Bt hinh 7 chuong 3

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∠ ! ∠ " !

#$ % &' (
∆

⇒ ) ⇒∠ ∠

* ⇒ ∠ *∠ +,- . / &0 12 3. 4
567∠ ∠ * ∠

∠ _89!!_{: +} !_;" !_{4 89!}!_{: 88!}! _!!
∠ *∠ *∠

⇒ * * +,- . / &0 12 3. 4

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# ( 12 => @A71 B C =C =<
⇒∆ ) 1D C

⇒∠=C< ∠ =<C +84

# <= / <> &0 <C
C 1 ∠><C *∠=<C +E4

#$ +84 &0 +E4 ∠_{><C *}∠_=C<
FG C>< ∠><C *∠>C<

-7 C> *>< +,- . / &0 12 3. 4 +"4
0 C> => ;=C => ;=< +H4

#$ +"4 &0 +H4 => ;=< *><

< =><I∠_{= J!}! _{# (} ₁₂ _{=< @A7C} _{=C K=<}
L2 > &M C < ? >< *>C

# ( =< @A71 B N =N =C
# =N K=< +5%=C K=<4

L( N / = &0 <
O0 >= ⊥ CN &0 C= =N

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# ∠_{>N= *}∠_{><N +}∠_{>N= @0} ₀ _>N<4
C 1 ∠_{>C< *}∠_><C

FG >C< ∠_{>C< *}∠_><C

-7 >< *>C +,- . / &0 12 3. P 4

< =>< => K=<IO @0 - 1 B ><
∠_{>=O &0} ∠_O=<

5' 12 O= &0 ( 1
@A71 B C OC O=
FG O=> &0 OC<

O= OC

∠_=O> ∠_{CO< +12 1D 4}
O> O< +O @0 #Q ><4
C 1 ∆ =∆ + 4

-7 => <C ∠_>=O ∠_OC<

# => <C => K=< ⇒ <C K<=
FG =C< <C K=<

⇒ ∠O=< K∠OC< +,- . / &0 12 3. 4
O0 ∠_{O=< K}∠_{OC< &0}∠_>=O ∠_OC<

-7 ∠O=< K∠>=O

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VC ⊥ ><
∆
=

∆ + -7W : X 4
⇒ =C C

∆ &-R ⇒ C KC<

∆ + &-R Y Z -7W 4
-7 =C KC<

"

< % &' ( 1 => *=<
< ? N> *N<

< % &G (

< ? >C ;<N K=> ;=<

=> *=< ⇒ > * <+1[\ ]( @M Z

%1[\ -@M Z 4

> * < ⇒ N> *N<

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# =CN &-R N -7 <N K=<
-7 >C ;<N K=> ;=<

< =><IO @0 - 1 B ><
< ? => ;=< *E=O

# ( 12 O= @A71 B C OC O=
FG ∆O=> &0 ∆OC<

O= OC

∠=O> ∠CO< +12 1D 4
O> O< + 4

C 1 ∆ =∆ + 4
⇒ => C<

FG =C< <C ;=< *=C + A 1^ ? 4
C 1 => ;=< *=C 0 =C E=O

-7 => ;=< *E=O

# < =>< T ) C U =< C
1P30 => &0 ><I >C< _

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# a b ∠_{>C< _}

∠C8*J!! ⇔ E∠C8*89!!

# =>C ∠_C8 ∠_{= ;}∠_>E ₊₈₄

# ><C ∠_C8_;∠_>8_;∠_<8 _89!! _+E4
<R a & +84 &0 +E4 1[c

E∠_C8_;∠_>8_;∠_< ∠_{= ;}∠_>E_;89!!
⇔ ∠= :∠< E∠C8: 89!!*! +∠C8 _4

⇒ ∠= *∠<
⇔ >< *=>

$ < =><IO @0 1 B
< ? O> ;O< K=> ;=<

5'1[\ ^ >O U =< C

5%O S =>< ( C / = &0 <
-7 =< =C ;C<

FG =>C C> K=> ;=C + A 1^ ? 4
⇒O> ;OC K=> ;=C +84

FG OC< O< KC< ;OC +E4 + A 1^ ? 4
<R +84 &M +E4 & &M &

O> ;O< ;OC K=> ;=C ;C< ;OC

⇒ O> ;O< K=> ;+=C ;C<4 ⇒O> ;O< K=> ;=<

% < =>< => *=< =C @0 T ) >=<
+C ∈ ><4 O @0 1 B ( 1 ^ =C

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# ( => @A71 B N =N =<
&%=> *=<I ( N / = &0 >

-7 =N ;N> =>

⇒ N> => : =N => d =<
FG ∆=NO &0 ∆=<O =N =<

∠_N=O ∠_{<=O +=C @0} _{T )} _>=<4
=O

-C 1 ∆ =∆ + 4
-7 ON O<

FG ON> O> : ON KN> + A 1^ ? 4
C 1 O> : O< K=> : =<

< =>< = J!! _{# (} _{=>I=< @` @[c @A7} _{1 B C &0 N}
< ? CN K><

L2 C &0 < =NI=< @` @[c @0 %
- % ]( CNIC< (
1[\ ^ =<

0 =N K=N +5%N -P =<4

-7 CN KC< +,- . / 1[\ ](
&0 % - 4

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-1[\ ]( C<I>< ( 1[\ ^ => 0 =C K=> +C -P =>4
-7 C< K>< +,- . / 1[\ ]( &0 % - 4

# CN KC< C< K>< ⇒ CN K><

< =>< &M >< *=> # T ) =>< U =< C
< ? <C *C=

gA7 ( >< > >=
< ∆ &0 ∆

< C>

-∠_>8 ∠_>E_{+5%>C @0} _{T )} _=><4
> >= + a @A71 B 4

567∆ ∆ + 4
-7 ∠C8 ∠CE C C=
Oe f < C @0 0

C> ( ∠_{< C *}∠_C8₊₈₄

∠_CE_@0 ₀ _{C>< (} ∠_CE_*∠_{><C +E4}
5%∠_C8 ∠_CE _{$ +84 &0 +E4 -7} ∠_{< C *}∠_><C
# <C &%∠_*∠_<

( <C *C 7<C *C=

< =>< +=< *=>4 ∠_{= _I1[\} _{= +1[\} ₌ ⊥><4 &0 - -7 =O
+1[\ =O 1 ,- - 1 B O ><4 < ?

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# ( =O @A71 B C O
@0 - 1 B =CI3h30

? 1[c ∆ =∆ + 4
-7 ∠_>=O ∠ _{C +84}

=> C<

# ∆ =< *C< 3 =< *=> + 4
50 => C< +i ( 4

L( ∠C * ∠O=< +E4

#$ +84 &0 +E4 -7 ∠_{>=O *}∠_O=<

=< *=> ⇒ < * > + -P 1 ^ >< 3 = @0 _&0 O> O<4
-7 >O *> 567 / 1 B > &0 O

< OL O *OLIOC @0 1[\ - -7 -P L
# ( OC @A71 B N C @0 - 1 B ON

< ? ∠_{ON *}∠_NO

∆
=

∆ + 4

CL C
CO CN

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O0 O *OL ⇒ O *N

# ON IO 12 3. &M ∠_ON
N 12 3. &M ∠_NO

C 1 ∠_{ON *}∠_NO

! < =>< +∠_{= J!}!_{4 &'= &-R} _{&M >< +} _{-P ><4}
< ? = ;>< *=> ;=<

# ( >< @A71 B C >C =>
# ( =< @A71 B N =N =
+5%=> K>< ( C / > &0 <I
= K=< ( N / = &0 <4
# =>C ) 1D > +5%>C =>4

⇒ ∠>=C ∠>C=

⇒ # ∠>=C ;∠C=N ∠>=C ;∠ =C J!!
C 1 ∠_C=N ∠ _=C

FG =C &0 N=C
= =N

∠ =C ∠C=N

=C

-C 1 ∆ =∆ + 4
⇒ ∠= C ∠=NC

0 ∠_{= C J!}! ₍ ∠_{=NC J!}!

# CN ⊥ =< ⇒ C< *N< +,- . / 1[\ ]( &0 1[\ &-R 4
C 1 = ;>C ;C< *=N ;=> ;N< => ;=<

567= ;>< *=> ;=<

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&M >< U =< N < ? >N * +CN ;><4

5'> ⊥CN + ∈ CN4INL ⊥ >< +L ⊥ ><4
FG ∆ >N +> N J!!4 &0 ∆LN> +NL> J!!4

>N - I

∠ _>N ∠_{LN> +&%CN ii><4}

C 1 ∆ =∆ + -7W : X 4

-7 > NL

Oe f ∠ _{>C ;}∠_C>< ∠ _{>< J!}!
∠LN< ;∠N<L J!!+∆LN< L J!!4

0∠_C>< ∠_{N<L +}∆=>< ) 1D =4
-7 >C LN<

FG ∆ >C &0 ∆LN<

∠C > ∠<LN + J!!4
> NL + a i ( 4

∠L>C ∠LN< +i ( 4

C 1 ∆ =∆ + 4 ⇒ C L<

O0 > ⊥CN -7 >N * N +,- . / 1[\ ]( &0 1[\ &-R 4
C 1 >N ;>j * N ;O>

O0 N ;>L CN ; C ;>L CN ;L< ;>L CN ;><
L( >N ;>N *CN ;><

⇒ E>N *>< ;CN⇒ >N * +CN ;><4

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V= ⊥ ><

: L -C _ %=C K=< &%= K=<
+1[\ &-R Y Z 1[\ ]( 4

L -C f R _

k b l C / &0 <I C K <

-7 =C K=< + % - Y Z %1[\ ]( Y Z 4
567=C Y Z ( =><

# < =>< < =

< ? =>< @0 &-R = &0 m 2 1 >I
<

V1[\ = < ? ∠_> ∠ _{=< <} ∠_>=

=
=

+
+

+
+
=
=

= + T3n m A 3o7 D 2 -4

567 = ⇒ = ( =>< @0 &-R =

5%= ⊥>< ( ∠ 8& -7 ∠> ;∠>= 8&

5%∠_{>= ;}∠ _{=< 8& -7} ∠_> ∠ _{=< +E} _{T n} _-4
$ < =>< => H =< 8

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# a A 1^ ?
=> : =< K>< K=> ;=<

⇒ H: 8 K>< KH;8
⇒ "K>< K

C 1 1P30 >< 8 2 -7( + 4 ( >< H
%

#m -& P ) H &0 J

< =>< 1 B C / > &0 < < ? =C Y Z l -& =><

< H f R B@0 ( &% - H @0 ( % 1 7@M Z p f
+J*H;H4 &M A 1^ ?

567 H @0 1 7 b o JKJ;H
< -& @0 H;J;J EE

FG =>C
=C K=> ;>C +84

FG =<C =C K=< ;C< +E4
<P $ & +84 &0 +E4

E=C K=> ;=< ;+>C ;C<4
-7 =C K + +

QP30 P @0 IE

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kX 1P30 q @ @0 ]+ 4
# a A 1^ ?

: E K]K ;E ? @0 K]KJ
C 1 ]@0 P 2 r ( @V ( ]
< q @

#m -& ) =><
=> =< 8E

=> =< 8"

# =>< ) => =< 8E % 1 7@0 =
# 6 &67 - ( => % ( ><

L [ &67 => ;>< 8! K<= 8E

1 @0 1 W-&R@m+ P p 1P30 \ s @M Z 1P30 ? 4
567 -& =>< @0 => ;=< ;>< ;E 8E EJ

< B]b7 [\ cT

: L -=> @0 1 7 %=> >< 8" @0 (
: L - -& =>< ;E 8" ""

: L -=> >< @0 ( %=< 8" @0 1 7
< -& =>< @0 8";E E

< =><IO @0 - 1 B >< < ?
L -= J!! _%=O _><

L -= *J!! _{%=O K ><}
L -= KJ!! _{%=O * ><}

&' ( )*

+, * *- . * / 0 1 * ) 23 - 4 . 56 7*

8 9 3 1 * : / ; 2< = : . > > / > ? . ; 2< = :

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5' 12 O= ( 1 @A71 B C OC O=
-7 =C E=O

FG ∆O=> &0 ∆OC<
O= OC

∠_=O> ∠_{CO< +12 1D 4}
O> O< + 4

C 1 ∆O=> ∆OC< + 4

-7 => C<
∠_>=O ∠_<CO

# ∠>=O ∠<CO

0 ∠_{>=O &0} ∠_{<CO + @a} ₄

( => ii<C ⇒ ∠>=< ;∠=<C 89!!
56 3n &0 m A ( ]G ∆=>< &0 ∆<C=
=> <C =<

-C 1

∠>=< ∠=<C +∠>=< J!! ∠>=< ;∠=<C 89!!4
( ∠_{=<C J!}!

⇒ ∠>=< ∠=<C

⇒ >< =C ⇒ =O ><

∠_{>=< *}∠_{=<C +}∠_{>=< *J!}! ∠_{>=< ;}∠_{=<C 89!}!_{4 (}
∠=<C KJ!!

⇒ ∠>=< *∠=<C
⇒ >< *=C

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∠_{>=< K}∠_{=<C +}∠_{>=< KJ!}! ∠_{>=< ;}∠_{=<C 89!}!₄
( ∠_{=<C *J!}!

⇒ ∠>=< K∠=<C
⇒ >< K=C

⇒ =O * ><

# @ L -∠_{= J!}! _%=O _><
L(-∠_{= *J!}! _{%=O K ><}
L -∠_{= KJ!}! _{%=O * ><}

< ? - P &-R P X "!!
% &-R 12 3. &M l -7W

FG =>< ∠= J!! ∠> "!!

<` ? =< ><

# ( >< @A71 B C <C <=

# =<C q ∠< t!!I=C =< <C
# =>C ∠_{> "!}! ∠_=E _"!!

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