CHUN ĐỀ BÀI TẬP HÌNH HỌC LỚP 10 ( có sử dụng tài liệu từ các nguồn khác).
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1

CHƢƠNG I - ĐẠI CƢƠNG VỀ VÉCTƠ

A: TÓM TẮT LÝ THUYẾT

 Vectơ là đoạn thẳng có dònh hướng Ký hiệu :
AB
;
CD
hoặc
a
;
b

 Vectơ – không là vectơ có điểm đầu trùng điểm cuối : Ký hiệu
0

 Hai vectơ cùng phương là hai vectơ có giá song song hoặc trùng nhau
 Hai vectơ cùng phương thì hoặc cùng hướng hoặc ngược hướng
 Hai vectơ bằng nhau nếu chúng cùng hướng và cùng độ dài TỔNG VÀ HIỆU HAI VECTƠ
 Đònh nghóa: Cho
AB a
;
BC b
. Khi đó

 Quy tắc hình bình hành . Nếu ABCD là hình bình hành thì
AB
+
AD
=
AC

 Quy tắc về hiệu vec tơ : Cho O , B ,C tùy ý ta có :
CBOCOB TÍCH CỦA VECTƠ VỚI MỘT SỐ
 Cho kR , k
a
là 1 vectơ được xác đònh:
* Nếu k  0 thì k
a
cùng hướng với
a
; k < 0 thì k
a
ngược hướng với
a

* Độ dài vectơ k
a
bằng k .
a

 Tính chất :


b
cùng phương
a
(
a

0
) khi và chỉ khi có số k thỏa
b
=k
a

 Điều kiện cần và đủ để A , B , C thẳng hàng là có số k sao cho
AB
=k
AC

 Cho
b
không cùngphương
a
, 
x
luôn được biểu diễn
x
= m
a
+ n
b

b)
AC
+
BD
=
AD
+
BC

c)
AB
+
CD
+
EA
=
ED
+
CB

d)
AD
+
BE
+
CF
=
AE
+
BF

4) 

MN BP
;
MA PN
.
5) Cho tứ giác ABCD, gọi M, N, P, Q lần lượt là trung điểm AB, BC, CD, DA.
Chứng minh :
;MN QP NP MQ

6) Cho tam giác ABC có trực tâm H và O tâm là đường tròn ngoại tiếp . Gọi B’ là điểm đối xứng
B qua O . Chứng minh :
CBAH '
.
7) Cho hình bình hành ABCD . Dựng
BCPQDCNPDAMNBAAM  ,,,
.
Chứng minh
OAQ 

8) 
a.
PQ NP MN MQ  
; c)
NP MN QP MQ  
;
b.
MN PQ MQ PN  
;
9) 

=
AE
+
BF
+
CD

c.
AB
+
CD
+
EF
+
GA
=
CB
+
ED
+
GF

d.
AB
-
AF
+
CD
-
CB

CHUYÊN ĐỀ BÀI TẬP HÌNH HỌC LỚP 10 ( có sử dụng tài liệu từ các nguồn khác).
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
1
4
GA . CMR
20MA MB MC  

17) 
a)
0OA OB OC OD   
;

4IA IB IC ID IO   
.
18) G G là tr tâ
a)
0GA GB GC  
b)
 
1
3
AG AB AC

19) G à tr tâm c tam giác ABC và 

AA' ' ' 3 'BB CC GG  

b)G M,N,P là các i tho:


AFAE AN MN  

28) 


a)
OA OC OB OD  

b)
BD ME FN

29) 

OM
=
OA
+
OB
;
ON
=
OB
+
OC
;
OP
=
OC
+

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4
32)  A
1
B
1
+ A
2
B
2
+ + A
n
B
n
= 0

33) Cho ngũ giác đều ABCDE tâm O Chứng minh :
OOEODOCOBOA 

34) Cho lục giác đều ABCDEF có tâm là O . CMR :
a)
OA
+
OB
+
OC
+
OD
+
OE

MB
+
MD
+
MF
( M tùy ý ).

35) Cho tam giác ABC ; vẽ bên ngoài các hình bình hành ABIF ; BCPQ ; CARS
Chứng minh rằng :
RF
+
IQ
+
PS
=
0

36)                       
0EA EB EC ED   
.
37) 
a)
0AN BP CM  
; b)
AN AM AP
;
c)
0AM BN CP  
.
38) 

. CMR v I b ki :
32IA IB IP  
.T qt tính ch trên.
44) Cho tam giác ABC và G là tr tâm c tam giác.Ch minh r
AG BG CG O  
. V I b kì
ta có :
3IA IB IC IG  
.
M thu o AG và
1
4
MG GA
. CMR :
2MA MB MC O  
. V I bki
24IA IB IC IM  
.
45) Cho t giác ABCD. G M, N c AB và CD . CMR :
a)
2AD BC MN
b)
2AC BD MN

c) Tìm v trí i I sao cho
IA IB IC ID O   

d) V M b kì, CMR :
4MA MB MC MD MI   


CHUYÊN ĐỀ BÀI TẬP HÌNH HỌC LỚP 10 ( có sử dụng tài liệu từ các nguồn khác).
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48) Cho l giác ABCDEF. G M, N, P, Q, R, S l l là trung i c AB, CD, EF, BC, DE, FA.
CMR hai tam giác MNP và QRS cùng tr tâm.
49) Cho hai tam giác ABC và A

B

C

là các i thu BC, CA, AB sao cho :

' ' ' ' ' '
,,A B k A C B C k B A C A kC B  
và
1k 
. CMR hai tam giác ABC và A

B

C

cùng
tr tâm.
50) Cho t giác l ABCD. G M, N , P, Q là trung i AB, BC, CD, DA. CMR hai tam giác ANP và
CMQ cùng tr tâm.
(Một số đẳng thức về trực tâm, trọng tâm, tâm đường tròn ngoại tiếp, tâm đường tròn nội
tiếp)
51) Cho tam giác ABC, G, H, O, I là tr tâm, tr tâm, tâm  tròn ngo ti và tâm  tròn

i I sao cho :
20IA IB

i K sao cho :
2KA KB CB

Cho tam giác ABC
a)Tìm i M tho mãn :
0AM MB MC  

b)Tìm i N tho mãn :
BN AN NC BD  

c)Tìm i K tho mãn :
0BK BA KA CK   

d)Tìm i M tho mãn :
20MA MB MC  

e)Tìm i N tho mãn :
20NA NB NC  

f)Tìm i P tho mãn :
20PA PB PC  

54) Cho hình bình hành ABCD. Tìm i M tho mãn:

4AM AB AC AD  

55) Cho l giác ABCDEF .Tìm i O tho mãn :

2 3 0; 2 0; 3 0PA PB QA QB RA RB      

CHUN ĐỀ BÀI TẬP HÌNH HỌC LỚP 10 ( có sử dụng tài liệu từ các nguồn khác).
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60) Cho tam giác ABC và M, N l l là trung i AB, AC.G P, Q là trung i MN và BC. CMR
: A, P , Q th hàng.Gi E, F tho mãn :
1
3
ME MN
,
1
3
BF BC
. CMR : A, E, F th hàng.
61) Cho tam giác ABC, E là trung i AB và F thu tho mãn AF = 2FC.
G M là trung i BC và I là i tho mãn 4EI = 3FI. CMR : A, M, I th hàng.
L N thu BC sao cho BN = 2 NC và J thu EF sao cho 2EJ = 3JF. CMR A, J, N th
hàng.
L i K là trung i EF. Tìm P thu BC sao cho A, K, P th hàng.
62) Cho tam giác ABC và M, N, P là các i tho mãn :
3MB MC O
,
3AN NC
,
PB PA O
.
CMR : M, N, P th hàng. (
1 1 1
,

TÓM TẮT LÝ THUYẾT :

 Trục là đường thẳng trên đó xác đònh điểm O và 1 vectơ
i
có độ dài bằng 1.
Ký hiệu trục (O;
i
) hoắc x’Ox
 A,B nằm trên trục (O;
i
) thì
AB
=
AB
i
. Khi đó
AB
gọi là độ dài đại số của
AB

 Hệ trục tọa độ vuông góc gồm 2 trục Ox  Oy. Ký hiệu Oxy hoặc (O;
i
;
j
)
 Đối với hệ trục (O;
i
;
j
), nếu

0
) khi và chỉ khi có số k thỏa x’=kx và y’= ky
 Cho M(x
M
; y
M
) và N(x
N
; y
N
) ta có
P là trung điểm MN thì x
p
=
2
MN
xx
và y
P
=
2
MN
yyMN
= (x
M
– x
N

= (2; 5),
c
= (4;1)

u
= 2
a

b
+ 3
c


x
sao cho
x
+
a
=
b

c


c
= k
a
+ h
b


Cho
u
= 2
i
 3
j
và
v
= k
i
+ 4
j

u
và
v

73) 
a
= ( 1;4),
b
= (2; 3),
c
= (1;6) Phân tích
c
theo
a
và
b


b
= ( 6;3)
e)
a
= (0;5) ,
b
= (3;0)
76) -
a/
23CM AB AC

b/
24AM BM CM

c/ ABCM là hình bình hành.

77) - 
a/
25AM BM CM

b/
2 3 0MA MB

\c/ ABMC là hình bình hành.
\
\
78) Tr


79) -3); B(1;0); C(3;2).

86) Cho A(-1;5) , B(3;-3)




e

OC AB
.

3DA DB AB

87) Cho A(1,2); B(2; 4); C(3,-3)







K Ox


88) --1;-
 
trùng nhau.
89)  3;2) ,B(2;4) ,C(3; 2).




CHƢƠNG II – TÍCH VƠ HƢỚNG CỦA HAI VÉCTƠ VÀ ỨNG
DỤNG

§1: GIÁ TRỊ LƯNG GIÁC CỦA MỘT GÓC BẤT KỲ ( TỪ
0
0
đến 180
0
)
TÓM TẮT LÝ THUYẾT
 Đònh nghóa : Trên nửa dường tròn đơn vò lấy điểm M thỏa góc xOM =  và M( x ; y)
*. sin góc  là y; ký hiệu sin  = y
*. cos góc  là x
0
; ký hiệu cos  = y
0

*. tang góc  là
y
x
( x

 0); ký hiệu tan  =
y
x

*. cotang góc  là
x
y
( y  0); ký hiệu cot  =

30
0
45
0
60
0
90
0
Sin 
0
2
1

2
2

2
3

1
Cos 
1
2
3

2
2

2
1

0
-cot 60
0
)
B= sin
2
90
0
+ cos
2
120
0
- cos
2
0
0
- tan
2
60
0
+ cot
2
135
0

102) Đơn gianû các biểu thức:
a) A= Sin 100
0
+ sin 80
0

2
3

106) Chứng minh rằng 1 + tan
2
x =
2
1
cos x
( Với x  90
0
)
107) Chứng minh rằng 1 + cot
2
x =
2
1
sin x
( Với 0
0
< x < 1800
0
)
108) Tính giá trò biểu thức:
A = cos 0
0
+ cos10
0
+ cos20
0

BC

d)
GB
và
GC
c)
GA
và
AC

§2: TÍCH VÔ HƯỚNG 2 VÉCTƠ
TÓM TẮT LÝ THUYẾT:
 Cho
OA
=
a
và
OB
=
b
. Khi đó góc AOB là góc giũa 2 vectơ
a
và
b
Ký hiệu (
a
;
b
)

= 
a

2
.
class="bi x4f y1d8 w73 h48" 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