ab < ac + bc tam - hoc360.net filea/ b/ mn // bc am an mn ab ac bc mn // bc amn abc abc ae ab db...
TRANSCRIPT
TAM
+
AB AC < BC < AB + AC
AB BC < AC < AB + BC
AC BC < AB < AC + BC
TAM
+ AB = AC
+
+ - -
+
+ nhau.
+ nhau.
mang
TAM + AB = AC = BC
+
nhau.
nhau.0.
+ 0.
TAM +
+
+ BC2 = AB2 + AC2
+
0
0
+
1)2
2)2
3)2
TAM + AB = AC
+
+
+ BC2 = AB2 + AC2
+ AM = BC :
+ + 0.
B C
A
B C
A
B C
A
C
A B
450
BA
C
TRUNG
1/
BM = MC = BC : 2
2/
ABC.
3/
Trong
2
3
AG BG CG
AD BE CF
ABC
CAO
1/
d
2/
AH
ABC
3/
Trong
ABC.
4/
AH
B
5/
AB, AC
MB C
A
GFE
D
A
CB
H
A
CB
HL
K
I
A
CB
H C
A
B
H
A C
B
TRUNG
1/
d MB = MC
2/
ABC
3/
Trong trung tr
: OA = OB = OC
ABC.
1/
Tia Oz
2/
ABC.
3/
Trong ABC, ba
IK = IL = IM
ABC.
+
+
+
+
+
+
+
+
d
M
A
CB
O
A
CB
D
A
CB
L
K
M
I
A
CB
a
b
c
4
3
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32
14
B
A
.a // b
Suy ra:+++
a c
b c
/ /a b
/ / ba
a c
b c
/ /
/ /
a c
b c
/ /a b
1/ .
THANG
1/ AB // DC.
2/ .
THANG
1/ AB // DC.
2/ .
.
THANG
1/ AB // DC.
2/ AD = BC.
3/ .
4/ .
5/ AC = BD.
1/
2/
3/
4/
5/
c
a
b
c
a
b
b
c
a
D C
A
B
D
A
C
B
D C
A B
BA
D C
I
B
D C
A
1/
2/
3/ .
4/ AC = BD.
5/ IA = IC = ID = IB.
THOI
1/2/ AB = BC = CD = DA.3/4/
5/6/ BD 7/
1/
2/ AB = BC = CD = DA.
3/ .
4/ AC = BD.
5/ IA = IC = ID = IB.
6/ BD
7/
1.
2S a h
Hthang
1.
2S a b h .HBHS a h
.HCNS a b 2HvuôngS a 1 2
1.
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1.
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A
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IA C
11
1
2
2
2
21
450
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BA
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a b
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a
h
a
h
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a
d1
d2
a
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a
h
a/
MA MB
NA NB
ABC.
a/ MA MD
NB NC
ABCD.
b/
ABC.MN // BC
1
2BC
b/
thang ABCD.MN // AB // CD
v MN = 1
2AB CD
c/
/ / BC
MA MB
MN
c/ thang ABCD,
/ / AB/ / CD
MA MD
MN
a/ b/
IA = IB
a/ b/
:
D
D
/ / D
AC B
A BC
AB C
MA MB
NA NB
d
KD
I BA
C
2
1
1 1
2
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IBA
M
N
M N
B C
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A B
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A B
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A
CD
B
M N
A
CB
I
A B
I
A B
d
I
A B
1 2
a/ b/
MN // BCAM AN MN
AB AC BC
MN // BCAMN ABC
ABCAE
AB DB EB
AC DC ECAM = BC : 2
ABC = DEF ABC DEF theo 1
2
hk
h
ABC
DEF
Chuvik
Chuvi
2ABC
DEF
Sk
S
EF
AB DE
AC DF
BC
(c.c.c)F
AB AC BC
DE DF E(c.c.c)
(c.g.c)(c.g.c)
(g.c.g) (g.g)
A
B C
N M
h1
CB
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h2
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A
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cgv1 cgv2
4/
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AB DE
(ch-cgv)F
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(ch-gn)
cao trong 1/ (cgv1)
2 = hc1 . ch(cgv2)
2 = hc2 . ch2/ cao2 = hc1 . hc2
3/ cao . ch = cgv1 . cgv2
4/ 2
22
12 )(
1
)(
11
cgvcgvcao
ch2 = (cgv1)2 + (cgv2)
2
ch = hc1 + hc2
trong
1/ sin =
2/ cos =
3/ tan =
4/ cot =
1 2
1 2 1 2
1 2 1 2
sin sin ;cos cos
tan tan ;cot cot
+ 0 < sin < 1.+ CM: sin < tan ; cos < cot
+ = 900
sin = cos
cos = sin
tan = cot
cot = tan
sin1/ tan
cos
cos2 / cot
sin
4 / tan .cot 1
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
) 3) cgv1 = cgv2 )
2) cgv = ch . 4) cgv1 = cgv2
ch
hc2hc1
caocgv2
cgv1
FE
D
CB
A
FE
D
CB
A
CB
A
FE
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CB
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FE
D
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.
ABC
Hay (O)
ABC
ABC
-
-
ABC
ABC
ABC
-
-
.
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m K trong
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C)
qua trung
MN
OA
CB
A
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D
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AB = AC
chung.
nhau
AB = AC
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cung
=
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)
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)
= 2
1
D
A B
C C
B
OA
I
O
A
B
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A
B
M
x
O A
B
O
A
B
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M
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OB
M
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1
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T 0.
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.
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0
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C = R2
C = d
180
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S =2R
360
2nRS
2
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B
D
C
D
C
O
M
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A
1
1
2
2
21
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m
n
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OR
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1/a c a c
b d b d
. .
2 /
a d b ca c
a b c db d
b d
1/ (A + B)2 = A2 + 2AB + B2
2/ (A B)2 = A2 2AB + B2
3/ A2 B2 = (A B)(A + B)
4/ (A + B)3 = A3 + 3A2B + 3AB2 + B3
5/ (A B)3 = A3 3A2B + 3AB2 B3
6/ A3 + B3 = (A + B)(A2 AB + B2)
7/ A3 B3 = (A B)(A2 + AB + B2)
6*/ A3 + B3 = (A + B)3 3AB(A + B)
7*/ A3 B3 = (A B)3 + 3AB(A B)
(d): y = ax + b (a 0)
(d)
a
(d) -1
1/ ' ' '
ax by c
a x b y c ' '
a b
a b
2/ ' ' '
ax by c
a x b y c ' ' '
a b c
a b c
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ax by c
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2/
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2/
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2A B A B ( A < 0)
4/
.A A AA
A A
2:. m.
n .An. .
m m A A
n A A A
3:
BA
BAm
BA
m2
.
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4:
1
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a aa aa
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a
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a b b a ab a b
2 2
a b a b a b a b
2
2a b ab a b
3 3
3 3
a a b b a b a b a ab b
a a b b a b a b a ab b
3 3
a a b b a b a b a ab b
1/
b: ax2 + c = 0 (a 0)
x2 = c
a
x2 > 0
c
a
2 < 0
2/
ax2 + bx = 0 (a 0)
x(ax + b) = 0
0
0
0
x
ax b
x
bx
a
0;b
a
3/ 2 + bx + c = 0 (a
0):
> 0
a
bx
21 ;
a
bx
22
= 0
a
bxx
221
< 0
1, x2
ax2 + bx + c = 0 (a
a
cxx
a
bxx
21
21
.
1/ a + b + c = 0
2 + bx + c = 0 (a
x1 = 1, x2 = a
c
2/ a b + c = 0
2 + bx + c = 0 (a
x1 = 1, x2 = a
c
3/
x1 2:
1 + x2
1 . x2
2 Sx + P = 0
4/
22 2
1 2 1 21 22x x x xx x
33 3
1 2 1 2 1 21 23x x x x x xx x
2 24 4 2 21 2 1 21 2
2x x x xx x2 2
1 2x x
2 2 21 2 1 21 2
2x x x xx x2 2
1 2x x
2 2 21 2 1 2 1 2 1 22x x x x x x x x
2 21 2x x
1; x2:
1 + x2 1 . x2
+
5/ ax2
0: .
> 0
= 0
< 0
0
a.c < 0
0
0P
0
0
0
P
S
0
0
0
P
S
4 + bx2 + c = 0
(a 0)2 = t 0
at2 + bt + c = 0
2 + bt + c = 0
t 0.
2 = t
t = t
7/ 2 0)
2 = bx + c (*)
< 0
= 0
> 0