1 8-sinf geom yangi. 1-8-bet. 2015(boshi). p65

ABCD parallelogrammda: 1) agar BC tomon AB dan 8 sm uzun, pe- rimetri esa 64 sm ga teng bo‘lsa, tomonlarni; 2) agar FA = 55° bo‘lsa, burchaklarni toping.

Agar parallelogrammning perimetri 2 m ga teng va: 1) qo‘shni tomonlari ayirmasi 1 sm ga teng; 2) qo‘shni tomonlarining nisbati 2 ga teng;

3. 
   ikkita teng yonli uchburchaklardan tashkil topgan bo‘lsa, parallelo­gramm tomonlari nimaga teng?
   

576. 
     ABCD parallelogramm A burchagining bissektrisasi BC tomonni P nuq­tada kesadi va shu bilan birga BP = PC. Agar parallelogrammning perimetri 42 sm ga teng bo‘lsa, uning tomonlarini toping.
     
577. 
     Ikkitta ABCD va ANCP parallelogrammni yasang.
     

1. 
   AC, BD va NP kesmalar bir nuqtada kesishishini isbotlang.
   
2. 
   BNDP to‘rtburchak parallelogramm ekanini isbotlang.
   

576. 
     Agar to‘rtburchakning ikki juft teng tomonlari bo‘lsa, bu to‘rtburchak har doim ham parallelogramm bo‘ladimi?
     
577. 
     Parallelogramm burchaklaridan birining bissektrisasi o‘zi kesib o‘tadigan tomonni 7 sm va 9 sm li kesmalarga bo‘ladi. Shu parallelogrammning perimetrini toping.
     
578. 
     To‘g‘ri to‘rtburchak diagonallarining kesishish nuqtasidan uning tomon- lariga o‘tkazilgan perpendikularlar, mos ravishda, 5 sm va 7 sm ga teng. Bu to‘g‘ri to‘rtburchakning perimetri va yuzini toping.
     
579. 
     To‘g‘ri to‘rtburchak diagonallarining kesishish nuqtasidan uning tomon- lariga o‘tkazilgan perpendikularlar, mos ravishda, 4 sm va 6 sm ga teng. Bu to‘g‘ri to‘rtburchakning perimetrini va yuzini toping.
     
580. 
     1) ABCD parallelogrammda ZA = 75°. Parallelogrammning qolgan bur- chaklari nimaga teng?
     

2. 
   Parallelogrammning ikkita qarama-qarshi burchaklarining yig‘indisi 220° ga teng. Shu parallelogrammning burchaklari nimaga teng?
   

576. 
     Agar ABCD rombda ZB = 100° va AB = 15 sm bo‘lsa, uning perimetri va burchaklarini toping.
     
577. 
     To‘g‘ri to‘rtburchak diagonallarining kesishish nuqtasidan uning tomon- lariga o‘tkazilgan perpendikularlar, mos ravishda, 4 sm va 11 sm ga teng. Bu to‘g‘ri to‘rtburchakning yuzini toping.
     
578. 
     ABCD romb berilgan. AC va BD diagonallar, mos ravishda, 30 sm va 12 sm ga teng. Rombning yuzini toping.
     
579. 
     1) ABCD teng yonli trapetsiyada BC = 20 sm, AB = 24 sm va FD = 60° bo‘lsa, uning AD asosini toping.
     

2. 
   Teng yonli trapetsiyaning burchaklaridan biri 105° ga teng. Tra- petsiyaning qolgan burchaklarini toping.
   

576. 
     Trapetsiyaning ketma-ket olingan burchaklarining nisbati quyidagicha bo‘lishi mumkinmi: 1) 7 : 4 : 3 : 5; 2) 8 : 7 : 13 : 14?
     
577. 
     To‘g‘ ri burchakli trapetsiyaning asoslari a va b ga, burchaklaridan biri esa a ga teng. Agar: 1) a = 7 sm, b = 4 sm, a = 60° bo‘lsa, katta yon to- monni toping; 2) a = 15 sm, b = 10 sm, a = 45° bo‘lsa, kichik yon to- monni toping.
     
578. 
     Parallelogrammning yuzi 40 sm² ga, tomonlari esa 10 sm va 8 sm ga teng. Shu parallelogrammning ikkala balandligini toping.
     
579. 
     ABCD rombning diagonallari 15 sm va 36 sm ga teng. AC diagonalida P nuqta shunday olinganki, unda AP: PC = 4:1 nisbatda. APD uch­burchakning yuzini toping.
     
580. 
     Teng yonli to‘g‘ri burchakli uchburchakning gipotenuzasi 20 sm ga teng. Shu uchburchakning yuzini toping.
     
581. 
     Teng yonli trapetsiyaning perimetri 32 sm ga, yon tomoni 5 sm ga, yuzi esa 44 sm² ga teng. Trapetsiyaning balandligini toping.
     
582. 
     To‘g‘ ri burchakli trapetsiyaning yuzi 120 sm² ga, perimetri 56 sm ga, kichik yon tomoni esa 6 sm ga teng. Katta yon tomonini toping.
     
583. 
     ABCD to‘g‘ri to‘rtburchak C uchining bissektrisasi AD tomonni P nuq­tada kesadi. Agar AP = 10 sm, PD = 14 sm ga teng bo‘lsa, shu to‘g‘ri to‘rtburchakning yuzini toping.
     
584. 
     To‘g‘ ri to‘rtburchak bilan parallelogramm bir asosga va bir xil perimetr- ga ega. Shu parallelogramm bilan to‘g‘ri to‘rtburchakning yuzlarini taq- qoslang.
     
585. 
     Uchburchakning tomonlari 21, 72 va 75 ga teng. Shu uchburchakning yuzini toping.
     
586. 
     Д ABC da AE va BD — balandliklar. AC = 20 sm, BD = 16 sm va BC = 32 sm. AE ni toping.
     
587. 
     Teng yonli trapetsiyaning diagonali 50 sm ga, balandligi esa 30 sm ga teng. Shu trapetsiyaning yuzini toping.
     
588. 
     Aylanaga ichki chizilgan BAC burchak 45° ga teng, u BC yoyga tiraladi. BOC burchakni toping, bunda O — aylana markazi.
     
589. 
     To‘g‘ri burchakli ABC uchburchakda (ZC = 90°) ZA = 30°, AC = 2^3 . Markazi A nuqtada va radiusi 2,2 ga teng bo‘lgan aylana o‘tkazilgan. Shu aylana BC tomon bilan nechta umumiy nuqtaga ega?
     
590. 
     Tashqi chizilgan to‘rtburchakning ikkita qarama-qarshi tomonlarining yig‘indisi 35 sm ga teng. Shu to‘rtburchakning perimetrini toping.
     
591. 
     Biror ABCD parallelogrammni chizing. Vektorlarni yasang:
     

1) AB + BC; 2) AD + DUC; 3) AB - AD; 4) DB - DA.

576. 
     Quyidagi vektorlar kollinearmi: 1) a (—2; 1) va b (4; —2); 2) a (1; —3) va b (1; 3); 3) a (3; -2) va b (-3; 2); 4) a (0; -1) va b (1; 0)?
     
577. 
     Vektorlar yig‘indisini toping: BH + HK + TP + MT + KM + PQ .
     
578. 
     FK vektorni EF va EK vektorlar orqali ifodalang.
     
579. 
     A (-1; 2), B (-4; -2), C (-1; 3), D (-4; -2) bo‘lsin. Hisoblang:
     

1) AB • CD ; 2) AC • BD ; 3) AD • BC ; 4) CA • DB.

7. 
   TEST
   

1. 
   To‘g‘ri burchakli uchburchakning katetlari 6 va 8 ga teng. Uning gipote- nuzasiga tushirilgan balandligini toping.
   

A) 4,8; B) 5; D) 4,5; E) 4,7.

2. 
   To‘rtburchakning burchaklari o‘zaro 3 : 5 : 4 : 6 nisbatda. To‘rtburchakning kichik burchagini toping.
   

A) 80°; B) 30°; D) 60°; E) 40°.

3. 
   Qavariq to‘rtburchakning diagonallari uni nechta uchburchakka ajratadi?
   

A) 4; B) 5; D) 6; E) 8.

4. 
   To‘g‘ri to‘rtburchakning eni 5 ga teng, bo‘yi undan 7 ga ortiq. To‘g‘ri to‘rtburchakning perimetrini hisoblang.
   

A) 32; B) 34; D) 24; E) 26.

5. 
   Har bir ichki burchagi 156° bo‘lgan qavariq ko‘pburchakning nechta to- moni bor?
   

A) 10; B) 15; D) 6; E) 12.

6. 
   To‘g‘ri to‘rtburchakning bo‘yi 20% va eni 10% ga orttirilsa, uning yuzi necha foiz ortadi?
   

A) 20%; B) 35%; C) 27%; D) 32%.

7. 
   Rombning yuzi 24 ga, diagonallaridan biri esa 6 ga teng. Uning tomonini toping.
   

A) 10; B) 5; C) 8; D) 4,8.

8. 
   Rombning balandligi 5 ga, diagonallarining ko‘paytmasi 80 ga teng. Uning perimetrini toping.
   

A) 32; B) 16; C) 24; D) 28.

9. 
   a(2; —3) va b (—2; —3) vektor berilgan. m =-a + 2b vektorning koordi­natalarini toping.
   

A) (-6; -3); B) (-3; 6); C) (-2; -9); D) (2; -3).

10. 
    a(3; 2) va b (0; -1) vektor berilgan. 2a - 4b vektorning modulini toping. A) 10; B) 6; C) 8; D) 3.
    

JAVOBLAR
7- sinfda o‘tilganlarni takrorlash 2. 85° dan. 3. ZAOC = 110°. 5. 1) 80°; 2) 38°; 3) 2°. 6. 1) 72° va
108°; 3) 36° va 144°; 4) 90° va 90°. 7. 1) 70°, 110°, 70°, 110°. 8. 104°. 9. Yo‘q. 11. ZAOC = 120°, ZBOD = 130°, ZCOD = 60°, ZCOE = 110°. 12. Ha, teng. 18. 3. 19. 9. 20. 8 sm, 8 sm, 12 sm. 21. BC = 12 sm. 22. 16 sm, 24 sm, 32 sm. 24. 9. 25. P = (3x - 3) sm. 30. Ha, teng. 31. 52°, 65°.

1. 
   115°. 43. 58°.
   

1. 
   §. 3. 1) 3 ta; 2) 4 ta. 4. (n - 2) ta. 6. 1) 8 ta, 44 ta; 2) 27 ta, 405 ta. 7. 8. 9. 12 sm, 36 sm. 12.
   

2. 
   sm. 13. 21 ta tomon va 189 ta diagonal. 14. 1) 3 ta; 2) 9 ta. 15. 18 sm. 20. 36°, 72°, 108°, 144°. 22. 1) n = 8; 3) n = 24. 23. a) 1) n = 10 ta; 3) n = 36 ta; b) 2) n = 15 ta; 3) n= 6 ta. Ko‘rsatma. Ichki burchaklari teng bo‘lgan n burchakning har bir burchagi 180°(n — 2): n ga teng. 24. n = 14. 25.
   

1. 
   n > 5 da o‘tmas burchak; 2) n = 4 da to‘g‘ri burchak (to‘g‘ri to‘rtburchak, kvadrat); 3) n = 3 da o‘tkir burchak (uchburchak) bo‘lishi mumkin. 26. 180°. 27. n = 5. 29. 1) n = 36; 2) n = 30. 32.
   
2. 
   60 sm. 34. 1) 35°, 145°, 35°, 145°. 35. 70°, 110°, 70°, 110°. 36. 12 sm, 15 sm, 12 sm. 37. ZC = 30°, ZD = 150°. 38. 16 sm, 4 sm. 41. 10 sm, 15 sm, 10 sm, 15 sm. 42. P_ABO = 20 sm, P_B0C = 24 sm. 51. ABCD to‘rtburchak parallelogramm bo‘ladi. 53. 12 sm, 15 sm. 54. 72 sm. 57. 12 sm. 61. AB = DC = 4 sm, BC = AD = 8 sm. 64. 1) Ikkita teng: teng tomonli uchburchakdan yoki teng yonli uchburchakdan; 2) to‘rtta teng to‘g‘ri burchakli uchburchakdan romb yasash mumkin. 73. ZA = ZC = 40°, ZB = ZD = 140°. 74. 64 sm. 77. 1) 10 sm. 81. 57 sm. 83. 18 dm 4 sm. 88. 1) 8 sm; 2) 12,3 sm. 89. P_DEF = 60 sm, DE = 25 sm, EF = 15 sm, DF = 20 sm. 90. m + n; 16 dm. 92. 2) A₁B₁ = 60 sm, B_lC_l = 24 sm, A₁C₁ = 48 sm. 93. 1) 6 sm. 95. 7,3 sm. 96. 28 sm. 100. Mumkin. 101. 150°. 103. 70°, 81°. 104. 1) 20 sm; 2) 50°. 105. 23 sm. 108. 108°; 94°. 109. 48 sm. 110. 90°, 90°, 110°, 70°. 113. 132 sm. 114. 33,5 sm, 9,5 sm. 119. 60°, 120°, 120°, 60°. 120. 55°, 125°, 125°, 55°. 122. 3,4 dm. 124. 1) 14 sm. 125. 20 sm. 126. 12 sm. 127. 40 sm. 131. 24 sm, 12 sm. 133. AE = 2 sm, EF = 8 sm, fD = 2,5 sm, AD = 10 sm. 134. 30 sm, 10 sm. 135. 4 sm, 10 sm. 136. 22 sm, 10 sm. 138. 4 sm, 2 sm. 140. ZC = 45°, ZD = 135°. 144. 44 sm. 145. 55°, 125°, 55°. 148. 25 sm, 15 sm. 151. AC = 5 sm. 152. OB₁ = 3,2 sm, OB₂ = 4,8 sm, OB₃ = 6,4 sm. 154. 4,5 sm, 9 sm, 13,5 sm. 155. 18 sm, 21 sm. 157. p. 159. Ha, parallel bo‘ladi. 161. 18 sm. 163. 1) AC: BD = = 0,5; BD: AC = 2; 2) o‘zgarmaydi. 165. 2) 6,25 sm. 166. 1) Ha, chunki 1,6 • 1,8 = 0,6 • 4,8;
   

2. 
   yo‘q, chunki - * -10-. 170. AB = CA • EF: CF. AB = 600 m. 172. 1) 20 sm, 15 sm. 180. 42 sm,
   

38 sm, 34 sm. 181. 5 dm. 182. 1) 16 sm. 189. A₁(a; -b) va A₂(-a; b). 196. ABCD kvadrat AC o‘qqa nisbatan simmetriyada o‘ziga-o‘zi o‘tadi. 197. A₁(-4; -4) va A₂(4; 4). 198. C(0; -2). 200. 1) 2 ta, rombning diagonallari; 2) 4 ta, o‘rta perpendikular va kvadrat diagonallari yotgan to‘g‘ri chiziqlar; 4) 1 ta, asosiga o‘tkazilgan medianasi yotgan to‘g‘ri chiziq teng yonli ucburchakning simmetriya o‘qi bo‘ladi. 201. 1) 12 sm. 206. 1) 6 sm, 14 sm, 14 sm; 2) 5 sm, 10 sm, 10 sm; 3) 24 sm, 21 sm, 21 sm yoki 21 sm, 24 sm, 24 sm. 207. 1) A, B, C, D, E, M, T, U, V, W, Y; 2) H, I, O, X. 209. P_EBCF= 55 sm, P_ABCD = 70 sm. 210. AB = BC = 16,5 sm; AC = 13 sm. 211. Agar u o‘q simmetriyasiga parallel bo‘lsa. 216. 2) A₁(2; —2), B₁(—2; 1). 219. 3) Ko‘rsatma. Koordinatalar boshiga nisbatan simmetriyada nuqtaning koordinatalari ishorasi qarama-qarshisiga o‘zgaradi. 4) Ko‘rsatma. Koordinatalar burchaklari bissektrisasiga nisbatan simmetriyada nuqta koordi­natalari o‘z o‘rinlarini almashtiradi. 222. 6 raqami 9 raqamiga o‘tadi. 223. H, I, N, O, S, X, Z. 225. 1) 4(1; -1), B^—2; 0), q(2; -3), ^(0; -1), E^-3; -4), F^-2; 2). 226. 1) A va C; 2) A va E;

3. 
   B va D. 234. 1) Ox o‘qiga nisbatan simmetriyada: A (2; -2), B (-2; 0), C(3; -4), D (0; -2), E(-2; 2), F(-4; -2), K(3; 2), L (-3; 3); Oy o‘qiga nisbatan simmetriyada: A (-2; 2), B (2; 0), C(-3; 4), D (0; 2), E(2; -2), F(4; 2), K(-3; -2), L (3; -3); 2) O(0; 0) ga nisbatan simmetriyada: A (-2; -2), B (2; 0), C (-3; -4), D (0; -2), E (2; 2), F(4; -2), K(-3; 2), L (3; 3). 246. 1) A va D.
   

2. 
   §. 254. 2 ta, ulardan teng yonli uchburchak va parallelogramm yasash mumkin. 257. 1) Yo‘q; 2) ha. 266. 1) 4 marta ortadi. 267. 1) n² marta ortadi. 270. Tomoni a₁ = 2a bo‘lgan kvadrat. 271.
   

1.