geometriya 9-sinf

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geometriya 9 o‘zbekiston respublikasi xalq ta’limi vazirligi umumiy o‘rta ta’lim maktablarining 9-sinfi uchun darslik sifatida tasdiqlagan b. haydarov, e. sariqov, a. qo‘chqorov toshkent — 2014 «o‘zbekiston milliy ensiklopediyasi» davlat ilmiy nashriyoti 2 3 respublika maqsadli kitob jamg‘armasi mablag‘lari hisobidan ijara uchun chop etildi. m u n d a r i j a 7–8-sinflarda o‘tilganlarni takrorlash 1. uchburchaklar...............................................................................................8 2. uchburchaklar (davomi)............................................................................. 10 3. to‘rtburchaklar............................................................................................ 12 4. to‘rtburchaklar (davomi) ............................................................................ 14 i bob. o‘xshash geometrik shakllar 5. ko‘pburchaklarning o‘xshashligi ................................................................ 18 6. o‘xshash uchburchaklar va ularning xossalari ............................................20 7. uchburchaklar o‘xshashligining birinchi alomati ....................................... 22 8. uchburchaklar o‘xshashligining ikkinchi alomati ....................................... 24 9. uchburchaklar o‘xshashligining uchinchi alomati ...................................... 26 10. to‘g‘ri burchakli uchburchaklarning o‘xshashlik alomatlari ....................... 28 11. o‘xshashlik alomatlarining isbotlashga doir masalalarga tatbiqlari ............. 30 12. masalalar yechish ....................................................................................... 32 13. bilimingizni sinab ko‘ring .......................................................................... 34 14. geometrik shakllarning o‘xshashligi ........................................................... 36 15. o‘xshash ko‘pburchaklarning xossalari ....................................................... 38 16. gomotetiya va …

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...............................................................40 17. o‘xshash ko‘pburchaklarni yasash .............................................................. 42 18. amaliy mashg‘ulot ...................................................................................... 44 19. masalalar yechish ....................................................................................... 46 20. masalalar yechish ....................................................................................... 48 21. i bobga doir qo‘shimcha masalalar va ma’lumotlar .................................... 49 ii bob. uchburchak tomonlari va burchaklari orasidagi munosabatlar 22. o‘tkir burchakning sinusi, kosinusi, tangensi va kotangensi ....................... 52 23. masalalar yechish ....................................................................................... 54 24. ba’zi burchaklarning sinusi, kosinusi, tangensi va kotangensini hisoblash .56 25. masalalar yechish ....................................................................................... 58 26. 0° dan 180° gacha bo‘lgan burchakning sinusi, kosinusi, tangensi va kotangensi ..................................................................................................60 27. asosiy trigonometrik ayniyatlar................................................................... 62 28. asosiy trigonometrik ayniyatlar (davomi).................................................... 64 29. bilimingizni sinab ko‘ring............................................................................ 66 30. uchburchak yuzini burchak sinusi yordamida hisoblash............................. 70 31. sinuslar teoremasi....................................................................................... 72 32. kosinuslar teoremasi................................................................................... 74 33. sinuslar va kosinuslar teoremalarining ba’zi tatbiqlari................................. 76 34. ikki vektor orasidagi

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burchakni hisoblash................................................... 78isbn 978-9943-07-296-1 fizika-matematika fanlari doktori, professor a. a’zamov tahriri ostida. taqrizchilar: a. narmanov – o‘zbekiston milliy universiteti geometriya va amaliy matematika kafedrasi mudiri, fizika-matematika fanlari doktori. g. yusupova – o‘zbekiston fa matematika institutining katta ilmiy xodimi, fizika-matematika fanlari nomzodi. m. akramov – toshkent viloyati parkent tumanidagi 5-sonddshdldldldli maktabning oliy toifali matematika o‘qituvchisi. m. shaniyazova – toshkent shahar sirg‘ali tumanidagi 300-sonli maktabning matematika o'qituvchisi 9-sinfda geometriyaning planimetriya qismini – yassi geometrik shakllarning xossalarini o‘rganish davom ettiriladi. unda siz geometrik shakllarning o‘xshashligi, uchburchakning tomonlari va burchaklari orasidagi munosabatlar, aylana uzunligi va doira yuzi, uchburchak va aylanadagi metrik munosabatlar bilan tanishasiz. ushbu “geometriya” darsligining mazmuni qat’iy aksiomatik tizim asosiga qurilgan. unda nazariy materiallar imkon boricha sodda va ravon tilda bayon etilgan. barcha mavzu va tushunchalarni turli-tuman hayotiy misollar orqali ochib berishga harakat qilingan. har bir mavzudan so‘ng berilgan savollar, isbotlash, hisoblash va yasashga doir masala va misollar o‘quvchini ijodiy fikrlashga undaydi, …

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........................................... 82 37. uchburchaklarni yechish usullarining amaliyotda qo‘llanishi...................... 84 38-39. ii bobga doir qo‘shimcha masalalar va ma’lumotlar.............................. 86 iii bob. aylana uzunligi va doira yuzi 40. aylanaga ichki chizilgan ko‘pburchak.........................................................90 41. aylanaga tashqi chizilgan ko‘pburchak........................................................ 92 42. muntazam ko‘pburchak............................................................................... 94 43. muntazam ko‘pburchakka ichki va tashqi chizilgan aylanalar..................... 96 44. muntazam ko‘pburchakning tomoni bilan tashqi va ichki chizilgan aylanalar radiuslari orasidagi bog‘lanish...................................................................... 98 45. bilimingizni sinab ko‘ring......................................................................... 100 46. aylana uzunligi.......................................................................................... 102 47. aylana yoyi uzunligi. burchakning radian o‘lchovi................................... 104 48. doira yuzi ................................................................................................ 106 49. doira bo‘laklari yuzi.................................................................................. 108 50. masalalar yechish ..................................................................................... 110 51. iii bobga doir qo‘shimcha masalalar va ma’lumotlar................................ 112 iv bob. uchburchak va aylanadagi metrik munosabatlar 52. kesmalar proyeksiyasi va proporsionallik.................................................. 116 53. proporsional kesmalarnitpng xossalari.......................................................... 118 54. to‘g‘ri burchakli uchburchakdagi proporsional kesmalar.......................... 120 55. berilgan ikkita kesmaga o‘rta proporsional kesmani yasash.....

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.................. 122 56. aylanadagi proporsional kesmalar............................................................. 124 57. masalalar yechish...................................................................................... 126 58. iv bobga doir qo‘shimcha masalalar va ma’lumotlar................................ 128 v bob. planimetriya kursini takrorlash 59. koordinatalar usuli.................................................................................... 132 60. koordinatalar usuli va vektorlar................................................................ 134 61. aylana va doira.......................................................................................... 136 62. takrorlash.................................................................................................. 138 63. takrorlash.................................................................................................. 139 64. takrorlash.................................................................................................. 141 65. takrorlash.................................................................................................. 142 66. takrorlash.................................................................................................. 143 67–68. yakuniy nazorat ishi........................................................................... 144 planimetriyaga oid asosiy tushuncha va ma’lumotlar ............................... 146 javoblar va ko‘rsatmalar .......................................................................... 154 aziz o‘quvchilar! axborot texnologiyalari asrida yashayapmiz. zamonaviy taraqqiyotda kechayotgan olamshumul o‘zgarishlar zamirida, albatta, fan va texnika rivoji yotibdi. bunday sharoitda yoshlarning asosiy vazifasi buyuk ajdodlarimizga munosib avlod bo‘lib, zamon bilan hamnafas qadam tashlash, ilm-fan cho‘qqilarini qunt bilan egallashdan iboratdir. bu borada matematikaning tutgan o‘rni beqiyosdir. ma’lumki, matemati

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geometriya 9 o‘zbekiston respublikasi xalq ta’limi vazirligi umumiy o‘rta ta’lim maktablarining 9-sinfi uchun darslik sifatida tasdiqlagan b. haydarov, e. sariqov, a. qo‘chqorov toshkent — 2014 «o‘zbekiston milliy ensiklopediyasi» davlat ilmiy nashriyoti 2 3 respublika maqsadli kitob jamg‘armasi mablag‘lari hisobidan ijara uchun chop etildi. m u n d a r i j a 7–8-sinflarda o‘tilganlarni takrorlash 1. uchburchaklar...............................................................................................8 2. uchburchaklar (davomi)............................................................................. 10 3. to‘rtburchaklar............................................................................................ 12 4. to‘rtburchaklar (davomi) .........................................

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