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Uchburchaklar xossalariga doir masalalar yechish

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10.08.2023

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Geometriya
Uchburchaklar 
xossalariga doir 
masalalar yechish. Mavzu: T	
e	
n	
g	
 	t	o	
m	
o	
n	
l	i  To‘g‘ri burchakli	
O	
‘	t	k	i	r	 	b	u	r	c	h	a	k	l	iUchburchaklar	
T	
e	
n	
g	
 	y	
o	
n	
l	i	
O	
‘	t	m	
a	s	 	b	
u	
r	c	h	
a	k	l	i Turli tomonli =    +
Ichki burchak
xossasi Tashqi burchak 
xossasi
Teng tomonli∆
xossasi c =  2a  (30°)
90° li∆
O‘tmas burchakli∆
O‘tkir burchakli∆ a =  b  ,  =
90° li∆
Teng yonli∆
Teng tomonli∆ 66          To‘g‘ri    burchakli ABC  uchburchakda     
to‘g‘ri  burchak,  A    uchidagi    tashqi   
burchak  120  ga  teng. 
  Agar,    AC  +  AB  =  18    sm    bo‘lsa, 
uchburchakning gipotenuzasini toping .Masala 7                                                         c =  2b  (30°)
A CB
120°Berilgan:
∆ ABC - 90°li,
= 120°; AC+AB=18sm
Topish kerak:   AB=c=?
= 180°-120°=60°
=90-= 30  c=2b
  b+ c = 18;
  b+2b=18;↔ 3b =18
  b = 6 cm;      c=2·6=12(sm)  
  bc
 
Javob: 12 sm 30°
60° 88Rasmda berilgan 
ma’lumotlardan  
foydalanib,  1 > 3  
ekanligini isbotlang. Masala 99Isbot: 
2 -  △  BDCning  tashqi gi    
2 =3+4 
(tashqi  burchak  xossasiga ) va 4 > 0 Berilgan:
ACD- teng yonli
Isbot qilish kerak:  
  > 3 ekanligini
△   ACD - teng yonli   bo‘lgani  uchun  1=2. 
Demak,  1 >3  bo‘ladi. 1010              Uchburchakning  117   li  tashqi ⁰
burchagiga  qo‘shni  bo‘lmagan  ichki 
burchaklarning  nisbati  5:4  kabi. 
Uchburchakning  ichki  burchaklarini 
toping.   10-masala  (4- bet) =    +
A CB
117°    Berilgan:
∆ ABC - ixtiyoriy
= 117°;  = 5:4
Topish kerak:   
Y: 1) 5x+4x =117⁰
         9x = 117	
⁰
          x=117 :9	
⁰
          x=13        	
⁰ 4x5x  
2) 5∙13 =65	
⁰ ⁰   ()
     4∙13 =52  
⁰ ⁰  ()
    180 -117 =63  	
⁰ ⁰ ⁰ (A)          To‘g‘ri burchakli ABC uchburchaknig 
C burchagi to‘g‘ri, A uchidagi tashqi 
burchagi esa 136  ga teng. B burchakni ⁰
toping.   19-masala  (4- bet)
C
A B =    +
C136⁰ B
ABerilgan:
△ ABC - 90  li	
⁰
= 136	
⁰
Topish kerak:  B =?
Yechish:
=    + (tashqi )
B = 136  - 90  = 46  	
⁰ ⁰ ⁰
  ?
Javob: 46	
⁰     To‘g‘ri burchakli teng yonli uchbur-
chakning peremetri 24cm, gipotenuza-
ning uzunligi 6 cm ortiq bo‘lsa,gipote-
nuza uzunligini toping?  Masala Yechim:
a
a a+6 P=2a+c
Yechish:
  24= 2a+a+6
     3a = 24-6
     3a = 18
     a=18:3
     a=6 (cm)         
c=6+6=12 (cm)Berilgan:
△ ABC - 90  li,⁰
        teng yonli.
P = 24 cm
a=b -? cm
c = a+6 -? cm
Javob: 6 cm va 12 cm Mustaqil bajarish uchun topshiriqlar
Darslikning  4- sahifasidagi
        13,- 16,- 18-  masalalarni 
yechish.

Geometriya Uchburchaklar xossalariga doir masalalar yechish. Mavzu:

T e n g t o m o n l i To‘g‘ri burchakli O ‘ t k i r b u r c h a k l iUchburchaklar T e n g y o n l i O ‘ t m a s b u r c h a k l i Turli tomonli

= + Ichki burchak xossasi Tashqi burchak xossasi Teng tomonli∆ xossasi

c = 2a (30°) 90° li∆ O‘tmas burchakli∆ O‘tkir burchakli∆

a = b , = 90° li∆ Teng yonli∆ Teng tomonli∆