Giáo án cô Bùi Thu Huyền hình học lớp 5 dành cho học sinh trường chuyên

CHƯƠNG I: VÉC TƠ
Bài 1: Các khái niệm cơ bản
và các phép toán cộng, trừ véc tơ, phép nhân véc tơ với một số



I. Mục tiêu:
  

 !"#$$
%%&$'$()*$$+
,  /& 0+
!"
1*23(45"6"0"7)289($5
",#$+
#$%&
:73;-,3,+
<-=!(4,
II. Chuẩn bị của giáo viên và học sinh:
>+ '()*+ ,-$./
,,-?0/(@A
BC!%!D4
'()*+ ,-0 
E"F
BC!%7
III. Phương pháp:
G(45-?HA+
IV. Tiến trình bài dạy:
 1%+2  345
 6789-* :
/(@

I8(6$(*$BJKB,DKG$
#84
Hoạt động của giáo viên Hoạt động của học sinh
1. Các khái niệm cơ bản
a) Vectơ
Vectơ2" ,DK)&L$
2"-,$=#$,DKMN
-O=",2"=P(=",2"=
(0+
b) Vectơ – không
Q)=P("=(0-%
$(2".; <=>+
c) Độ dài của vectơ
RS  Q  T(  )       !"  )  2"
,*$=P("=(0#$
Q)+
U3(2"
a
r
Q) !"'+
d) Hai vectơ cùng phương cùng hướng
?@$#$Q
AB
uuur
VQW2"
JK AB.XQ 
AA
uuur
?
JK9($YT(2"#$)+

Z1$Q2" A5B<5(5(
),,,[-%$(+
ZI5($Q%?,[
%&\&+
e) Hai vectơ bằng nhau
1$Q2"bằng nhau5(
%&"% !"+
I5($Q
a
r
"
b
r
'$(?$
5
a b=
r r
+
f) Góc giữa hai vectơ:
, $    
a

 " 
b

T(      
+G. =]",)$^
_L 5`
_L 5`
  3!a>,?(

Ybc+BK`",!&
/4$d
Y+
DACDBCAB ===
b+
eeee
DACDBCAB ===
+Yb
e 
fb
e 
fc
e 
fcY
e
c+YbfbfcfcY+
_L 5`
Y
b
Hình 1
 
AO

f
a

 g
BO

f

b

+U)0,#$
)Y]b2"0,#$)*$$
a

"
b

$42")*$$
a

"
b

"3(2"V
a


b

W+
I5(V
a


b

Wfhi
i

?$)-'$
a

"
b

()&$(3(2"
a


⊥

b

+
2. Các phép toán cộng, trừ vectơ và nhân
vectơ với một số.
a) Phép cộng vectơ
Định nghĩa: Cho hai véc tơ
a
và
b
. Từ một
điểm A bất kỳ ta lấy
AB
=
a
;
BC
=

b
thì
AC
được gọi là véctơ tổng của hai véc tơ
a
và
b
.
U3(
AC a b= +
uuur r r
<2H4j#$$Q2"
 Q+
Tính chất:
ZG3H$,, :
a b b a+ = +
r r r r
* G3H5:
V W V Wa b c a b c+ + = + +
r r r r r r
ZG3H#$Q:
ia a+ =
r r r
Các quy tắc:
* C(D *-%78
&$=HkA, B, C+G$)

AB BC AC+ =
uuur uuur uuur
?C(D E*E

,ABCD 2"?"+G$)
_L 5`
3!ae,l=Yb
c+BK`",!&/4
d
Y+
BDACCDAB +=+
+
b+
BCADCDAB +=+
+
+
CBADCDAB +=+
+
c+
BCDACDAB +=+
+
3!am+1M4T
-,T$(
Y+  G`    Ybc 2"  ?
?"5(
CDAB =
+
b+ G`  Ybc  2"  ?
?  "  5(
i=+++ DACDBCAB
+
+ G`  Ybc  2"  ?
?"5(
ADACAB =+

+

Y
b

AB AD AC+ =
uuur uuur uuur


?C(D E&5
,? ABCD.A’B’C’D’ . G$)

n nAC AB AD AA= + +
uuuur uuur uuur uuur
b) Phép trừ véc tơ
?F <%: I5(
a

≠

i
?
∃

x
$,,
x
o
a
f

i
g
x
2"0#$
a
"3(2"
a
+
 ZĐịnh nghĩa1(#$$ 
a
"
b
2"j#$
a
"0#$
b
3
(2"
a

b
+74
a

b
f
a
oV
b
W+

<2H4(#$$Q2" 
 Q+
* C(D 9G : &$=Hk]Y
b$)
OB

OA
f
AB
c, Phép nhân véc tơ với 1 số
* Định nghĩaG3 
a
 & 0
62" 3(2"k+
a
;
p$(
I5( k qi?Q k
a
 %&&
Q 
a
+  I5( k r  i  ?  Q k
a
 
Ví dụ 4: ,  ?   
Ybc+Ysbscss&/]+
1M4  N  -$  K  `  $
-,K`$(/4
Y+

Ynn AADABAC ++=
+
b+
inn =+++ ADCDBCAB
+
+
Ynnc AABDAD +=+
+
c+
AOCOCCBCAB +=++ nn
&5`+
3!at: ,m=H?
Yb+BK`",!&
/4d
Y+
CACBAB −=
+
b+
ACABBC −=
+
+
BACBAC =−
+
c+
ABCBCA =−
+
3!au,$Yb+
R2" =-8,D
b  $,  ,  RbfeR+
`    -'

Y
c

b
Y
c
Ys
cs

s
bs
b
&&Q
a
+
B 2&
+ +k a k a=
r r
?H I
o+
i
f
i

oV+
a
WfV+W+
a
oV
a

o
b
Wf
a
o
b

oVoW
a
f+
a
o+
a

Phần trắc nghiệm
Câu 1.  ,?`!Ybc)-
/+RT",$(/42"$d
Y+
WV
l
>
ODOCOBOAOG +++=
+
b+
i=+++ GDGCGBGA
+
+
WV
m
e

ADACABAG ++=
+
c+
WV
l
>
ADACABAG ++=
+
Câu 2. ,`!Ybc+2"-
/#$`!"Ys2"-/#$$
bc+G-,Kp$(K
p",2"$d
Y+
i=+++ GDGCGBGA
+
b+
n
m
e
AAGA −=
+
+
MGMDMCMBMA =+++
&R2"
 =H?+
c+
m nAB AC AD AA+ + =
uuur uuur uuur uuur
Câu 3.,u=Ybcvw+BK
`",!&/4d

 Y+
iw =+++++ DEEBCFACDAB
+
 b+
ww ADEEBCFACDAB =+++++
+
 +
vw ADEEBCFACDAB =+++++
+
> e
m m
AM AB AC= +
uuuur uuur uuur
+
3!ax ,$Yb
?  7    =  R  @$
M
$W
MA BC MA MB+ = −
uuur uuur uuur uuur
+
W
kMA MB kMC+ =
uuur uuur uuuur
+
Phần tự luận:
Bài 1.,$Yb
+<yz2P22"-(
=#$DYbb
Y+1M4^?"?-8

?  ^        '
<y QR RP
uuur uuuruuur
+
Bài 2. ,  $  
Yb+2"-/#$
$Yb"R2"=
(k+`-'
$W
iGA GB GC+ + =
uuur uuur uuur r
+
          W
mMA MB MC MG+ + =
uuur uuur uuuur uuuur
+
 c+
cw ADEEBCFACDAB =+++++
+
Câu 4.BT(",!&/42"P"#
==]2"-(=#$,DYb+
Y+]Yf]b+
b+
OBOA =
+
+
BOAO =
+
c+
i=+ OBOA

Bài 3. ,$$
Yb"Ysbss)-/
2P22""s+`
  -'
n n n nGG AA BB CC= + +
uuuur uuur uuur uuuur
+
V.Củng cố và hướng dẫn học ở nhà:
 U/(2D5`T",+
 {8(P(2""7-,|G
1(:p5`TQ%QCK
"!a+

Bài 2: Véc tơ cùng phương, véc tơ đồng phẳng và áp dụng


#
I. Mục tiêu:
  

%BpL$p2}"9(+
CKBpL$p2}"9(+
!"
1*23(45"6"0"7)289($5
%CK+
o`e%
o`$=K"
o`mCK
o`0=CK
#$%&

:73;-,3,+
<-=!(4,
II. Chuẩn bị của giáo viên và học sinh:
 '()*+ ,-$./
,,-?0/(@A
BC!%!D4
'()*+ ,-0 
E"F
BC!%7
III. Phương pháp:
G(45-?HA+
IV. Tiến trình bài dạy:
 1%+2  345
 6789-* :
/(@
I8(9(4#$ y(4m=9(4?
?"9(4-(=9(4-/+
#84
Hoạt động của giáo viên Hoạt động của học sinh
1. Vectơ cùng phương
* Định nghĩa1$Q2"%
5(),,,[
'$(+
* Định lýQ
b
%&Q
a
V
a


≠

i
W"N)0$,,
b
f+
a
+

ZHệ quảBT(P"#=$=
/YbK"2")$,,
AB
f+
AC
+
Z{8(P(2"3!a!a
9(+
2. Vectơ đồng phẳng
* Định nghĩab$
a

b

c

2" C K 5(2P2'-8
$[K ,,V,[-%
$(W+
* Định lý
I5($

a
g
b
 (45?
$
a

b

c
CK"N
CD!(4H[02$,,

c
f+
a
o2
b
+
     I5($ 
a

b

c
  C
_L 5`
_L 5`
3!a>,$Yb+
  Ys  bss  2P  2  2"

-(=DbY
Yb+     
nn BA
 %
&",d
 Y+
AB
+
b+
nAC
+
+
BA
+
c+
BCn
+
_"3!a!a
9($(
3 !a  e ,  ?   
Ybc+Ynbnncn+    ~  2"
-(  =  #$ bnng  R 2"
=$,DcnQ,•
0egI=$,Dbc
K?
∀
x
T(CD!(4H $0
2$,,
x

f+
a
o2
b
o+
c
+

Z Hệ quảb0=]Yb%'
-8 [K"N
OCOBOA 
CK+

Z{8(P(2"3!a!a
9(+
Bài tập:
Câu 1:G-,T$(T
",2"$d
Y+,$%
ba
+U)$
cba 
CK
"N)[0$,,
bnamc +=
+
b+I5()
i=++ cpbnam
" -,
$0i?$

cba 
C
K+
+b$
cba 
CK"
N$)%)(  
[K+
c+b$$];]4]€()&
$(. ?$$)C
K+
Câu 2: ,$=/Yb"
 =]H?+1M4;;QT",
$(/42"d
Y+B=R( JKYb
"N
BAkOBOM ==
+
b+B=R( JKYb
Q,  •  0  e+  `  
-'  $  =  ~RI  K
"+

3  !a  m  ,  $  
Yb2H4=~•,M

e
m e i
IA IB
JA JC

=
+ =
uur uur
uur uuur r
`-'~•9($
-  /   #$ $ 
Yb+
3!al1M4?T
$-,T$(
Y+b$     
cba 
C
K5() -,$
)'
i
+
b+b$
cba 
CK
5()$-,$)
%+
+  G-,  ?   
Ybc+Ysbsscs$    
nnnn DAACAB
CK+
c+     
cbax ++=
 2(
2(CK&$


ba
+

"N
WV OAOBkOBOM −==
+
+B=R( JKYb
"N
OAkOBkOM W>V −+=
+
c+B=R( JKYb
"N
OAOBOM +=
+
Câu 3:,$=RI<K"
-,)=I'*$$=R"<+
U)[",!&/4%&d
Y+
MN
"
PN
+b+
MN
"
MP
+
+
MP
"
PN

+c+
NM
"
NP
+
Câu 4:,$T(Yb&J
$,Y1+BK`",!&/4d
Y+
HCHB =
+b+
HCAC e=
+
+
BC
e
m
Y1 =
+c+
ACAB =
+
Câu 5: ,?$Ybc&D
42"Ybfm$cfu$+U)
CDAB +
'$,8(d
Y+h$+b+m$+
+m$+c+i+
Câu 6: ,$T(Yb)D
'$+-p
CAAB −
'$,8(d

Ye$+b+$+
+
ma
+c+
e
ma
+
Câu 7:,=b'*$$=Y
"&Ybfe$Yfu$+BK`",
!&/4d
Y+
ABBC =
+b+
ABBC e−=
+
+
ABBC l=
+c+
ABBC e=
+
Câu 8:,$=/Yb+
  3 !a  t  , ? 27
  Ybc+ Y
>
b
>

>
c
>

+
  =  R  I  2P  2
( DYcbb
>
$,
,YRfbI+`
-' 
DBABMN
>

 C
K+
3!au ,2\-a$
Yb+Ynbnn+~U2"
-(=#$bbn"Ynn+
R  2" =  $ ,D  bnn
Q,•0
e
>
+`
-'0=YU~R
%(  [K+
b"7
Câu 10:,$=0
pY"b/+G7
=R,MK
`
ABkMBMA =+
&>r
r>2"

Y+  ‚Ybƒ+
b+BJKYb ,D
Yb+
+  B,D  K  Yb+
c+BJ-X/~&~2"
-(=#$Yb+
I5(
ACAB m−=
?K`",!&/4
d
Y+
ACBC l=
+b+
ACBC e−=
+
+
ABBC l=
+c+
BABC e−=
+
Câu 9:,Yb2"$=/+R
2" =,MK`
i=+ MBkMA
+  UK  p  ",  $(  /4
d
Y+Uf>?R2"-(=#$
Yb+
b+Uf>?R0;`&Y
9($b+
+Ufi?R-%&Y+

c+Ufe?R0;`&b
9($Y+
Câu 11: &  $  =
Yb    K  "+
G7=R,M
MCnMBmMA +=
 &o
fi2"
Y+G7-S+
b+BJKb+
+BJK9($Y
",,&b+
c+BJK9($Y
"()&b+
V.Củng cố và hướng dẫn học ở nhà:
 U/(2D5`T$%$C
K+
 {8(P(2""7|G
E72D5`MT3&#$$Q,+

Bài 3: Tích vô hướng của hai véc tơ và áp dụng



I. Mục tiêu:
  

G3&#$$BpL$3H+
b?&+
!"

1*23(45"6"0"7)289($5
G3&#$$+
oG33&
oG3)*$$
o`K`
#$%&
:73;-,3,+
<-=!(4,
II. Chuẩn bị của giáo viên và học sinh:
 '()*+ ,-$./
,,-?0/(@A
BC!%!D4
'()*+ ,-0 
E"F
BC!%7
III. Phương pháp:
G(45-?HA+
IV. Tiến trình bài dạy:
 1%+2  345
 6789-* :
/(@
I8(`
b$=K"
b0=CK
#84
Hoạt động của giáo viên Hoạt động của học sinh
H .>B4 ,--.; <
aJK+!-
  G3&#$$Q
a

r
"
b
r
2"
 03(2" 
a
r
.
b
r
;pA
( )
+ + ab a b cos a b=
r r r r r r
+
Tính ch\t:
*
a
.
b
=
b

a
* (k.
a
.).
b
= k.(

a
.
b
)
*
a
.(
b
+
c
) =
a
.
b
+
a
.
c

*
a
.(
b
-
c
) =
a
.
b
-

a
.
c
*
a

⊥

b

⇔

a
.
b
= 0
,848(P(2"3!a"
&!„,,2"3!aQ,p
L$"3H+
B0c
3  !a  >:,  $     
 AAB
)
i
mi
…
eYb === AaAC
+UKp",!&
/4d
Y+

e
l+ aACAB =
+
b+
e
m+ aACAB =
+
+
el+
e
aACAB −=
+
c+R 59(+

_L 5`
_L 5`
3!a>
B0c
+
+
3!ae:,$T(Yb)Ybfm$
?
+AAB
7-p",!&/4
Y+h$
e
+


b+

e
h
$
e
+
+h$
e
+
c+
e
h
−
$
e
+
3!am,?(YbcD'
> /  ]+  &    3& 
BCOB+

DCOB+
 
ODOB+
 " 
OAOB+
 ?  0  3  
&)59('
e
>
−
2"

Y+i+b+>+
+e+ c+l+
 E5B<.>B4
?K+!-
b?&#$ Q
'? !"#$)U3
(
e
ie
i,+ aaaa

==
+
,8,2"3!a"&
!„!a23(45=2"+
# L5M
,8-$"7!a3
&#$$+
Bài 1. ,$ ABC &$J
-((45AD, BE, CF+`-'
+ + iBC AD CA BE ABCF+ + =
uuur uuur uuur uuur uuuruuur
,8&!„2""
†!a9(4-(=$)
eAD AB AC= +
uuur uuur uuur
3!aeB0b
3!amB0b
Ví dụ 4: ,$T(
Yb)D$"-/

+ G3    3   &
$(
AB
+
AC
g
BCCA


+
g
BAGA


+
g
CGBG


+
g
AGGB

+
g
CBAG

+
+
b">12""Q,

&!„#$,8+
G$)

+ + +
>
+ V W
e
>
+ V W
e
>
+ V W
e
i
BC AD CA BE AB CF
BC AB AC
CA BA BC
AB CA CB
+ +
= +
+ +
+ +
=
uuur uuur uuur uuur uuuruuur
uuur uuur uuur
uuur uuur uuur
uuur uuur uuur
b"e12""Q,
eBE BA BC= +
uuur uuur uuur

eCF CA CB= +
uuur uuur uuur
G.)!%3H#$3&
(4-$T(`+
Bài 2. ,,DKAB) !"2a"
k
2
+  G?  7      = M $,  ,
e
+MA MB k=
uuur uuur
+
,8&!„2""+
‡?&j
e
e
V WV WAB AM MB MA MB
a
= + +
=
uuur uuuur uuur uuur uuur
G5a/&=?7
=R+
Bài tập
Câu 1.,J-X(O;R)"=R
0p+R JK
∆
$4j2(
9($RJ-XD$=Y"
b+`-'


e e
+MA MB MO R= −
uuur uuur
Câu 2. ,? 27  Ybc+
Ynbnncn)D'$+G-8bc"Ycn
2H4$=RgI$,,cRfYIf
m
ea
+
`-'RI2"J()
(#$bc"Ycn+
Câu 3.,? Ybc+Ynbnncn+
1$[KVYnbcW"VbncnWYnD
gn+`-'
$+gnQ,`62"-/
∆
Ynbc"
∆
bncn+
+Yfnfn+
Câu 4: , 
α
 2" )*$ $  J
&!„#$,8

e
e
e e e
e e e e

V WV W
e +
e
AB AM MB MA MB
a
AM AM MB MB a
MA MB a k
= + +
=
⇔ + + =
⇔ + = +
uuur uuuur uuur uuur uuur
uuuur uuur
G.)(4-$/=R
@$MT(-8+
Câu 7: ,$=0
p  Y  "  b+G7    
=R$,, 
aAMAB =+
V$2"'0W2"
Y+ R   J  K
,,&Yb+
b+ BJ  -X  7
/  2"  -(  =
#$Yb+
+BJK(
)&Yb+
c+ BJKYb+
Câu 8: I5(  ?  ,
Ybc)Ybf!"

i
ui
…
=B
?@,",!&/4
d
Y+
e
+ dADAB =
+
b+
e
+
e
d
ACAB =
+
+ 
e
m
+
e
d
ACAB =
+
K`$$
>
v
r


e
v
uur
+UKp",
!&/4d
Y+
> >
e e
+ iv v v v= ⇔ ⊥
r uur r uur
+
b+
>
e > e
+ + ,v v v v
α
=
r uur ur uur
+
+
e e
> >
e e
v v v v= ⇒ =
r uur r uur
+
c+
e e
V + Wv v v
uur uur r

2" 0+
Câu 5: , 
α
 2" )*$ $  J
K`$$
v

>
v
+UKp",
!&/4d
Y+
> >
e e
+ + ,v v v v
α
=
r uur r uur
+
b+
e e
> >
e e
v v v v= ⇒ = −
r uur r uur
++
> e
V + Wv v v
ur uur r
2" 0+

c+
>
v
r
%&&
e
v
uur
> e > e
+ +v v v v⇒ =
ur uur ur uur
+
Câu 6:,$Yb(/D
b+I5(Ybf?K`",!&/4
d
Y
e
+ kACAB =
+b+
e
+ kACAB −=
+
 
kACAB e+ =
+c+
kACAB e+ −=
+

c+
e

+
e
d
ACAB −=
+
Câu 9: ,  $  
Yb+G7=R
$,,
ABMA+
f
CAM Y+
2"
Y+BJK+
b+BJ-X+
+G7-S+
c+B=Y+
Câu 10:,Yb2"$
T(D$+G-,
Kp$(Kp
",2"$d
Y+
e
+
e
a
ACAB =
+
b+
e
+

e
a
AGAB =
+
+
u
+
e
a
BGAG −=
+
c+
l
+
e
a
GCGA −=
+
V.Củng cố và hướng dẫn học ở nhà:
 U/(2D5`T3&#$$
?&+
 {8(P(2""7|G


Bài 4: Ôn tập



I. Mục tiêu:
  

E72D
",  /
& 0+
%CK"!a+
G3&#$$"!a+
!"
1*23(45"6"0"7j)28
9($5",  
/ & 0, %CK"!a
3&#$$"!a+
#$%&
:73;-,3,+
<-=!(4,
II. Chuẩn bị của giáo viên và học sinh:
>+ '()*+ ,-$./
,,-?0/(@A
BC!%!D4
'()*+ ,-0 
E"F
BC!%7
III. Phương pháp:
G(45-?HA+
IV. Tiến trình bài dạy:
 1%+2  345
 6789-* :
/(@
{8(P(2D5`M#$+
#84
Hoạt động của giáo viên Hoạt động của học sinh
Giáo viên yêu cầu học sinh làm các bài

tập sau:
Câu 1:,
v

>
v

e
v
2"$H?2"
06+<@,",!&/4d
 Y+
e>e>>
++ vvvvvv =⇒=
+
b+
e>
W+V vvv
f
W+V
e>
vvv
+
 +
WV
e>
vvv −
f
e>
++ vvvv +

+
c+
W+V
>
vkv
f
W+V
>
vvk
+
Câu 2:I5( 
e>
+vv
fi" 
me
+vv
fi?K
p",!&/4d
 Y+
m>
vv =
+
b+
m>
vv −=
+
 +
i
m>
== vv

+
c+
m>
vv
,,+
Câu 3 : _\-a$Yb+Ysbss+B[
n   AA a AB b AC c BC d= = = =
uuur uuur uuur uuur
+G-,=(
`$(=(`",2"d
Y+
cba +=
+
b+
i=+++ dcba
+
+
i=−+ cdb
+
c+
dcba =++
+
Câu 4 : ,?*7Ybc+G-,
K`!&/4K`",d
Y+
CDAB =
+
b+
DABC =
+

Câu 1:Bc
Câu 2
Bc
Câu 3B
Câu 4Bc
+
BDAC =
+
c+
BCAD =
+
Câu 5:,=b'*$$=Y"
&Ybfe$bft$+B !" 
AC
'$,8(d
Y+x$+
b+m$+
+
e
ta
+
c+>i$
e
+
Câu 6:,?(Ybc)D'
$+U)-p
CDAB +
'$,8(d
Y+
eea

+b+e$++$+c+i+
Câu 7:,$$Yb"Ysbss2P
2)-/2""s+BK`",
!&/42"$d
Y+
nnYnnm CCBBAGG ++=
+
b+
nnbnnm CABCAGG ++=
+
+
nnnnm CBBAAGG ++=
+
c+
nnYnnm CCBBAGG ++=
+
Câu 8:I5(2"-/$Yb?
K`",!&/4d
Y+
e
ACAB
AG
+
=
+b+
m
ACAB
AG
+
=

+
+
e
WVm ACAB
AG
+
=
+c+
m
WVe ACAB
AG
+
=
+
Câu 9:I5( 
CDMNAB +Yb+ =
?Kp
",!&/4d
Y+
MNCD =
+b+CD = MN.
+
MNCD −=
+c+R 59(+
Câu 10: G-,Kp$(K
p",$d
Câu 5
BY
Câu 6
Bc

Câu 7
Bc
Câu 8
Bb
Câu 9
BY
Câu 10
B
Y+I5(
OBOA u=
?
OBOAOBOA ++ =
+
b+I5(
OBOA m−=
?
OBOAOBOA ++ −=
+
+I5(
OBOA e=
?
e
e+ OBOBOA =
+
c+R -,$Kp-8$+
Câu 11: G-,Kp$(K
p",d
Y+I5(
e>
vv

,,?
e>
+vv
qi+
b+I5(
e>
+vv
f>?
e>
vv
%&+
+I5(
e>
+vv
f>?
e>
vv =
f>+
c+I5(
e>
vv −=
?
e>
+vv
f
WV
e
>
v−
+

Câu 12:UKp",!&/4d
Y+
e>
W+V vvv
2"+
b+
e>
WV vvv +
2"+
+
W+WV+V
e>
vvvv
2"+
c+
i+v
2"+
Câu 11
Bc
Câu 12
BY
V.Củng cố và hướng dẫn học ở nhà:
 E72DH2}(45#$+
 {8(P(,""5"7,48(P(2""
*"DMˆ$+

CHƯƠNG II: Đường thẳng và mặt phẳng trong không gian
Bài 1: Đại cương về đường thẳng và mặt phẳng
NN#
OJ#N.

NN#
#
I. Mục tiêu:
  

3H.$7-,?$+
BT(;p[K+
U?`!"?)+
 ",`m=K"?$,(45#$
$[K?$,=#$JK"[K;p5
!+
!"
1*23(45"6"0"7)289($5
`m=K"?$,(45#$$[K?$,
=#$JK"[K;p5!++
#$%&
:73;-,3,+
}^?73;+
<-=!(4,
II. Chuẩn bị của giáo viên và học sinh:
 '()*+ ,-$./:
,,-?0/(@A
BC!%!D4
'()*+ ,-0 
E"F
BC!%7
III. Phương pháp:
G(45-?HA+
IV. Tiến trình bài dạy:
 1%+2  345

 6789-* :
/(@
G??[K$("$JK,
$(-,2&d
# 84
Hoạt động của giáo viên Hoạt động của học sinh
1. Các tính ch\t thừa nhận của hhkg:
Tính ch\t 1:) "N JK
9($$=/+
Tính ch\t 2:) "N [K
9($$=K",-&.
Tính ch\t 3: GCDl=%'
-8 [K+
Tính ch\t 4:I5($[K/)
 =(?)JK
(!(4H`$H=(
#$$[K)+
Tính ch\t 5:G-,S[K5
9(M5#$?KT(
2. Điều kiện xác định của mặt phẳng
_L 5`
_L 5`
_L 5`+
$WR[K,",";p5(
5)9($$=K"+
WR[K,",";p5(
5  )     = " `$     J
K9($=)+
WR[K,",";p5(
5)`$$JK$(+

3. Hình tứ diện và hình chóp
a) Hình chóp
G-,[KV
α
W,$
> e
+++
n
A A A
"
, =|',"V
α
W+I0S &
N A
>
, A
e
, ,A

 $ n $
SA
>
A
e
, SA
e
A
m
, , SA


A
>
. 1?C$
Y
>
Y
e
+++Y

"$|Y
>
Y
e
|Y
e
Y
m
+++
|Y

Y
>
 2"?)"3(2"
|+Y
>
Y
e
+++Y

+

B=S2"N#$?)+
,DKA
>
A
e
, A
e
A
m
, , A

A
>
2"
D4#$?)+
B$A
>
A
e
A

2"[4#$?
)+
,DKSA
>
, SA
e
, , SA

2"

D8#$?)+
_L 5`
&5`

T$ SA
>
A
e
, SA
e
A
m
, , SA

A
>
2"[8#$?)+
I5(4#$?)2" T$
`+++??)`2"?
)$?)`+++
WG`!
 ,0=YbcC
K+1?C0$YbYc
Ybc"bc2"?`!V$4
2"`!W"}(2"Ybc+
=|bc2"N#$`
!+
,DKYbbccYYbc
2"D#$`!+
1$D)=(2"$

D0!+
$YbYcYbc"bc
2"[#$`!+
BN'-8 [2"N
0!&[)+
4. Các bài toán cơ bản
Bài toán 1: `$=K"
  B=`m=YbK
"$P`Yb'-8
$,(45#$$[K+
,8&!„2""+

&5`+

Ví dụ 1.,$ABC
B=`cvwK"P
`'-8$,(45#$
$[KVYbW"VYsbssW+
Bài toán 2: G?$,(45#$$[
K
B=?$,(45#$$[KV
α
W
"V
β
W$P?$=Yb%( 
$[KM,+$,(45P?2"
JKYb+
,8&!„2""+
$,(452"

VYscW"VYbcW2"c
VYscW"V|YbW2"YsvVv2"$,#$Yb
"cW
VYscW"V|bW2"wVw2"$,#$Ysv
"|bW
VYscW"V|cW2"c
VYscW"V|YcW2"Ysc
"    = O ' ,"
[  K  VABCW+  A’,
B’, C’ 2"=2P2
-8,DKOA, OB,
OC "-%&
P(#$,DK
)+`-'5(
[JKA’B’ "ABg
B’C’"BCgC’A’"CA
$(2P2DD, E, F?
$=D, E, FK"+
_L 5`+
Ví dụ 2. ,?)`
S.ABCDAB"CD
$(+   A’ 2"     =
' *$ S " A+G? 
$,  (45  #$  VA’CDW
&[KVABCDW
VSABWVSBCWVSCDWVSDAW+