Hệ thống lý thuyết cơ bản Toán Hình học THCS
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A
+
TAM
AB AC < BC < AB + AC
B
C
AB BC < AC < AB + BC
AC BC < AB < AC + BC
A
nhau.
+
TAM
nhau.
+
+ AB = AC
+
+
B
C
-
mang
+
+ AB = AC = BC
A
TAM
-
nhau.
nhau.
+
0
0
+
.
C
B
TAM
.
C
0
+
+
+ BC2 = AB2 + AC2
A
B
C
450
+ BC2 = AB2 + AC2
A
B
+
2
1)
+
+ AB = AC
+
+
TAM
0
+ AM = BC :
+
+
2
2)
0
.
2
3)
1/
2/
3/
A
A
F
E
G
TRUNG
BM = MC = BC : 2
B
B
C
M
C
D
Trong
AG
AD
ABC.
BG
BE
CG
CF
2
3
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
2
+
3
4
a
1
+
+
+
2
3
b
1
4 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
2/ AB = BC = CD = DA.
.
3/
1
1
2
450
4/ AC = BD.
5/ IA = IC = ID = IB.
I
1
6/ BD
2
2
1
D
C
7/
a
h
b
a
h
h
h
a
b
a
S
1
a.h
2
SHthang
1
a b .h
2
a
S HBH
a.h
a
d1
a
d1
d2
d2
b
S HCN
a.b
SHvuông
a2
S
1
d1.d 2
2
SHthoi
1
d1.d 2
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
1
BC
2
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
1
AB CD
v MN =
2
b/
A
A
B
B
I
I
IA = IB
b/
a/
d
C
D
d
K
M
1 2
A
B
MA MB
I
A
I
B
1
A
1
I
2
:
12
N
AC BD
AD BC
AB / / CD
2
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 : 2
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
+ 0 < sin
+ CM: sin
cot
ch
trong
1/ sin
cao trong
1/ (cgv1)2 = hc1 . ch
(cgv2)2 = hc2 . ch
2/ cao2 = hc1 . hc2
3/ cao . ch = cgv1 . cgv2
1
1
1
4/
2
2
cao
(cgv1 )
(cgv 2 ) 2
=
3/ tan
=
4/ cot
=
sin
tan
ch2 = (cgv1)2 + (cgv2)2
ch = hc1 + hc2
1/ tan
sin
cos
2 / cot
cos
sin
4 / tan .cot
< tan ; cos
1
1
sin 2 ;cos
tan 2 ; cot
3) cgv1 = cgv2
4) cgv1 = cgv2
= 900
+
2
1
)
< 1.
<
=
2/ cos
1
2) cgv = ch .
E
AB
DE
D
hc2
hc1
BC
EF
A
E
C
D
A
cos
cot
1
1
2
sin
= cos
cos
= sin
tan
= cot
cot
= tan
2
300
450
600
sin
1/2
2 /2
3 /2
cos
3 /2
2 /2
1/2
tan
3 /3
1
3
cot
3
1
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
trong
(O)
d
AB = AC
nhau
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
1
2
=
=
1
2
)
)
)
M
M
N
M
M
O
O
O
B
B
A
B
A
N
O
D
B
A
C
A
=
1
2
)
)
(O))
=
M
O
A
B
x
O
1
2
A
)
)
)
B
x
1
=
2
D
=
O
B
C
1
2
)
M
A
B
A
C
1
=
2
M
-
)
B
O
O
n
C
m
D
O
D
D
=
B
1
2
-
2
1
)
=
1
2
-
)
0
T
B
A
A
A
H
1
2
.
1
2
2
G
1
C
D
B
(BCx
0
R, cung n0
C= 2 R
R
O
C=
d
l
Rn
180
A
R
n0
l
R
O
O
S = R2
S
R2n
360
S
lR
2
n0
B
.
1/
a
b
c
d
1/ (A + B)2 = A2 + 2AB + B2
a c
b d
2
3/ A
a
b
a.d
c
d
6/ A3 + B3 = (A + B)(A2 AB + B2)
2
2/ (A B) = A
2
2/
2
2AB + B
7/ A3
2
B = (A B)(A + B)
B3 = (A B)(A2 + AB + B2)
b.c
a b
b
3
3
2
5/ (A B) = A
2
0)
(d)
a
-1
3
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'
3
3AB(A + B)
3
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
0
A(x)
A(x)
A( x)
B ( x)
B(x) > 0
A2
0
A.B
A
B
2/
A2
B
A
B
A
A
A
B 0
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 0
B
B
B
A
A
A
A B2
0
A 0
B 0
A B
A B
A2 B
A2 B
(
(
A
0)
A < 0)
A
2
4/
0
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
2
a
a
a
a 1
1
a
a1
a
b
a 1
b
2
a
b
a
b
a b 2 ab
a
a a b b
a
a a b b
a
3
a
ab
a
1
a
a
3
b
3
b
a a b b
2/
a
a
b a
ab b
a
b a
ab b
3
b
3
ab
b
1/
3
b
a
b a
2
3/
b: ax2 + c = 0 (a 0)
x2 =
b
a
a
a b b a
a
b
ab b
+ bx + c = 0 (a
0):
c
a
ax2 + bx = 0 (a 0)
x(ax + b) = 0
x 0
ax b
x2 > 0
x
c
a
x
>0
0
x1
0
b
a
=0
b
0;
a
<0
<0
1,
a.
2
a a
a
2
a. a
a b b a
4:
a
1
2
a
m. A
n .A
x2
ax2 + bx + c = 0 (a
x1
x1.x2
b
a
x2
c
a
b
2a
x1
b
; x2
x2
2a
b
2a
1/
a+b+c=0
2
2/
a
2
+ bx + c = 0 (a
c
a
x1 = 1, x2 =
3/
b+c=0
x1
+ bx + c = 0 (a
x1 = 1, x2 =
c
a
2:
1
+ x2
1
. x2
2
4/
ax2
5/
2
2
1
2
x x
x1 x2
3
3
1
2
x x
4
4
1
2
x x
x12
1
2 x1 x2
3
x1 x2
x12
x x
2
x2
3x1 x2 x1 x2
2 2
2 x1 x2
.
0:
2
>0
=0
x2 2
2
x12
2
2
1
x
x2
x1 x2
<0
x2 2 2 x1 x2
0
2
a.c < 0
x1 x2
x12
Sx + P = 0
2
x12
0
P 0
x2 2 2 x1 x2
x2 2
0
1;
1
+ x2
1
x2:
P
0
S
0
0
. x2
+
P
0
S
0
7/
4
+ bx2 + c = 0
2
0)
2
(a 0)
2
=t
= bx + c (*)
0
<0
at2 + bt + c = 0
2
+ bt + c = 0
t
2
t=
0.
=0
=t
t
>0
