Qo’shni burchaklar 5: 11 nisbatda. Ular ayirmasining modulini toping

Burchaklar

1. 
   Qo’shni burchaklar 5:11 nisbatda. Ular ayirmasining modulini toping.
   

A) 62,5^o B) 64,5^o C)65,5^o D)67,5^o
2) Qo’shni burchaklarning ayirmasi 80^o ga teng. Ularning kattasi kichigidan necha marta katta?
A) 2 B) 2,5 C) 2,6 D)3
3) Yoyiq burchak uchidan 3 ta nur chiqarilgan. Hosil bo’lgan burchaklar 2:3:5:8 nisbatda. Ularning eng kattasi eng kichigidan necha marta kata bo’ladi?
A) 2 B) 4 C) 6 D)1,8
4) Qo’shni burchaklar 13 va 17 sonlariga teskari proporsional. Ulardan kattasini toping.
A) 78^o B) 84 ^o C) 108 ^o D)102 ^o
5) Ikki qo’shni burchaklardan biri ikkinchisining 3 barobaridan 16^o ga kichik. Kichik burchak necha gradus?
A) 59 ^o B) 49 ^o C) 47 ^o D)31 ^o
6) Qo’shni burchaklar ayirmasi ularning yig’indisidan 5 marta kichik. Katta burchak necha gradus?
A) 108 ^o B) 144 ^o C) 120 ^o D)102 ^o

a

x

x

7) a||b , x=?

b

70 ^o

A) 110 ^o B) 125 ^o C) 105^o D)120 ^o

c

b

a

8) a||b va c||d bo’lsa, x=?

5x

d

3x

2x

A) 18 ^o B) 24 ^o C) 36 ^o D)12 ^o

a

9) a||b bo’lsa, x=?

x

126^o

b

43^o

A) 87^o B) 97 ^o C) 77 ^o D)107 ^o

58^o

10)

α

3x

a||b bo’lsa, α=?

x

A) 63^o B) 45 ^o C) 72 ^o D)77 ^o

Uchburchak burchaklari

1) Agar uchburchakning burchaklari 3,4,5 sonlariga proporsional bo’lsa, eng kichik burchak eng katta burchakning necha foizini tashkil etadi?
A) 45% B) 50% C)60% D)72%
2) Agar uchburchak burchaklari 2,5,10 sonlariga teskari proporsional bo’lsa, eng kichik burchak necha gradus?
A) 15^o B) 22,5^o C) 25^o D)12,5^o
3) Uchburchakning ikkita tashqi burchagi 142^o va 117^o bo’lsa, uchinchi ichki burchakni toping.
A) 89 ^o B) 47 ^o C) 101 ^o D)79 ^o
4) Uchburchakning ikkita ichki burchagi 58^o va 64 ^o bo’lsa, uchinchi tashqi burchakni toping.
A) 102 ^o B) 112 ^o C) 122 ^o D)130 ^o



5)

x

shaklga ko’ra x=?

108^o

7x

4x

A) 9^o B) 12 ^o C) 16 ^o D)18 ^o

116^o

6) shakldagi x ning qiymatini toping.

β

x

α

α

β

A) 154 ^o B) 148 ^o C) 152 ^o D) 172 ^o

B

7) AB=AD bo’lsa , x=?

D

x

48^o

18^o

A

C

A) 36 ^oB) 42 ^o C) 48 ^o D)66 ^o

B

8) AD=BD=DC va burchak C =32^o bo’lsa,

A ni toping.

A

C

D

A) 64 ^o B) 58 ^o C) 62 ^o D)54 ^o

B

36^o

9) BAD= DAC va AD=DC bo’lsa, x=?

D

x

A) 68 ^o B) 48 ^o C) 82 ^o D)84 ^o

C

A

10) Teng yonli uchburchakning yon tomonlariga o’tkazilgan balandliklari 100^o li burchak ostida kesishadi. Uning uchidagi burchagini toping.
A) 80 ^o B) 90 ^o C) 100 ^o D)110 ^o

Uchburchakda o’xshashlik

1) Ikkita o’xshash uchburchak yuzlari 28 va 63, ulardan birining perimetri ikkinchisinikidan 8 ga ortiq. Katta uchburchak perimetrini toping.
A) 18 B) 24 C) 28 D)32
2) Perimetrlari 24 va 60 bo’lgan ikki o’xshash uchburchak yuzlari yig’indisi 87 bo’lsa, kichik uchburchak yuzini toping.
A) 10 B) 18 C) 12 D)24
3)Uchburchak asosiga parallel to’g’ri chiziq uning yon tomonini uchidan hisoblaganda 3:8 nisbatda, yuzini esa yuzlari ayirmasi 206 ga teng bo’lgan ikki qismga ajratadi. Berilgan uchburchak yuzini toping.
A) 242 B) 280 C) 300 D)320
4)Uchburchak yon tomoni uchidan boshlab hisoblaganda 3:5:7 kabi nisbatda bo’lindi va bo’linish nuqtalari orqali asosiga parallel to’g’ri chiziqlar o’tkazildi. Hosil bo’lgan figuralar yuzlarining nisbatlarini toping.
A) 3:5:7 B) 9:25:49 C)9:64:225 D)9:55:161
5) Uchburchak tomonlari a:b:c nisbatda. O’rta chiziqlaridan hosil qilingan uchburchak perimetri d. Berilgan uchburchak tomonlarini toping.
A) B)
C) ; D)
6) Teng yonli uchburchakning uchidagi burchagi 36^o, yon tomonlari ga teng bo’lsa,uning asosini toping.
A) 1 B) C) 2 D)
7) Teng yonli uchburchakning uchidagi burchagi 36^o, asosi esa ga teng bo’lsa, yon tomonini toping.
A) 1 B) C) 2 D)

C

x

B

3,2

8) BD||CE , bo’lsa, x=?

A

A) 2,4 B) 1,6 C) 2,6 D)1,8

2,4

D

E

1,8

9) ABCD trapetsiyaning BC va AD asoslarida mos ravishda K va L nuqtalar olingan. KL kesma trapetsiyaning diagonallari kesishgan nuqtadan o’tadi. Agar AL=7, LD=10 va BK=3 bo’lsa, KC kesmani toping.
A) B) 2,1 C) D) 4,3
10) Asoslari 7 va 13 bo’lgan trapetsiya diagonallari kesishgan nuqtadan asoslariga parallel va yon tomonlarini tutashtiruvchi kesma o’tkazilgan. Shu kesma uzunligini toping.
A) 8,4 B) 7,2 C) 6,8 D)9,1

Sinuslar teoremasi

1. O’tkir burchakli ABC uchburchakda AB=5, BC=9, bo’lsa , ni toping .

1. 
   B) C) D)
   

2. ABC uchburchakda A burchak B burchakdan ikki marta katta. Agar AC=b , AB=c bo’lsa, BC tomonni toping.
A) B)
C) D)
3. ABC uchburchak uchun sinA+sinB=sinC tenglik bajarilsa , uchburchak turini aniqlang.
A) o’tkir burchakli
B) o’tmas burchakli
C) to’g’ri burchakli
D) bunday uchburchak mavjud emas
4. Parallelogramm diagonali o’tkir burchagini li burchaklarga ajratsa, tomonlar nisbatini toping.
A) B) C) D)
5. Teng yonli uchburchak uchidagi burchagi , yuzi esa ga teng bo’lsa, uchburchak asosini toping.
A) B)
C) D)
6. Teng yonli uchburchak uchidagi burchagi , asosi esa bo’lsa, yon tomonini toping.
A) B) C) D) 2
7. Uchburchakning bir tomoni 20, unga yopishgan burchaklari ga teng. Uchburchakka tashqi chizilgan doira yuzini toping
A) 100π B) 200π C) 300π D) 400π
8. Teng yonli uchburchakka tashqi chizilgan doira yuzi 49π ga, asosiga yopishgan burchagi ga teng bo’lsa, asos uzunligi qanday?
A) 49 B) 14 C) 2 D) 7
9. ABC uchburchakda AC=5sm, BC tomoni AB tomonidan 2sm uzun va A uchidagi burchagi C uchidagi burchagidan 2 marta katta. Uchburchakning AB va BC tomonlari uzunliklarini toping.
A) 7;9 B) 3;5 C) 4;6 D) 5;7
10. Uchburchak burchaklari 1:4:7 nisbatda. Agar uchburchakka tashqi chizilgan aylana radiusi R bo’lsa, uchburchak yuzini toping.
A) B) C) D)

Kosinuslar teoremasi

1. 
   ABC uchburchakda AC=13, AB+BC=22 va B= bo’lsa, AB va BC tomonlar uzunliklarini toping.
   

A) 6;16 B) 9;13 C) 5;17 D) 7;15
2. ABC to’g’ri burchakli uchburchakda M nuqta AB gipotenuzani AM=3 va MB=6 bo’laklarga ajratdi. Agar BC katet 3ga teng bo’lsa, CM kesma uzunligini toping.
A) 6 B) C) D)
3. Uchburchakning a,b,c tomonlari orasida munosabat o’rinli bo’lsa, c tomon qarshisidagi burchakni toping.
A) B) C) D)
4. Uchburchakning ikki tomoni 3:8 nisbatda, ular orasidagi burchak teng. Uchinchi tomon 21 bo’lsa, qolgan tomonlarni toping.
A) 12;8 B) 14;19 C) 9;24 D) 12;24
5. ABC teng tomonli uchburchak tomoni 3ga teng. CB tomondan olingan M nuqta shu tomonni 1:2 nisbatda bo’ladi. AM kesma uzunligi qanday?
A) B) C) D)
6. Uchburchak tomonlari 1:2 nisbatda. Ular orasidagi burchak bo’lsa, uchburchak turini aniqlang.
A) o’tkir burchakli B) to’g’ri burchakli
C) o’tmas burchakli D) aniqlab bo’lmaydi
7. Uchburchakning a,b,c tomonlari uchun tenglik o’rinli bo’lsa, a tomon qarshisidagi burchakni toping.
A) B) C) D)
8. ABC uchburchakda CD mediana o’tkazilgan. Agar CD AC va AC=CD=a bo’lsa, CB tomon uzunligini toping.
A) B) C) D)
9. Uchburchak tomonlari a,b,c, yuzi S hamda c va b tomonlar orasidagi burchak ga teng bo’lsa, ni toping.
A) 1 B) 2 C) 3 D) 4

14
10.
x= ?
13

10

5

x
A) B) C) D)

Uchburchak bissektrisasi, medianasi, balandligi.

1. Tomonlari 3,5,7 bo’lgan uchburchakning eng katta tomoniga o’tkazilgan bissektrisasini toping.
A) B) C) D)
2. Tomonlari 5, 7, bo’lgan uchburchakning kattaligi bo’yicha o’rtacha tomoniga o’tkazilgan medianasini toping.
A) 5,5 B) 6,5 C) 5 D)
3. Tomonlari 5,9, bo’lgan uchburchakning eng kichik balandligini toping.
A) 3,6 B) 4 C) 4,8 D)
4. Tomonlari 6 va 8 bo’lgan uchburchakning shu tomonlariga o’tkazilgan medianalari o’zaro perpendikulyar. Uchburchakning uchinchi tomonini toping.
A) B) C) D)
5. Uchburchak tomonlari 13,20,21 bo’lsa, eng kichik balandligini toping.
A) 10,4 B) 12 C) 8 D) 9,6
6. Teng yonli ABC uchburchakning yon tomoniga o’tkazilgan AD bissektrisa uchburchak yuzlarini mos ravishda S₁ va S₁ bo’lgan ABD va ADC uchburchaklarga ajratadi. ABC uchburchak asosini toping.
A) B)
C) D)
7. Uchburchak ikki tomoni va ular orasidagi burchak bissektrisasi mos ravishda 10,15,6 bo’lsa, uchinchi tomon uzunligini toping.
A) B) C) D)
8. Medianalari 13,14,15 bo’lgan uchburchak yuzini toping.
A) 84 B) 63 C) 112 D) 128
9. Teng yonli uchburchakning yon tomoniga o’tkazilgan bissektrisasi teng ikkiga bo’ladi. Agar bissektrisasi 2ga teng bo’lsa, asosiga o’tkazilgan medianani toping.
A) 1 B) 2 C) 1,8 D) aniqlab bo’lmaydi
10. Uchburchak tomonlari 5,6,7. Katta burchak bissektrisasi bissektrisalarning kesishishgan nuqtasi orqali uchburchak uchidan boshlab qanday nisbatda bo’linadi?
A)5:3 B) 11:7 C) 8:5 D) 2:1

Teng yonli uchburchak

1. 
   Teng yonli uchburchak tomonlari 5:3 nisbatda. Perimetri 143 bo`lsa, asosini toping.
   

1. 
   33 B) 65 C) 33 yoki 65 D) 39 yoki 63
   

2. 
   ABC teng yonli uchburchakning BC asosida D nuqta olingan. Agar AB=AC=20, BD=21, DC= 11 bo`lsa, AD kesma uzunligini toping.
   

1. 
   12 B) 13 C) 14 D) 10
   

3. 
   Teng yonli uchburchak uchidagi burchagi α, asosi a ga teng. Uchburchakni yuzini toping.
   

1. 
   B) C) D)
   

4. 
   Teng yonli uchburchak uchidagi burchagi α ga, yuzi S ga teng bo`lsa, uchburchak asosini toping.
   

1. 
   B)
   

C) D)

5. 
   Teng yonli uchburchakka ichki chizilgan aylana radiusi r. Asosiga o`tkazilgan balandlik aylana bilan kesishib 1:2 nisbatda bo`linadi. Uchburchak yuzini toping.
   

A) B)
C) D)

6. 
   Teng yonli uchburchak asosidagi burchagi sinusi uchidagi burchagi kosinusidan 3marta katta. Asosidagi burchagi sinusini toping.
   

A) B) C) D)

7. 
   Teng yonli uchburchak asosidagi burchagi sinusi va uchidagi burchagi kosinusi yig’indisi 0 ga teng. Uning asosidagi burchagi necha gradus? A) 60^o B) 45 ^o C) 30 ^o D) 15 ^o
   
8. 
   Teng yonli to`g`ri burchakli uchburchak katetlariga o`tkazilgan medianalar orasidagi o`tkir burchakni toping.
   

A) arccos 0,6 B) arccos 0,8
C) arccos 0,1 D) arccos 0,3

9. 
   Asosi 8, uchidagi burchagi 120 ^o bo`lgan teng yonli uchburchakka ikki uchi asosda, ikki uchi esa yon tomonlarda yotuvchi eng katta yuzali to`g`ri to`rtburchak ichki chizilgan. Shu to`g`ri to`rtburchak yuzini toping.
   

A) B) C) D)

10. 
    Tomonlari 15,15,18 bo`lgan teng yonli uchburchakka eng katta yuzaga ega bo`lgan parallelogramm shunday ichki chizilganki, uning bir burchagi uchburchakning asosidagi burchagi bilan umumiy. Parallelogramm yuzini toping.
    

1. 
   58 B) 56 C) 64, D) 54
   

To’g’ri burchakli uchburchak

1. To’g’ri burchakli uchburchakning bir kateti ikkinchisidan 5 sm ga uzun, lekin gipotenuzadan 5 sm ga qisqa bo’lsa, gipotenuzani toping.
A)20sm B)25sm C)15 sm D)30sm
2. To’g’ri burchakli uchburchakning o’tkir burchaklaridan chiqqan medianalari 12 va 16 bo’lsa, gipotenuzani toping.
A)6 B) C) D)
3. To’g’ri burchakli uchburchakka ichki chizligan aylana radiusi 4 ga, tashqi chizilgan aylana radiusi 8 ga teng bo’lsa, uchburchak yuzini toping.
A)60 B)72 C)84 D)80
4. To’g’ri burchakli uchburchakka ichki chizilgan aylana gipotenuzani 2:3 nisbatda bo’ladi. Agar uchburchak perimetri 72 bo’lsa, katetlar yig’indisini toping.
A)42 B)36 C)48 D)54
5. To’g’ri burchakli uchburchak katetlari 18 va 24. Unga ichki va tashqi chizilgan aylanalar markazlari orasidagi masofani toping.
A)5 B) C) D)
6. To’g’ri burchakli uchburchak gipotenuzasiga tushirilgan balandligi h. Katta katetga tushirilgan mediana uzunligining eng kichik qiymatini toping.
A)h B)1,2h C) h D)1,5h
7. To’g’ri burchakli uchburchak to’g’ri burchagidan chiqarilgan bissektrisasi va mediana mos ravishda 4 va ga teng bo’lsa, uchburchak yuzini toping.
A)12 B)2 C)20 D)
8. To’g’ri burchakli uchburchakning kichik burchagi a ga teng. Unga doira shunday ichki chizilganki, u gipotenuza o’rtasiga urinadi va kichik katet o’rtasidan kesib o’tadi. Doira va uchburchak yuzlari nisbatini toping.
A) B) C) D)
9. To’g’ri burchakli uchburchakka ichki chizilgan aylana markazidan gipotenuza uchlarigacha masofalar va ga teng. Gipotenuza uzunligini toping.
A) B) C)4 D)
10. ABC to’g’ri burchakli uchburchak o’tkir burchaklaridan AM va BN medianalar o’tkazilgan. Ular O nuqtada kesishadi. Agar bo'lsa,
A)2S B)3S C)4S D)1,5S

Muntazam uchburchak

1. Muntazam uchburchak bissektrisasi 24 sm. Unga ichki chizilgan doira yuzini toping.
A)256π sm² B)128π sm² C)64π sm² D)32π sm²
2. Muntazam uchburchak medianasi 18 sm. Unga tashqi chizilgan doira yuzini hisoblang.
A)324π sm² B)144π sm² C)36π sm² D)81π sm²
3. Muntazam uchburchak yuzi 4 bo’lsa, uning perimetrini toping.
A)8 B)10 C)12 D)14
4. Muntazam uchburchak perimetri 6 bo’lsa, uning yuzini toping.
A)2 B)3 C)4 D)
5. Balandligi 9 ga teng muntazam uchburchakka doira, doiraga muntazam uchburchak, muntazam uchburchakka yana doira, doiraga yana muntazam uchburchak,… ichki chizilgan. Hosil bo’lgan doiralar yuzlari yig’indisini toping.
A)6π )9π C)12π D)18π
6. Tomoni 9 ga teng muntazam uchburchak ichiga tomoni 2 ga teng kvadratchalardan ko’pi bilan nechtasini sig’dirish mumkin?
A)4 ta B)6 ta C) 8ta D)9ta
7. Muntazam ABC uchburchakning A uchidan BC tomonni kesuvchi nur chiqarilgan. Shu nurda uchburchak tashqarisidan M nuqta olingan bo’lib, u ABC uchburchakka tashqi chizilgan aylanaga tegishli. Agar AMB=20^o va AMC=30^o bo’lsa, MAB=? A)20 ^o B)30 C)40 ^o D)aniqlab bo’lmaydi.
8. Muntazam uchburchakka eng katta yuzali kvadrat ichki chizilgan. Agar muntazam uchburchak tomoni 6+4 bo’lsa, kvadrat tomonini toping.
A)2+ B)3 C)6 D)2+4
9. Muntazam uchburchakka r radiusli 3 ta teng aylana shunday ichki chizilganki, ular o’zaro hamda ikkitadan tomonlarga urinadi. Muntazam uchburchak tomonini toping.
A)2r( ) B)
C) D) +2
10. Muntazam ABC uchburchakning BC tomonidan M nuqta olingan bo’lib, BM=5, MC=3 bo’lsa, AM kesma uzunligini toping.
A)6 B)7 C)8 D)9

Uchburchak yuzi

1. 
   

Shakldan ni toping.

AB=2, BD=1.

A) B) C) D)

2) Tomonlari 12, 20 va 24 bo’lgan uchburchakning yuzini toping.
A) B) C) D)
3) Uchburchakning bir tomoni a ga, unga yopishgan burchaklar esa va bo`lsa, shu uchburchak yuzini hisoblang.
A) B)
C) D)
4) Uchburchak ikki tomoni a va b bo`lib, yuzi bo`lsa, uchinchi tomonni toping.
A) B)
C) D)
5) Uchburchak tomonlari 5, 12, va 13 sonlariga proporsional. Eng katta tomon eng kichigidan16 ga katta. Uchburchak yuzini toping.
A) 240 B) 160 C) 120 D) 210
6) Teng yonli uchburchakning yon tomoniga o`tkazilgan balandligi 12, asosiga o’tkazilgan balandligi esa 10 bo`lsa, uchburchak yuzini toping.
A) 90 B) 84 C) 72 D) 75
7) Yuzi 90 bo`lgan qavariq to`rtburchak berilgan. Uning diagonallari kesishish nuqtasida 2:3 va 4:5 nisbatlarda bo`linadi. Diagonallar kesishishidan hosil bo’lgan 4 ta uchburchakdan eng kichigi yuzasini toping.
A) 12 B) 18 C) 16 D) 24
8)



AE=14, ED=24, CD=7
Rasmdagi ni toping.

1. 
   225 B) 625 C) 575 D) 485
   

9)

ABCD- to’g’ri to’rtburchak. AB=6, BC=9, BE va KC – bissektrisalar.
A) 3,25 B) 4,75 C) 2,25 D) 5,5
10) ABCD- trapetsiya, , bo`lsa, ni toping.

A) 48 B) 50 C) 98 D) 84