e1c \u0111\u1ec9nh A(2, 4), B(6, 8) v\u00e0 C(10, 6). T\u00ecm to\u1ea1 \u0111\u1ed9 c\u1ee7a tr\u1ef1c t\u00e2m v\u00e0 tr\u1ecdng t\u00e2m.<\/li>\n
- X\u00e9t tam gi\u00e1c ABC c\u00f3 c\u00e1c \u0111\u1ec9nh A(1, 2), B(-1, -4) v\u00e0 C(5, -6). T\u00ecm to\u1ea1 \u0111\u1ed9 c\u1ee7a t\u00e2m ngo\u1ea1i ti\u1ebfp v\u00e0 tr\u1ef1c t\u00e2m.<\/li>\n<\/ul>\n
<\/span>7. \u0110\u1ecbnh l\u00fd trong t\u00e2m, t\u00e2m ngo\u1ea1i ti\u1ebfp, tr\u1ef1c t\u00e2m v\u00e0 t\u00e2m n\u1ed9i ti\u1ebfp c\u1ee7a tam gi\u00e1c.<\/span><\/h2>\n<\/span>\u0110\u1ecbnh l\u00fd trong t\u00e2m:<\/span><\/h3>\nTrong tam gi\u00e1c ABC, \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua t\u00e2m v\u00e0 trung \u0111i\u1ec3m c\u1ee7a m\u1ed9t c\u1ea1nh l\u00e0 \u0111\u01b0\u1eddng cao c\u1ee7a tam gi\u00e1c \u0111\u00f3.<\/p>\n
<\/span>\u0110\u1ecbnh l\u00fd t\u00e2m ngo\u1ea1i ti\u1ebfp:<\/span><\/h3>\nTrong tam gi\u00e1c ABC, g\u1ecdi O l\u00e0 t\u00e2m ngo\u1ea1i ti\u1ebfp. Khi \u0111\u00f3, t\u1ee9 gi\u00e1c ABOC l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt.<\/p>\n
<\/span>V\u00ed d\u1ee5:<\/span><\/h4>\n\n- X\u00e9t tam gi\u00e1c ABC c\u00f3 c\u00e1c \u0111\u1ec9nh A(2, 4), B(6, 8) v\u00e0 C(10, 6). Ch\u1ee9ng minh r\u1eb1ng \u0111\u01b0\u1eddng th\u1eb3ng AG l\u00e0 \u0111\u01b0\u1eddng cao c\u1ee7a tam gi\u00e1c ABC.<\/li>\n
- X\u00e9t tam gi\u00e1c ABC c\u00f3 c\u00e1c \u0111\u1ec9nh A(1, 2), B(-1, -4) v\u00e0 C(5, -6). Ch\u1ee9ng minh r\u1eb1ng t\u1ee9 gi\u00e1c ABOC l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt.<\/li>\n<\/ul>\n
<\/span>8. \u0110\u01b0\u1eddng trung tuy\u1ebfn v\u00e0 c\u00f4ng th\u1ee9c t\u00ednh.<\/span><\/h2>\n<\/span>\u0110\u01b0\u1eddng trung tuy\u1ebfn:<\/span><\/h3>\n\u0110\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a m\u1ed9t tam gi\u00e1c l\u00e0 \u0111o\u1ea1n th\u1eb3ng n\u1ed1i trung \u0111i\u1ec3m hai c\u1ea1nh b\u1ea5t k\u1ef3 c\u1ee7a tam gi\u00e1c.<\/p>\n
<\/span>C\u00f4ng th\u1ee9c t\u00ednh to\u1ea1 \u0111\u1ed9 \u0111i\u1ec3m tr\u00ean \u0111\u01b0\u1eddng trung tuy\u1ebfn:<\/span><\/h3>\nTo\u1ea1 \u0111\u1ed9 x v\u00e0 y c\u1ee7a m\u1ed9t \u0111i\u1ec3m M n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng trung tuy\u1ebfn c\u00f3 th\u1ec3 t\u00ednh b\u1eb1ng c\u00f4ng th\u1ee9c:<\/p>\n
x = (x1 + x2) \/ 2<\/p>\n
y = (y1 + y2) \/ 2<\/p>\n
<\/span>V\u00ed d\u1ee5:<\/span><\/h4>\n\n- X\u00e9t tam gi\u00e1c ABC c\u00f3 c\u00e1c \u0111\u1ec9nh A(2, 4), B(6, 8) v\u00e0 C(10, 6). T\u00ecm to\u1ea1 \u0111\u1ed9 c\u1ee7a trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh AB.<\/li>\n
- X\u00e9t tam gi\u00e1c ABC c\u00f3 c\u00e1c \u0111\u1ec9nh A(1, 2), B(-1, -4) v\u00e0 C(5, -6). T\u00ecm to\u1ea1 \u0111\u1ed9 c\u1ee7a trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh BC.<\/li>\n<\/ul>\n
<\/span>9. C\u00e1ch ch\u1ee9ng minh 3 \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u1ed3ng quy trong to\u00e1n h\u1ecdc.<\/span><\/h2>\n![\"9.](\"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-content\/uploads\/2023\/09\/dong_quy_kham_pha_khai_niem_va_tinh_chat.jpeg\" "\\"9.")
<\/p>\n
<\/span>C\u00e1ch ch\u1ee9ng minh s\u1eed d\u1ee5ng t\u00ednh ch\u1ea5t g\u00f3c b\u00f9:<\/span><\/h3>\n\n- Cho hai g\u00f3c b\u00f9 l\u00e0 A v\u00e0 B.<\/li>\n
- Ch\u1ee9ng minh r\u1eb1ng t\u1ed5ng hai g\u00f3c b\u00f9 l\u00e0 180\u00b0.<\/li>\n
- K\u1ebft lu\u1eadn: Hai g\u00f3c A v\u00e0 B l\u00e0 hai g\u00f3c t\u1ea1o th\u00e0nh m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng.<\/li>\n<\/ol>\n
<\/span>C\u00e1ch ch\u1ee9ng minh s\u1eed d\u1ee5ng t\u00ednh ch\u1ea5t giao nhau:<\/span><\/h3>\n\n- Cho hai \u0111\u01b0\u1eddng th\u1eb3ng AB v\u00e0 CD.<\/li>\n
- Ch\u1ee9ng minh r\u1eb1ng AB v\u00e0 CD c\u1eaft nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m O.<\/li>\n
- Ch\u1ee9ng minh r\u1eb1ng t\u1ed5ng hai g\u00f3c t\u1ea1o th\u00e0nh b\u1edfi AB v\u00e0 CD l\u00e0 180\u00b0.<\/li>\n
- K\u1ebft lu\u1eadn: \u0110\u01b0\u1eddng th\u1eb3ng AB v\u00e0 CD l\u00e0 \u0111\u1ed3ng quy.<\/li>\n<\/ol>\n
<\/span>10. H\u00ecnh ch\u00f3p v\u00e0 c\u00f4ng th\u1ee9c t\u00ednh chu vi, di\u1ec7n t\u00edch, th\u1ec3 t\u00edch.<\/span><\/h2>\n<\/span>H\u00ecnh ch\u00f3p:<\/span><\/h3>\nH\u00ecnh ch\u00f3p l\u00e0 m\u1ed9t kh\u1ed1i h\u1ed9p c\u00f3 m\u1ed9t \u0111\u00e1y l\u00e0 m\u1ed9t h\u00ecnh \u0111a gi\u00e1c v\u00e0 c\u00e1c c\u1ea1nh b\u00ean \u0111\u1ec1u h\u1ee3p l\u1ec7 v\u1edbi c\u00e1c c\u1ea1nh c\u1ee7a \u0111\u00e1y v\u00e0 giao nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t n\u1eb1m tr\u00ean tr\u1ee5c c\u1ee7a h\u00ecnh ch\u00f3p.<\/p>\n
<\/span>C\u00f4ng th\u1ee9c t\u00ednh chu vi \u0111\u00e1y:<\/span><\/h3>\nChu vi \u0111\u00e1y c\u1ee7a m\u1ed9t h\u00ecnh ch\u00f3p c\u00f3 th\u1ec3 t\u00ednh b\u1eb1ng c\u00f4ng th\u1ee9c:<\/p>\n
Chu vi = T\u1ed5ng c\u00e1c c\u1ea1nh c\u1ee7a \u0111a gi\u00e1c \u0111\u00e1y<\/p>\n
<\/span>C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch xung quanh:<\/span><\/h3>\nDi\u1ec7n t\u00edch xung quanh c\u1ee7a m\u1ed9t h\u00ecnh ch\u00f3p c\u00f3 th\u1ec3 t\u00ednh b\u1eb1ng c\u00f4ng th\u1ee9c:<\/p>\n
Di\u1ec7n t\u00edch = (1\/2) x Chu vi x Chi\u1ec1u cao<\/p>\n
<\/span>C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n:<\/span><\/h3>\n