GIÁO ÁN HÌNH HỌC 12 HKII (2015 2016)

Hình học 12_HKII – Nguyễn Phúc Đức
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Hình học 12_HKII – Nguyễn Phúc Đức

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Hình học 12_HKII – Nguyễn Phúc Đức
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Hình học 12_HKII – Nguyễn Phúc Đức
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./$%
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89.5:&1.5)&+23- ./%
;.5 .123%
$*+ ,-#
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A BC/%A-35 D %
'$./01#H.123%
*$"234#
5 +67 !#& E"F-G

HD %
" *%
5/8 #&I)JD .'KLF-G
<M?1%
" *KNEO%
9$ %.:#
9$;,4<&7=> ?1@ A#69B/ 'C'(I *%
9$' ?1.B1 A#
=A?&%
9$*C= 1D #
Hoạt động của GV và HS Nội dung bài học
PQG
=R;G&
P[OTBQ9C23:t
+%
4jUdk-?1\
=PXGRD?
>TBQ9C
ROM =
)^ .123
PQ$G
=R;G &N&9B+
=PXGN9B+%
=R;Gf.+)*$
=PXG";l$
=R;Gu )*1 .
& .1,v0.5\
G$ghiQ
C= 6+#; .123:t,770
+

Rd,V7O7Y0B&wN23
-    -G 
( ) ( ) ( )
( ) ( ) ( )
'
'''
'''
rczbyax
rczbyaxOM
=−+−+−⇔
=−+−+−=
4TU#4UVOY23,X0:
t,7  7  0    +    -  .  1  B&  G
( ) ( ) ( )
$ $ $
$
# %  & $ ' )− + − + − =
,v0
;l

G .123:t,7=$7`0+
kmB&
( ) ( ) ( )
']*'
'''
=−+++− zyx
;l
$
GH.123:U+B&
''''

rzyx =++
H.  1  ,v0  -  )Q  Q    B&G
P'''
'''
=+−−−++ dczbyaxzyx
,vv0
;/
''''
rcbad −++=
ZfjG
d  .  1  -  )Q
Trang 5
Hình học 12_HKII – Nguyễn Phúc Đức
=PXG;)Q .1
,v0
=R;G<& .1,vv0B& .
1.bF\
=PXGKDV!
PQ`G
=R;Gf.+)*`
=PXG";l`
PQG41:&+23
=R;G41:&+23
lQG
$ $ $ $
0 , 0 , 0,# %  & $ ' )+ + =− − −
$ $ $
$ $ $ ]#  $ !# " $ *+ + + + + + =
=PXG"Bb&"&D %
P'''

'''
=+−−−++ dczbyaxzyx
 /
P
'''
>−++ dcba
B&  .  1  2  3  :
t,770+
dcbar −++=
'''
;l`G  8  9  :  &    +  2  3  -
.1G
P'k9
'''
=+−+−++ zyxzyx
R"%
H.  1  2  3  -  )Q
P'''
'''
=+−−−++ dczbyaxzyx





=
−=
=
⇔






=−
=−
−=−
⇒

*
'
''
k'
9'
c
b
a
c
b
a
;DO  :  t,$7=`70    +
*
'''
=−++= dcbar
&G41:&+23-
.1G
x
$ $ $
0 , 0 , 0 y, ` z #  $+ + =− − +
4:t,`7z7{0+k`

x
$ $ $
r $ r $r ]#  $ #  $+ + − + − − =
4:t,`7{7|0
+
$ $ $
, 0 | $r ]`) + − + + ==
x
$ $ $
$ $ |$ z $ ]] ]#  $ #  $+ + + − − − =
$ $ $
z $ r m] ]#  $ #  $+ + +⇔ − − − =
4:t,{$77`0
+
$ $ $
 ` m] |, $0) + + + == −
)x
$ $ $
| $  ]#  $ # + + − − + =
x
$ $ $
` ` r` | m ` ]#  $ #  $+ + − + + − =
9$90"X Y3= Z[J\#
=; .123:t+
9$]D@^/8 _/#
=f(/&p&OGT.5 .123%
=f(/&p Gq&&D XR<
]$`>  A1#
=>)G%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

=H.  G%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
=Xs)*I)J9)QOG%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Trang 6
Hình học 12_HKII – Nguyễn Phúc Đức
 NL
 
 !"#
$ %&#
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Hình học 12_HKII – Nguyễn Phúc Đức
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0 , 0 , 0 m, ` ` #  $+ + =− + −
x4:t,{$77{`0&B&Ut
+Utk
$ $ $
, 0, $0 ` z+ − + =−
;DO .123B&G
$ $ $
0 , 0 , 0, $  ` z#  $+ + =+ − −
)xA-:t,,m7{`7~0&+k$
;DO .123B&G
$ $ $
0 , 0 , 0, m ` ~ z#  $+ + =− + −
9$90"X Y3= Z[J\#
=;+"
=; .123:t+

9$]D@^/8 _/#q&&D XR<FBQ%
]$`>  A1#
Trang 8
Hình học 12_HKII – Nguyễn Phúc Đức
 'ghn
9: 9
 !"#
$ %&#
P  O2 W%
 .16@2 W?-2''$2
W+"j2 W%
$'()#
89.5  O2 W%
 .16@2 W&+.5"j
2 W%
$*+ ,-#
.#<4=<>/?<4=<>@%
A BC/%A-35 D %
'$./01#
=;  O2 W%
=H.16@2 W%
*$"234#
=R;G .  %
=PXGMBN@2 Wn .  O2
W%
9$ %.:#
9$;,4<&7=> ?1@ A#69B/ )%
9$' ?1.B1 A#
=A
, 7 7 07 , 7 7 07 , 7 7 07 , 7 7 0

! ! ! " " "    * * *
! #  $ " #  $  #  $ * #  $
 $ $  $ `  $ `
, 7 7 07 , 7 7 07 , 7 7 0% % % % & & & & ' ' ' '= = =
r
r r
>N
9$*C= 1D #
Hoạt động của GV và HS Nội dung
PQG
=R;G Nhắc lại khái niệm vectơ pháp
tuyến của đường thẳng, vectơ chỉ phương
của đường thẳng đã học.
- HS: Vectơ pháp tuyến là vectơ
0≠
r
vuông góc với đường thẳng đó.
Vectơ chỉ phương là vectơ
0≠
r
nằm trên
đường thẳng song song hoặc trùng với
đường thẳng đó
PQ$G
=R;G/++-
./&1%
=R;G )*";l
=PXGi"&.@"%
t%;  O2 WG
f9CGVectơ

r
n

0≠
r
được gọi là vectơ pháp
tuyến của mặt phẳng
( )
α
nếu đường thẳng chứa
vectơ
r
n
vuông góc với mp
( )
α
(gọi tắt là vectơ
r
n
vuông góc với mp
( )
α
)
Kí hiệu:
r
n
⊥
mp
( )
α

vAK}G
> 
r
n
B& vect  OJ2 W1
r
kn
cMB&;4H42 W-%
>trong hệ tọa độ Oxyz nếu
a
r
= (a
1
, a
2
, a
3
),
b
r
= (b
1
, b
2
, b
3
) là hai vectơ không cùng phương và
các đường thẳng chứa chúng song song hoặc nw
trong một mp
( )

α
thì vectơ
n
r
=
a,b
 
 
r r
=
2 3 3 1 1 2
2 3 3 1 1 2
a a a a a a
, ,
b b b b b b
 
 
 
 
là một vectơ p
tuycủa mp
( )
α
.
Khi đó cặp vectơ
a
r
,
b
r

được gọi là cặp vectơ chỉ
Trang 9
Hình học 12_HKII – Nguyễn Phúc Đức
x
€  •% &
r
r
k,{$z7{$7{$0
x
€  •% &
r
r
k,$z7`7$~0
=R;GDV!'s'BD%
=R;Gu )*i;l$%
=PXGi"&.@"%
,$77 $0!" = −
uuur
, $7r7]0! = −
uuur
 •€ ,$7$z7$z0!" ! = =
uuur uuur
r
PQ`G
=R;G'&'OC?$
&
=R;G/ .16@
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=PXG)‚! %
=R;GNBD  @2 W

=PXG1&  O
2 W
PQzG
=R;G )*9C .1
2 W%4i;l`;lz%
=PXGi"+)*%
=R;GDV!'s'%
phöông cuûa mp
( )
α
.
;+)*G4+
€  •% &
r
r
G
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%
r
k,`7]7{r0
&
r
k,$7{z7]0
x
%
r
k,7{r7$0
&
r
k,z7`7{m0

R"G
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€  •% &
r
r
k,{$z7{$7{$0
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€  •% &
r
r
k,$z7`7$~0
;+)*$G4UVOY`o,$7{
7`0,z7]70A,{]7m7`0%41
 O,oA0
,$77 $0!" = −
uuur
, $7r7]0! = −
uuur
 •€ ,$7$z7$z0!" ! = =
uuur uuur
r
tt%H.16@2 WG
%f9CG .16@2 W
B& .1-)QoVOAYlk]/
oAIbw],
$ $ $
]! " + + ≠
0
>DV!G
>,

α
0- .16@B&oVO
AYlk]1;4H4G

r
k,o77A0
,
α
0@
] ] ] ]
, 7 7 0 #  $
&D
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A0
]
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] ] ]
0 0 0 ], , ,! # # "    $ $+ + =− − −

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rY~k]
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
r
k,z7{$7{r0
;+)*zG qD  . 16@ 2 W
,d>H0/d,770>,z7`7$0H,m7$70

,`7$70  =
uuuur
,z77]0  =
uuur
 •€ , 7z7 m0   = = − −
uuuur uuur
r
;DO .16@,d>H0-)QG
, z0 z, `0 m, $0 ]
z m $ ]
#  $
#  $
− − + − − − =
⇔ − + − + =
9$90"X Y3= Z[J\#
=>N;4H42 W%
=>N .16@2 W%
=>N @2 W%
9$]D@^/8 _/#
=f(/&p&OGT.5&)Q
=f(/&p GV&ƒH.12 W„
]$`>  A1#
=>)G%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
=H.  G%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
=Xs)*I)J9)QOG%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Trang 10
Hình học 12_HKII – Nguyễn Phúc Đức
 'ghnNL

9: ;
 !"#
$ %&#
P  O2 W%
 .16@2 W?-2''$2
W+"j2 W%
$'()#
89.5  O2 W%
 .16@2 W&+.5"j
2 W%
$*+ ,-#
.#<4=<>/?<4=<>@%
A BC/%A-35 D %
'$./01#
=H.16@2 W%
=;9+.($2 W%
*$"234#
=R;G .  %
=PXGMBN@2 Wn .  O2
W%
9$ %.:#
9$;,4<&7=> ?1@ A#69B/ )%
9$' ?1.B1 A#
=>N .16@2 W
9$*C= 1D #
Hoạt động của GV và HS Nội dung
PQG
=R;GV!.b5 2
>lk]
>`'(oAw]

>``'(oAk]
4j-12 W
=PXG)‚! %
=PXG )*i";lm%
PQ$G
=R;G./)^"+%
=PXG)‚! %
$%A.b5 NG
4      UVOY    2  W  ,
α
0  -
.1GoVOAYlk]
xlk]
, 0
α
⇒
@(U- GoVO
AYk]
xok]
, 0
α
⇒
''2*UV- G
OAYlk]
k]
, 0
α
⇒
''2*UO- G
oVAYlk]

Ak]
, 0
α
⇒
''2*UY- G
oVOlk]
xokk]
, 0
α
⇒
''2J,UVO0-
GAYlk]
kAk]
, 0
α
⇒
''2J,UOY0- G
oVlk]
okAk]
, 0
α
⇒
''2J,UVY0- G
Olk]
v>DV!Gd2 W@`o,7]7]0,]7
7  ]0  A,]7  ]7  0  -  .  1G
 ]
#  $
%&'
% & '

+ + = ≠
,  QT0
;+)*mG`d,$7]7]0>,]7
{7]0H,]7]7`0%; 2 W,d>H0
Trang 11
Hình học 12_HKII – Nguyễn Phúc Đức
PQ$G
=R;G.+)*$ )*%
=PXGBN"B&&
1
=PXG )*9+.($2
W%
4-G
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ttt%;9+.($2 WG
A2 W
, 0
α
G
   
]! # "   $ *+ + + =
, 0
β
G
$ $ $ $

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v4PG
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≠⇔ ≠
v4P$G
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xx
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v4P`G
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J
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v4PzG
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]
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⇔ ⊥
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r r
;+)*G8!9+.(2 2 WG
0
 
0 G, $ ` z ] , 0G m y ]#  $ #  $
α β
+ + + = + − − =

0
$ $
0 G, m ] , 0G $ $ $ ] ]#  $ #  $
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+ + + = + + + =
0
` `
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R"G
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0
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,
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α β
≡= = = ⇒
;+)*$G412 2 W'-G
0 G $, $ y ] , 0G r ] ]#  $ #  $
α β
+ + − = − − − =
4-G
,$7 7$ 0  
α
=
r
,r7 7 0
β
= − −
r
0, , 0 $%r , 0 , y0%, ]0 ] z 
α β
⊥ ⇔ + − + − − = ⇔ =
9$90"X Y3= Z[J\#
=>N @2 W%
=>NV!9+.($2 W%
9$]D@^/8 _/#

=f(/&p&OGT.5&)Q
=f(/&p GV&ƒH.12 W„ 3FBQ
]$`>  A1#
=>)G%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
=H.  G%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
=Xs)*I)J9)QOG%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Trang 12
Hình học 12_HKII – Nguyễn Phúc Đức
 'ghnNL
9: :
 !"#
$ %&#
P  O2 W%
 .16@2 W?-2''$2
W+"j2 W%
$'()#
89.5  O2 W%
 .16@2 W&+.5"j
2 W%
$*+ ,-#
.#<4=<>/?<4=<>@%
A BC/%A-35 D %
'$./01#
=4+"j2 W%
*$"234#
=R;G .  %
=PXGMBN@2 Wn .  O2
W%

9$ %.:#
9$;,4<&7=> ?1@ A#69B/ )%
9$' ?1.B1 A#
=>N9+.($2 W%
=>N .16@2 W
9$*C= 1D #
Hoạt động của GV và HS Nội dung
PQG(BD  .1
6@2 W%
=R;G.+)*`zm%
=PXG"
;+)*`G; .12 W@`
G
o,{7$7`0,$7{z7`0A,z7m7r0
,`7 r7]0
,m7`7`0
!"
!
= −
=
uuur
uuur
 ,|7 y7`y0!" !
 
 
= −
uuur uuur
;4H42 W
, |7 y7`y0 = − −
r

;DO .12 W31B&G
|, 0 y, $0 `y, `0 ]
| y `y ]~ ]
#  $
#  $
− + − − + − =
⇔ − − + − =
;+)* zG; .1 
, 0
α
@ $
o,`77{0,$7{7z0&-2 WG
$ ` ~ ]#  $− + + =
, 7 $7m0!" = − −
uuur
7
,$7 7`0
3
 = −
r
 , 7`7m0
3
!" 
 
 
= −
uuur
r
;4H4
, 0

α
B&G
, 7`7m0 = −
r
;DO @2 WB&G
, `0 `, 0 m, 0 ]
` m m ]
#  $
#  $
− − + − + + =
⇔ − + + − =
;+)*mG; @2 W@d,7{$7
`0  &  '  '  2  W  ,H0G
Trang 13
Hình học 12_HKII – Nguyễn Phúc Đức
PQ$G
=R;G./)^"+%
=PXG)‚! %
PQ$G
=R;G.+)*$ )*%
=PXGBN"B&&1
= PXG )* 9 +.(  $ 2
W%
$ ` z $ ]#  $+ − − =
, 0
α
'  '  ,H0  N 
, 0
α
 -  ;4H4G

,$7`7 z0 = −
r
;DO @
, 0
α
B&G
$, 0 `, $0 z, `0 ]
$ ` z r ]
#  $
#  $
− + + − − =
⇔ + − + =

t;%<"j2 WG
4    UVOY"    j
d,V
]
7  O
]
7  Y
]
0    2  W 
, 0
α
G
]!# " $ *+ + + =
.5+G
] ] ]
]
$ $ $

, 7, 00
!# " $ *
8
! " 
α
+ + +
=
+ +
;+)*GAo,7{7$0,`7z70& 
, 0
α
-
.  1G 
$ $ ] ]#  $+ + − =
% 4+"
jo2 W
, 0
α
$ $ $
 $ z ]
~
, 7, 00
`
 $ $
8 !
α
− + −
= =
+ +
$ $ $

` | $ ]
, 7, 00 
 $ $
8 "
α
− + −
= =
+ +
;+)*$G4+"#$2 W'
'
, 0
α
&
, 0
β
p 
, 0 G $ $  ]
, 0G $ $ $ ]
#  #
#  $
α
β
+ + + =
+ + + =
qEOd,]7]7{0
, 0
β
∈
$ $ $
,, 07, 00 , 7, 00

] $%] $, 0 
`
 $ $
8 8
α β α
=
+ + − +
= =
+ +
9$90"X Y3= Z[J\#
=>N @2 W%
=>N+"j2 W%
9$]D@^/8 _/#
=f(/&p&OGT.5&)Q
=f(/&p GB&&D XR<&&O%
]$`>  A1#
=>)G%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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=H.  G%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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=Xs)*I)J9)QOG%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Trang 14
Hình học 12_HKII – Nguyễn Phúc Đức
 'ghnNL
9: :
 !"#
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W%

$'()#
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 .16@2 W&+.5"j
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9$ %.:#
9$;,4<&7=> ?1@ A#69B/ )%
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9$*C= 1D #
Hoạt động của GV và HS Nội dung
PQG
=R;GNBD  @2 W
=PXG1   &;4H4 2
W
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=PXG"
0=R;G1;4H42 W
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r r r

0=R;G1;4H42 W
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x|]; .12 WG
xf@d,7{$7z0&D
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7
r
k,`7$70&
4
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k,{`7]70
xf@`o,{`7]7]0,]7{$7]0A,]7]7{0
R"G
0H@2 WB&G
$, 0 `, $0 m, z0 ]
$ ` m r ]

#  $
#  $
− + + + − =
⇔ + + − =
0;4H42 WB&G
 =
r
,$7{r7r0
H@2 WB&G
$, ]0 r, 0 r, $0 ]
$ r r | ]
` ` r ]
#  $
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− − + + − =
⇔ − + − =
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0
,`7 $7]0 ,`7]7 0!" != − = −
uuur uuur
;4H4G
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= =
uuur uuur
r
H@2 WB&G
$, `0 `, ]0 r, ]0 ]

$ ` r r ]
#  $
#  $
+ + − + − =
⇔ + + + =
$x|]; .12 Wi
QWo/o,$7`7~0,z77`0
Trang 15
Hình học 12_HKII – Nguyễn Phúc Đức
QWo
=PXG2 WiQW
B&2 W@Q
W&-/QW-%
=R;G1&;4H42 W
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d2 WiQWo @
do 
⇒
d,`7$7m0&-;4H4
,$7 $7 z0!" = − −
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$ $ z | ]
$ y ]
#  $

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− − − − − =
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`x|]0qD  .12 W
,UVO0,UVY0,UOY0
0qD  .12 W@
d,$7r7{`0&B3B.5''/2 W
%
R"G
0 ,UVO0GYk] ,UVY0GOk] ,UOY0GVk]
0 @d&xx,UVO0- GY`k]
 @d&xx,UVY0- GO{rk]
 @d&xx,UOY0- GV{$k]
9$90"X Y3= Z[J\#
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9$]D@^/8 _/#
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=f(/&p GB&&D XR<&&O%
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Trang 16
Hình học 12_HKII – Nguyễn Phúc Đức
 'ghnNL
9: :
 !"#
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 .16@2 W&+.5"j
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=>N+"j2 W%
9$*C= 1D #
Hoạt động của GV và HS Nội dung
PQG
=R;GNBD  .12
W\
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u )*G
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  41  2      2   W  B&
! !*
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A&D ?V!UVOY
zx|]qD  .12 WG
0A*UV&H,z7{7$0
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,z7 7$0
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⇒
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], ]0 $, ]0 , ]0 ]
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4.i/:
mx|]A)-nB&o,m77`0,,7r7
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Trang 17
Hình học 12_HKII – Nguyễn Phúc Đức
41  O
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Trang 18
Hình học 12_HKII – Nguyễn Phúc Đức
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Trang 19
Hình học 12_HKII – Nguyễn Phúc Đức
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Trang 20
Hình học 12_HKII – Nguyễn Phúc Đức
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Trang 21
Hình học 12_HKII – Nguyễn Phúc Đức
'$A3V9O(&\
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0q& iQo/o,$7`7~0,z7
7`0%
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r7$0A,m7]7z0l,z7]7r0%
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$ $ y ]− + − =#  $
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Trang 22
Hình học 12_HKII – Nguyễn Phúc Đức
(( Fq
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Tieát 36
 !"#
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Trang 23

Hình học 12_HKII – Nguyễn Phúc Đức
Trang 24
Hình học 12_HKII – Nguyễn Phúc Đức
( *gsn
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.#<4=<>/?<4=<>@%
A BC/%A-35 D %
'$./01#=H.1'(.bW%
*$"234#
5 +67 !#& E"F-GHD %
5/8 #&I)JD .'KLF-GO+
9$ %.:#
9$;,4<&7=> ?1@ A#69B/ 'C'(I *%
9$' ?1.B1 A#/&/%
9$*C= 1D #
Hoạt động của GV và HS Nội dung bài học
PQ    G      ?    n
.
=R;G/G

%
r


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∆

%
r

=PXG)‚DV!j-.
n ..bW%
PQ$G .1.bW
= R;G BD  . 1   .b
W31G

n .
4j-BD .5 .1'(2
.1+T.bW%
=R;GB.}j .1'(.
.5? .1+T&.5BQ
PQ`G
=R;G )*&BD  .1.b
W
=PXG D)*B}O? BD  .
1.bW
A:x
=PXG1&n .
.bW%
t%H.1.bWG
%;n ..bWG
]% ≠
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%
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%
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f.bW@G
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] ] ]
, 7 7 0 #  $
;&-n .
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, 7 7 0% % % %=
r
A- .1'(B&G
] 
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# # % 
  % 
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



A- .1+TB&G
] ] ]
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# #   $ $
% % %
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`%;+)*G
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W
∆
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xf@d,$7{`70&-n .
, 7m7 $0% = −−
r
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, 7m7 $0% = −−
r
H.1'(

∆
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