
ГДЗ Погорелов 7-9 клас / ГДЗ. Геометрия 7-9_Погорелов_9кл_2001_Решения пр11-14
.pdf
Imklv $%&' ² ljZi_pby :< |
&' f :K f |
|||
$' f |
|
|
|
|
< û:K? ‘? |
ƒ $& |
f $( ± ('Ih l_hj_f_ |
||
IbnZ]hjZ |
|
|
|
|
|
K? |
:K ± :( ± ± (' |
||
± (' ± (' ± (' ± (' |
||||
lh _klv&( |
(' |
(' ± |
|
|
< û&'(‘( ƒ&' |
f Ih l_hj_f_ IbnZ]hjZ bf__f |
|||
|
(' K? |
&' |
||
IhemqZ_f qlh |
|
|
||
(' ± (' |
(' f |
|||
ke_^h\Zl_evgh $+ (' |
f <K |
± ˜ f K? |
||
± |
K? f Lh]^Z |
|
f
Hl\_l f
‹>hdZ`bl_ qlh kj_^b \k_o iZjZee_eh]jZffh\ k ^Zg gufb ^bZ]hgZeyfb gZb[hevrmx iehsZ^v bf__l jhf[
Imklv $%&' ² iZjZee_eh]jZff $&b K'² ^bZ]hgZeb
‘$.% .
|
|
|
|
|
|
|
6 |
|
Â:%ÂK'ÂVLQ. |
||
|
|
$%&' |
|
|
|
6 |
[m^_l gZb[hevr_c dh]^Z VLQ. lh _klv D ƒ |
ke_^h\Zl$%&' _evgh ^bZ]hgZeb ^Zggh]h iZjZee_eh]jZffZ i_j_k_

dZxlky ih^ ijyfuf m]ehf Z lZdhc iZjZee_eh]jZff y\ey_lky jhf[hf Qlh b lj_[h\Zehkv ^hdZaZlv
‹ <u\_^bl_ ke_^mxsb_ nhjfmeu ^ey jZ^bmkh\ hib kZgghc 5 b \ibkZgghc U hdjm`ghkl_c lj_m]hevgb dZ ]^_ D E F ² klhjhgu lj_ m]hevgbdZ Z 6 ² _]h iehsZ^v
AZ^ZqZ j_r_gZ \ i mq_[gbdZ klj
‹ GZc^bl_ jZ^bmku hibkZgghc 5 b \ibkZgghc U hd jm`ghkl_c ^ey lj_m]hevgbdZ kh klhjhgZfb
D E F
Ihemi_jbf_lj lj_m]hevgbdZ
Ih nhjfme_ =_jhgZ ihemqZ_f
Ke_^h\Zl_evgh
D E F
Ihemi_jbf_lj lj_m]hevgbdZ
Ih nhjfme_ =_jhgZ ihemqZ_f

Ke_^h\Zl_evgh
D E F
Ihemi_jbf_lj lj_m]hevgbdZ
Ih nhjfme_ =_jhgZ ihemqZ_f
Ke_^h\Zl_evgh
D E F
Ihemi_jbf_lj lj_m]hevgbdZ
Ih nhjfme_ =_jhgZ ihemqZ_f
Ke_^h\Zl_evgh

‹ ;hdh\Zy klhjhgZ jZ\gh[_^j_ggh]h lj_m]hevgbdZ |
|
kf \ukhlZ ijh\_^_ggZy d hkgh\Zgbx kf GZc^b |
|
l_ jZ^bmk hibkZgghc hdjm`ghklb |
|
Imklv :<K ² jZ\gh[_^j_gguc lj_m]hevgbd :< |
<K |
kf <G kf² \ukhlZ ijh\_^_ggZy d hkgh\Zgbx |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Lh]^Z \ û:<G ‘G |
|
ƒ Ih l_hj_f_ IbnZ]hjZ ihemqZ_f |
||||||||||||||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
kf |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Lh]^Z |
|
|
|
kf b |
||||||||||||||||||||
|
|
|
||||||||||||||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
kf |
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||
Ke_^h\Zl_evgh |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
kf |
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Hl\_l kf
‹ GZc^bl_ jZ^bmku hdjm`ghkl_c hibkZgghc hdheh jZ\gh[_^j_ggh]h lj_m]hevgbdZ k hkgh\Zgb_f Z b [h dh\hc klhjhghc E b \ibkZgghc \ g_]h
Imklv :<K² jZ\gh[_^j_gguc lj_m]hevgbd :< <K E
:K Z GZclb 5 U

Lh]^Z |
|
|
|
|
|
|
|
|
|
|
|
Ke_^h\Zl_evgh
GZc^bl_ jZ^bmk U \ibkZgghc b jZ^bmk 5 hibkZgghc hdjm`ghkl_c ^ey jZ\gh[_^j_ggh]h lj_m]hevgbdZ k hkgh\Zgb_f kf b [hdh\hc klhjhghc kf
Imklv :<K ² jZ\gh[_^j_gguc lj_m]hevgbd :< <K
kf :K kf
|
|
|
|
|
|
Lh]^Z |
kf |
kf Ke_^h\Zl_evgh

kf kf
>hdZ`bl_ qlh \ ijyfhm]hevghf lj_m]hevgbd_ jZ^b mk \ibkZgghc hdjm`ghklb jZ\_g iheh\bg_ jZaghklb f_`^m kmffhc dZl_lh\ b ]bihl_gmahc
Imklv \ û:<K ‘K ƒ&% D $& E $% F >hdZ`_f qlh
|
|
|
|
|
|
|
Bf__f |
|
gh |
|
lZd qlh |
||
|
|
qlh lj_[h\Zehkv ^hdZaZlv
‹ DZl_lu ijyfhm]hevgh]h lj_m]hevgbdZ jZ\gu kf b
kf GZc^bl_ jZ^bmku hibkZgghc b \ibkZgghc hd jm`ghkl_c
Imklv \ û:<K ‘K ƒ :K kf <K kf

Lh]^Z |
|
|
|
|
|
|
|
|
kf >Ze__ ih l_hj_f_ |
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
||
IbnZ]hjZ$% |
$& %& |
|
kf |
||||||
|
|
:< |
|
|
|
kf |
|||
Imklv :< |
k :K E <K Z Lh]^Z |
kf
kf
Hl\_l kf kf
‹>hdZ`bl_ qlh iehsZ^v fgh]hm]hevgbdZ hibkZggh]h hdheh hdjm`ghklb jZ\gZ iheh\bg_ ijhba\_^_gby i_ jbf_ljZ fgh]hm]hevgbdZ gZ jZ^bmk hdjm`ghklb
Imklv $ $ :Q ² fgh]hm]hevgbd hibkZgguc hdheh hd jm`ghklb $ $ $ $ $ $ ² klhjhgu fgh]hm]hevgbdZ
2$ 2$ 2$ Q U Q Q
Kh_^bgbf \_jrbgu fgh]hm]hevgbdZ k p_gljhf hdjm`gh klb Fgh]hm]hevgbd jZa[bl gZQlj_m]hevgbdh\ Lh]^Z

Qlh b lj_[h\Zehkv ^hdZaZlv
‹ Q_j_a k_j_^bgm \ukhlu lj_m]hevgbdZ ijh\_^_gZ i_j i_g^bdmeyjgZy d g_c ijyfZy < dZdhf hlghr_gbb hgZ ^_ebl iehsZ^v lj_m]hevgbdZ"
Imklv û:<K <G² \ukhlZ <H HG
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||
':<K a '0%1 ihwlhfm |
|
|
|
|
lZd qlh :K 01 |
||||||||||||||
Lh]^Z |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
6 |
|
|
|
|
|
$&˜%+ 01˜%+ |
|||||||||||
|
|
|
|
|
|
||||||||||||||
|
|
|
|
û:<K |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||||
6 |
|
|
|
|
|
01˜%2 |
|
|
01˜%+ |
||||||||||
|
|
û0%+ |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
Ihwlhfm |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
Hl\_l |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
‹IjyfZy i_ji_g^bdmeyjgZy \ukhl_ lj_m]hevgbdZ ^_ ebl _]h iehsZ^v ihiheZf GZc^bl_ jZkklhygb_ hl

wlhc ijyfhc ^h \_jrbgu lj_m]hevgbdZ ba dhlhjhc ijh\_^_gZ \ukhlZ _keb hgZ jZ\gZ :
6Imklv \ û:<K <G ² \ukhlZ01A %+ %+ K 6û%01
$01&
û:<K a ûF<1lZd dZd01__ $&
LZd dZd 6û%01 6$01& lh 6û%01 6û$%&
hldm^Z ihemqZ_f
Hl\_l
‹I_jbf_lju ijZ\bevguoQm]hevgbdh\ hlghkylky dZd Z E DZd hlghkylky bo iehsZ^b"
Hl\_l D E

‹ |
|
GZc^bl_ iehsZ^v djm]Z _keb ^ebgZ hdjm`ghklb O |
||
|
O |
Œ5 hldm^Z bf__f |
|
Lh]^Z |
|
|
Hl\_l
‹GZc^bl_ iehsZ^v djm]h\h]h dhevpZ aZdexq_ggh]h f_`^m ^\mfy hdjm`ghklyfb k h^gbf b l_f `_ p_g ljhf b jZ^bmkZfb kf b kf f b fZ b E Z !E
|
6 |
|
6 |
|
|
± 6 |
|
S5 |
|
± S5 |
|
S 5 |
|
± 5 |
|
|
LZd qlhdhevpZ |
|
dj |
|
dj |
|
|
|
|
|
|
|
|
|
|||
6 |
|
α S kf |
|
|
|
|
|
|
||||||||
6dhevpZ |
Œ |
± |
α |
|
S kf |
|||||||||||
6dhevpZ |
Œ D ± |
E kf |
|
|
|
|
|
|
|
|
|
|||||
|
dhevpZ |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
‹ |
<h kdhevdh jZa m\_ebqblky iehsZ^v djm]Z _keb _]h |
|||||||||||||||
|
^bZf_lj m\_ebqblv \ jZaZ \ jZa \ P jZa" |
|||||||||||||||
?keb ^bZf_lj m\_ebqblv \ Q jZa lh jZ^bmk m\_ebqblky lh`_ |
||||||||||||||||
\ Q jZa lh]^Z iehsZ^v m\_ebqblky \ Q |
jZa |
|
|
|
|
|||||||||||
Q |
lZd qlh |
|
|
|
|
|
|
|
|
|
|
|
|
l _ 6 djm]Z m\_ebqblky \ jZaZ