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

2

1

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.

2S d d Hthoi 1 2

1.

2S d d

I

B

D C

A

B

D

IA C

11

1

2

2

2

21

450

I

BA

C D

a b

b

a

h

a

h

b

ad2

d1

a

d1

d2

a

h

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

2

IBA

M

N

M N

B C

A

NM

D C

A B

M N

B C

A

NM

D C

A B

NM

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

A

h2

E F

D

CB

A

F

D

E

CB

A

F

D

E

F

D

ECB

A

x

E DB C

A

M

A

B C

cgv1 cgv2

4/

EFBC

AB DE

(ch-cgv)F

BC AB

E DE

(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

D

CB

A

FE

D

(hay

.

ABC

Hay (O)

ABC

ABC

-

-

ABC

ABC

ABC

-

-

.

-

m K trong

ABC

C)

qua trung

MN

OA

CB

A

K

F

E

D

(O)

d

AB = AC

chung.

nhau

AB = AC

IB = IC

OA

cung

=

)

1

2

)

= 2

1

)

= 1

2

) ) (O))

)

= 2

1

)

)

= 2

1

D

A B

C C

B

OA

I

O

A

B

O

A

B

M

x

O A

B

O

A

B

M

A

B

O

M

NA

OB

M

B

D

C

N

O

A

M

x

O A

B

M

x

O A

B

= 2

1)

=2

1- )

= 1

2- ) =

1

2- )

(BCx

T 0.

H

.

G

B

0

R, cung n0

C = R2

C = d

180

Rnl

S =2R

360

2nRS

2

lRS

M

O

A

B

D

C

D

C

O

M

B

A

1

1

2

2

21

12

B

A

CD

R

ln0O

CO

AD

B

m

n

D

O

A

B

R

OR

n0O

A

B

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

3/ ' ' '

ax by c

a x b y c ' ' '

a b c

a b c

1/

)(

)(

xB

xAB(x) 0

)(xA A(x) 0

)(

)(

xB

xA B(x) > 0

2/

BBhayAA

BBABA

02

0( 0)B hayAA B

A B

2

0

BA

BBA

00

0

AA B

B

2/

2 AA A

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22 . AAAAA

. .A B A B 0; B 0)

A A

B B( A 0, B > 0)

2A B A B 0)

2A B A B ( A 0)

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

.

BA

BAm

BA

m .

4:

1

1 1

a aa aa

a a

aa

aa

a

aa1

1

abba

baab

ba

abba

5/ 0

2

.a aa

a

. . 1a a a a a a a

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