Hệ thống lý thuyết cơ bản Toán Hình học THCS

A + TAM AB AC < BC < AB + AC B C AB BC < AC < AB + BC AC BC < AB < AC + BC A + TAM + + AB = AC + + B C - mang + + AB = AC = BC A TAM - nhau + 0 + C B TAM C + + + BC2 = AB2 + AC2 A B C 450 + BC2 = AB2 + AC2 A B + 1) + + AB = AC + + TAM + AM = BC : + + 2) 3) 1/ 2/ 3/ A A F E G TRUNG BM = MC = BC : B B C M C D Trong AG AD ABC BG BE CG CF ABC 1/ 2/ 3/ A A K L CAO B d C H B AH H C I Trong ABC ABC 4/ 5/ A B H H B C A AH B AB, AC C 1/ 2/ 3/ A A d O TRUNG d MB = MC B M C C B Trong trung tr : OA = OB = OC ABC ABC 2/ 1/ 3/ A A L M I B D B C K Trong Tia Oz ABC, ba IK = IL = IM ABC ABC c A + a + + + b B + + + + C c c a a a b b b c a // b Suy ra: + + + a b c c a / /b a//b a c b / /c b a / /b a / /c c B A 1/ D C A B 1/ AB // DC THANG 2/ D C A B 1/ AB // DC THANG 2/ C D A 1/ AB // DC B 2/ AD = BC THANG 3/ 4/ D C 5/ AC = BD 1/ A B 2/ 3/ I D 4/ C 5/ 1/ A B 2/ 3/ I 4/ AC = BD C D 5/ IA = IC = ID = IB 1/ 2/ AB = BC = CD = DA 3/ 4/ B THOI A C I 5/ 6/ BD 7/ D 1/ A B 2/ AB = BC = CD = DA 3/ 1 450 4/ AC = BD 5/ IA = IC = ID = IB I 6/ BD 2 D C 7/ a h b a h h h a b a S a.h SHthang a b h a S HBH a.h a d1 a d1 d2 d2 b S HCN a.b SHvuông a2 S d1.d 2 SHthoi d1.d 2 a/ a/ A NA NB N M MA MD NB NC B A MA MB M N ABC B C C D ABCD b/ b/ A B A ABC MN // BC N M BC B N C D C c/ M thang ABCD, c/ A B A MA MB MN / / BC N M MA MD M a/ MN / / AB/ / CD N C D C B thang ABCD MN // AB // CD AB CD v MN = b/ A A B B I I IA = IB b/ a/ d C D d K M A B MA MB I A I B A I : 12 N AC BD AD BC AB / / CD NA NB B a/ N b/ MN // BC AM AN MN AB AC BC M A B MN // BC AMN C ABC x ABC A AE A B E B D C AB AC ABC = DEF C M ABC DB DC EB EC AM = BC : A DEF theo h1 k h2 Chuvi Chuvi h1 C B D S S h2 F E AB DE AC DF BC EF D A C E F k DEF k2 DEF AB DE (c.c.c) B ABC ABC AC DF BC EF (c.c.c) D A (c.g.c) (c.g.c) C B E F D A (g.g) (g.c.g) B C E F 4/ D A B E C F A BC EF AB DE (ch-cgv) B C D B cgv1 cao F (ch-gn) B C F E F cgv2 + < sin + CM: sin cot ch 1/ sin cao 1/ (cgv1)2 = hc1 ch (cgv2)2 = hc2 ch 2/ cao2 = hc1 hc2 3/ cao ch = cgv1 cgv2 1 4/ 2 cao (cgv1 ) (cgv ) = 3/ tan = 4/ cot = sin tan ch2 = (cgv1)2 + (cgv2)2 ch = hc1 + hc2 1/ tan sin cos / cot cos sin / tan cot < tan ; cos 1 sin ;cos tan ; cot 3) cgv1 = cgv2 4) cgv1 = cgv2 = 900 + ) < < = 2/ cos 2) cgv = ch E AB DE D hc2 hc1 BC EF A E C D A cos cot 1 sin = cos cos = sin tan = cot cot = tan 300 450 600 sin 1/2 /2 /2 cos /2 /2 1/2 tan /3 cot 3 /3 ) cgv1 cgv2 ABC (hay Hay (O) ABC ABC ABC - ABC ABC A mK ABC B D C E F K C) - MN qua trung OA (O) d AB = AC chung B A AB = AC B O I C D IB = IC A OA C cung M A O O O B B x B A A = = ) ) ) M M N M M O O O B B A B A N O D B A C A = ) ) (O)) = M O A B x O A ) ) ) B x = D = O B C ) M A B A C = M - ) B O O n C m D O D D = B - ) = - ) T B A A A H 2 G C D B (BCx R, cung n0 C= R R O C= d l Rn 180 A R n0 l R O O S = R2 S R2n 360 S lR n0 B 1/ a b c d 1/ (A + B)2 = A2 + 2AB + B2 a c b d 3/ A a b a.d c d 6/ A3 + B3 = (A + B)(A2 AB + B2) 2/ (A B) = A 2/ 2AB + B 7/ A3 B = (A B)(A + B) B3 = (A B)(A2 + AB + B2) b.c a b b 3 5/ (A B) = A 0) (d) a -1 3 3A B + 3AB (d): y = ax + b (a (d) 6*/ A3 + B3 = (A + B)3 4/ (A + B)3 = A3 + 3A2B + 3AB2 + B3 c d d 7*/ A B 1/ ax by c a'x b' y c' 2/ ax by c a'x b' y c' 3/ ax by c a'x b' y c' 3AB(A + B) B = (A B) + 3AB(A B) a a' a a' b b' a a' b b' c c' b b' c c' 2/ 1/ A( x ) B ( x) B(x) A2 A(x) A(x) A( x) B ( x) B(x) > A2 A.B A B 2/ A2 B A B A A A B A BhayA B 0(hayA 0) A B A B A ( B A A A 0; B A 0) 0, B > 0) B A2 B A B 0) B B B B A A A A B2 A B A B A B A2 B A2 B ( ( A 0) A < 0) A 4/ 5/ A A A A A m 2: n A A a a a m A n A A a 3: m A m A A2 B m A B B m A B A B B a a b a a ab a a a a 1 a a1 a b a b a b a b a b ab a a a b b a a a b b a a ab a a a b b a a b b 2/ a a b a ab b a b a ab b b ab b 1/ b a b a 3/ b: ax2 + c = (a 0) x2 = b a a a b b a a b ab b + bx + c = (a 0): c a ax2 + bx = (a 0) x(ax + b) = x ax b x2 > x c a x >0 x1 b a =0 b 0; a