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 + + + BC2 = AB2 + AC2 A TAM C B TAM B C + BC2 = AB2 + AC2 A B + + + AB = AC + + 450 + AM = BC : + + 1) 2) 3) 1/ 2/ 3/ A A F TRUNG BM = MC = BC : B B C M E G 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 AH B A 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 a // b c Suy ra: + + + a c b c a a a b b b 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 D C A B 2/ 1/ AB // DC THANG 2/ 1/ AB // DC B 2/ AD = BC THANG 3/ D C 4/ 5/ AC = BD 1/ A B D 2/ 3/ 4/ I C D A C 5/ A 1/ 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 D 5/ 6/ BD 7/ 1/ A 450 B 2/ AB = BC = CD = DA 3/ 4/ AC = BD 5/ IA = IC = ID = IB I 6/ BD D C 7/ a h b a h h h a a S b a.h SHthang a b h a a.h S HBH 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 N M NB MA MD NB NC B A MA MB M N ABC B C b/ C D b/ A MN // BC N M B BC C c/ M C D thang ABCD MN // AB // CD AB CD v MN = thang ABCD, B A MA MB MN / / BC N MA MD M C B N c/ A M B A ABC ABCD C D a/ MN / / AB/ / CD N b/ A A B B I I IA = IB b/ a/ C d A d K D M B MA MB I A I : B A 1 I 12 N AC BD AD BC AB / / CD B NA NB b/ a/ N MN // BC AM AN MN AB AC BC M A B MN // BC AMN C ABC x A AE A B E B ABC = DEF D C AB AC ABC ABC DB DC EB EC AM = BC : DEF theo A h1 k h2 Chuvi Chuvi h1 C B D S S h2 F E AB DE AC DF BC EF C M D A (c.c.c) C B E F C E (g.c.g) B C E AC DF BC EF (c.c.c) F D A k2 (c.g.c) (c.g.c) B DEF DEF AB DE D A ABC k ABC (g.g) 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 cgv2 ch 1/ sin = 3/ tan = 4/ cot = sin tan ch2 = (cgv1)2 + (cgv2)2 ch = hc1 + hc2 sin cos / cot cos sin / tan cot 2) cgv = ch E F < < < tan ; cos 1 sin ;cos tan ; cot 3) cgv1 = cgv2 4) cgv1 = cgv2 = 900 + ) AB DE = 2/ cos 1/ tan F + < sin + CM: sin cot 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 ) BC EF D hc2 hc1 E 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 A B B C O IB = IC A I D AB = AC OA C cung M A O O O B B A x B A = = ) ) ) M M M O N M O O B B N A A B O B A = A ) ) O A B x O ) C (O)) = M D B A x ) = ) D = O C B M ) A B A C = M - ) D = - ) = - ) T B m A A O n D D B A O C O B H D 2 G C B (BCx R, cung n0 C= R C= d R O l Rn 180 n0 l O R R O S = R2 A n0 B S S R2n 360 lR 1/ 2/ a b a b c d 1/ (A + B)2 = A2 + 2AB + B2 a c b d 2 3/ A b.c a b b c d d 2AB + B B = (A B)(A + B) 6*/ A3 + B3 = (A + B)3 4/ (A + B)3 = A3 + 3A2B + 3AB2 + B3 3 5/ (A B) = A (d) a -1 3 3A B + 3AB 0) B3 = (A B)(A2 + AB + B2) 7/ A3 (d): y = ax + b (a (d) 6/ A3 + B3 = (A + B)(A2 AB + B2) 2/ (A B) = A a.d c 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) > 0 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 A a a a m A n A A m 2: n A a m A n A a 3: m A A2 m A B B a b 4: a a a a a 1 a a1 a a a a ab b a a b b a a a b b a a a b ab b a a b b a b a b b a b a 3 b b b 3 a a b a ab b a b a ab b b a 3/ b: ax2 + c = (a 0) ab b + bx + c = (a 0): c a ax2 + bx = (a 0) x(ax + b) = x ax b x2 > x c a x >0 x2 ax2 + bx + c = (a x1 x1.x2 x2 c a b a x1 b a b 0; a