ᠠᠷᠪᠠᠨ ᠨᠢᠭᠡᠳᠤᠭᠡᠷ ᠪᠥᠯᠥᠭ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ （ᠨᠢᠭᠡᠴᠢ ᠶᠢᠨ ᠪᠠᠢᠴᠠᠭᠠᠯᠲᠠ 2） .pdf

ᠠᠷᠪ ᠠᠨ ᠨᠢ ᠭᠡᠳᠤ ᠭᠡᠷ ᠪ ᠥᠯᠥ ᠭ ᠦᠨ ᠪᠠ ᠢᠴᠠ ᠭᠠᠯᠲ ᠠ ᠠᠩᠭᠢ ᠪᠥᠯᠥᠭ᠄ ᠨᠡᠷ ᠡ ᠄ ︵90 ᠮ ᠢᠨᠦ᠋ᠲ ᠂ ᠨᠠᠢ ᠲᠡ 120 ᠬᠤ ᠪᠢ ︶ ᠨᠢᠭᠡ ᠂ ᠰ ᠤᠩᠭᠤ ᠬᠤ ᠰ ᠡᠲᠤᠪ ᠃ ︵ ᠰᠡᠲ ᠤᠪ ᠪ ᠦᠷᠢ 3 ᠬᠤᠪᠢ ᠂ ᠨ ᠠᠢᠲ ᠡ 30 ᠬᠤ ᠪᠢ ︶ 1.ᠭ ᠤᠷᠪᠠ ᠨ ᠭ ᠡᠷᠴᠢ ᠮ 𝑎 , b , c ᠶᠢᠨ ᠤᠷ ᠳᠤ ᠨ ᠢ ᠴ ᠦ᠋ᠮ ᠪᠦᠬ ᠦᠯᠢ ᠲᠤᠭ ᠠ ᠪᠤ ᠯᠤᠨ ᠠ᠂ 𝑎= 3 , b= 5 ᠲ ᠡᠭᠡᠪᠡᠯ 𝑎 , b , c ᠪᠡᠷ ᠲᠠᠯ ᠠ ᠪᠤᠯ ᠭᠠᠭᠰᠠᠨ ᠭ ᠤᠷᠪᠠ ᠯᠵᠢᠨ ᠨᠡᠢ ᠳᠡ ( ) ᠪᠠᠢ ᠨ ᠠ᠃ A. 4 B . 5 C. 6 D. 7 2.ᠵ ᠢᠷᠤᠭ 1 ᠮ ᠡᠳᠤ᠂ AD ᠪᠤᠯ ∆AB C ᠶ ᠢᠨ ᠲᠤᠮᠳ ᠠ ᠱ ᠤᠭᠤᠮ ᠂ DE ᠪᠤᠯ ∆AD C ᠶ ᠢᠨ ᠲ ᠤᠮᠳᠠ ᠱᠤᠭᠤ ᠮ᠂ ∆AB C ᠶ ᠢᠨ ᠲ ᠠᠯᠠᠪᠠ ᠢ ᠨᠢ 10 ᠂ ᠲ ᠡᠭᠡᠪᠡᠯ ∆AD E ᠶ ᠢᠨ ᠲ ᠠᠯᠠᠪᠠ ᠢ ᠨᠢ ( ) A. 5 B .3 C. 2.5 D. 2 3. ᠨᠢᠭᠡᠨ ᠤᠯ ᠠᠨ ᠦᠨ ᠴᠦᠭᠳ ᠤ ᠶᠢ ᠨ ᠲ ᠤᠳᠤᠭᠠ ᠳᠤ ᠦᠨᠴ ᠦᠭ ᠨ ᠢᠬᠡᠪᠦ ᠷᠢ ᠨ ᠢ ᠬᠠᠷ ᠢᠯᠴᠠᠨ ᠲᠡᠨᠭ ᠴᠡᠭᠦ ᠦ᠂ ᠨ ᠢᠭᠡ ᠲᠤᠳ ᠤᠭᠠᠳ ᠤ ᠦᠨᠴ ᠦᠭ ᠪᠠ ᠲᠡᠭᠦ ᠨ ᠦ ᠵᠡᠷᠭᠡᠯ ᠡᠳᠡᠭᠡ ᠭᠠᠳ ᠠᠭᠠᠳ ᠤ ᠦᠨᠴ ᠦᠭ ᠦᠨ ᠬᠠᠷᠢ ᠴᠠᠯ ᠨᠢ 3᠄1᠂ ᠲᠡᠭᠡᠪᠡᠯ ᠡᠨᠡ ᠤᠯᠠᠨ ᠦᠨ ᠴᠦᠭᠳ ᠤ ᠶᠢ ᠨ ᠲ ᠠᠯ ᠠ ᠶᠢᠨ ᠲᠤᠭ ᠠ ᠨᠢ ( ) A. 8 B. 9 C. 10 D. 12 4. ᠵᠢᠷᠤᠭ 2 ᠮ ᠡᠳᠤ᠂ ᠢᠵᠢ ᠯᠢ ᠨ ᠢᠭᠡᠨ ᠬᠠᠪᠳ ᠠᠭᠠᠢ ᠲᠡᠭᠡᠷᠡᠬ ᠢ ᠲ ᠦ᠋ᠷᠪᠡᠨ ᠴᠡᠭ A , B , C , D ᠶᠢ ᠲᠡᠰ ᠲᠠᠷᠠᠭᠠᠯ ᠠᠭᠤᠯ ᠤᠨ ᠬᠤᠯ ᠪᠤᠨ ᠠ ᠂ ᠦᠭ ᠭᠦᠭᠳ ᠡᠭᠰᠡᠨ ᠨᠢ ∠A = 40 0,∠ 𝐶 = 20 0, ∠AD C= 120 0 ᠂ ᠡ ᠡᠷᠪ ∠A BC ᠶ ᠢᠨ ᠲᠠᠯᠠᠯ ᠠᠨ ᠬ ᠤᠪᠢᠶ ᠠᠭᠴᠢ B E ᠨ ᠢ ᠴᠡᠭ D ᠶᠢ ᠲᠠᠭᠠᠷᠢ ᠪᠠᠯ᠂ ∠A BE ᠶᠢᠨ ᠭᠷᠠᠳ ᠦ᠋ᠰ ᠦᠨ ᠲᠤᠭ ᠠ ᠨ ᠢ ( ) A. 20 0 B. 30 0 C. 40 0 D. 60 0 5. ᠵᠢᠷᠤ ᠭ 3 ᠮᠡᠳᠤ᠂ ∆AB C ᠳᠦ ᠂ ∠A BC ᠂ ∠A CB ᠶᠢᠨ ᠲ ᠠᠯᠠᠯᠠᠨ ᠬ ᠤᠪᠢᠶ ᠠᠭᠴᠢ BE ᠂ CD ᠨᠢ ᠴ ᠡᠭ F ᠳᠦ ᠣᠭᠲᠤᠯ ᠤᠯᠴᠠᠨ ᠠ᠂ ∠B FC = 116 0᠂ ∠A = ( ) A. 51 0 B. 52 0 C. 53 0 D. 58 0 6. ᠵᠢᠷᠤᠭ 4 ᠮᠡᠳᠤ᠂ ∠A CD ᠪᠤᠯ ∆AB C ᠶᠢᠨ ᠨᠢᠭᠡ ᠭᠠᠳ ᠠᠭᠠᠳ ᠤ ᠦᠨᠴ ᠦᠭ᠂ CE ᠨᠢ ∠A CD ᠶᠢ ᠲᠠᠯᠠᠯ ᠠᠨ ᠬ ᠤᠪᠢᠶ ᠠᠨ ᠠ ᠂ F ᠪᠤᠯ CA ᠶᠢᠨ ᠦᠷᠭᠦ ᠯᠵᠢᠯ ᠡᠯ ᠱ ᠤᠭᠤᠮ ᠲᠡᠭᠡᠷᠡᠬ ᠢ ᠨ ᠢᠭᠡ ᠴᠡᠭ᠂ FG // CE ᠪᠦᠭᠡ ᠳ AB ᠲᠡᠢ ᠴᠡᠭ G ᠳᠦ ᠤᠭᠳ ᠤᠯᠤᠯ ᠴᠠᠨ ᠠ᠂ ∠1 = 70 0᠂ ∠2 = 30 0 ᠲᠡᠭᠡᠪᠡᠯ ∠3 = ( ) A. 30 0 B. 40 0 C. 45 0 D. 70 0 7. ᠵᠢᠷᠤ ᠭ 5 ᠮᠡᠳᠤ᠂ ᠲᠠᠪ ᠤᠨ ᠦᠨᠴ ᠦᠭᠳᠤ A , B , C , D , E ᠳᠦ᠂ ∠A + ∠B + ∠E = ∠E DC + ∠B CD + 140 0᠂ DE , C F ᠨ ᠢ ᠲ ᠤᠰ ᠲᠤᠰ ∠E DC , ∠B CD ᠶ ᠢᠨ ᠲᠠᠯᠠᠯ ᠠᠨ ᠬᠤᠪᠢ ᠶᠠᠭᠴ ᠢ᠂ᠲ ᠡᠭᠡᠪᠡᠯ ∠F ᠶᠢ ᠨ ᠭᠷᠠᠳ ᠦ᠋ᠰ ᠦᠨ ᠲᠤᠭ ᠠ ᠨᠢ ( ) A. 100 0 B. 90 0 C. 80 0 D. 70 0 8. ᠵᠢᠷᠤᠭ 6 ᠮᠡᠳ ᠤ᠂ ᠲᠦ᠋ ᠷᠪᠡᠯ ᠵᠢᠨ AB CD ᠶ ᠢ ᠰ ᠢᠯᠤᠭᠤ ᠨ (1) (2) (3) (4) (5) (6) (6) 𝑀𝑁 ᠤ ᠲᠠᠭᠠᠤ ᠨᠤᠭᠤ ᠯᠪᠠᠯ᠂ A , B ᠬᠤᠶ ᠠᠷ ᠴ ᠡᠭ ᠨ ᠢ ᠲ ᠤᠰ ᠲᠤᠰ ᠲᠦ᠋ ᠷᠪᠡᠯ ᠵᠢᠨ ᠦ ᠲ ᠤᠳᠤᠭᠠ ᠳᠤ ᠳ ᠠᠬᠢ A1 ,B 1 ᠬᠤ ᠶᠠᠷ ᠴᠡᠭ ᠳᠡᠭᠡ ᠷ ᠡ ᠤᠨᠠ ᠨ ᠠ᠂ ᠡᠡᠷᠪ ∠1 = 30 0 , ∠2 = 80 0 ᠪᠤᠯ᠂ ∠C + ∠D = ( ) A. 110 0 B. 125 0 C. 130 0 D. 135 0 9. ᠵᠢᠷᠤ ᠭ 7 ᠮᠡᠳᠤ᠂ ᠡᠡ ᠷᠪ ∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6 + ∠7 = n∙ 90 0 ᠲᠡᠭᠡᠪᠡᠯ 𝑛= ( ) A. 4 B. 5 C . 6 D. 7 10. ᠵᠢᠷᠤᠭ 8 ᠮᠡᠳᠤ᠂ ∆AB C ᠶᠢᠨ ᠭᠤ ᠷᠪᠠᠨ ᠲ ᠠᠯ ᠠ ᠶᠢᠨ ᠤᠷᠳ ᠤ ᠨᠢ ᠴᠦ᠋ᠮ ᠪᠦᠬ ᠦᠯᠢ ᠲᠤᠭ ᠠ᠂ ᠬᠦᠷᠢ ᠶᠡᠨ ᠦ ᠤ ᠷᠳᠤ ᠨᠢ 22᠂ AM ᠨᠢ ᠲᠠᠯ ᠠ BC ᠲᠠᠯ ᠠ ᠲ ᠡᠭᠡᠷᠡᠬ ᠢ ᠲ ᠤᠮᠳᠠ ᠱᠤᠭᠤ ᠮ᠂ ∆AB M ᠶᠢᠨ ᠬᠦᠷᠢ ᠶᠡᠨ ᠦ ᠤ ᠷᠳᠤ ᠨᠢ ∆A CM ᠶᠢᠨ ᠬᠦᠷ ᠢᠶᠡᠨ ᠦ ᠤ ᠷᠳᠤ ᠡᠴᠡ 2 ᠶ ᠡᠬᠡ᠂ ᠲᠡᠭᠡᠪᠡᠯ BC ᠶᠢᠨ ᠤᠷ ᠳᠤ ᠶ ᠢᠨ ᠪᠤᠯᠤ ᠯᠴᠠᠭ ᠠ ᠪᠦᠬ ᠦᠢ ᠡ ᠡᠮᠵᠢᠭ ᠳᠡᠯ ᠨ ᠢ ( ) ᠪᠤ ᠢ᠃ A. 4 B. 5 C. 6 D. 7 ᠬᠤᠶ ᠠᠷ᠂ ᠬᠤᠭ ᠤᠰᠤᠨ ᠳᠤ ᠲ ᠠᠭᠯᠠᠬᠤ ᠃ (ᠰᠡᠳ ᠤᠪ ᠪ ᠦᠷᠢ 3ᠬᠤ ᠪᠢ᠂ ᠨᠡᠢ ᠳᠡ 2 4ᠬ ᠤᠪᠢ ) 11. ᠪᠠᠳ ᠤ ᠤ ᠷᠳᠤ ᠨᠢ 5c m , 6c m , 11c m , 16c m ᠪᠤᠯᠬᠤ ᠲᠦ᠋ ᠷᠪᠡᠨ ᠮᠤ ᠳᠤᠨ ᠰᠢᠳ ᠠᠮ ᠳᠣᠲ ᠤᠷ ᠠ ᠠᠴᠠ ᠭᠤ ᠷᠪᠠ ᠶᠢ ᠰᠤᠨᠭ ᠭᠤᠵᠤ᠂ ᠭᠤ ᠷᠪᠠᠯ ᠵᠢᠨ ᠪᠦᠳ ᠦᠭᠡᠪᠡᠯ᠂ ᠡᠨᠡ ᠭᠤᠷᠪᠠ ᠯᠵᠢᠨ ᠤ ᠬ ᠦᠷᠢ ᠶᠡᠨ ᠦ ᠤᠷᠳ ᠤ ᠨᠢ _______ cm 12. ∆AB C ᠳ ᠦ ᠂ ᠡᠡᠷᠪ ∠A = 12 ∠ B= 13 ∠ C ᠲ ᠡᠭᠡᠪᠡᠯ ∠A = ___ ___ ∆AB C ᠪ ᠤᠯ _____ ___ᠭ ᠤᠷᠪᠠ ᠯᠵᠢᠨ ᠪᠤᠯ ᠤᠨ ᠠ ᠃ 13. ᠨᠢᠭᠡᠨ ᠵᠦ᠋ ᠪ ᠤ ᠯᠠᠨ ᠦᠨᠴ ᠦᠭᠳᠤ ᠶᠢᠨ ᠳᠣᠲ ᠤᠭᠠᠳ ᠤ ᠦᠨᠴ ᠦᠭ ᠨᠢᠭᠡᠪ ᠦᠷᠢ ᠨᠢ 108 0 ᠂ ᠲᠡᠭᠡᠪᠡᠯ ᠲᠡᠭᠦ ᠨ ᠦ ᠲᠠᠯ ᠠ ᠶᠢ ᠨ ᠲ ᠤᠭ ᠠ ᠨᠢ _____ _᠃ 14. ᠵᠢᠷᠤᠭ 9 ᠮᠡᠳᠤ᠂ D , E , F ᠨᠢ ᠲᠤᠰ ᠲᠤ ᠰ BC , AD , BE ᠶᠢ ᠨ ᠲ ᠤᠮᠳᠠ ᠴᠡᠭ᠂ ᠡᠡᠷᠪ ∆B FD ᠶᠢ ᠨ ᠲ ᠠᠯᠠᠪᠠ ᠢ ᠨᠢ 6 ᠪ ᠤᠯ᠂ ∆AB C ᠶᠢᠨ ᠲ ᠠᠯᠠᠪᠠ ᠢ ᠨᠢ __ ____ 15. ᠨ ᠢᠭᠡ ᠤᠯᠠᠨ ᠦᠨᠴ ᠦᠭᠳᠤ ᠶᠢᠨ ᠲᠤᠳ ᠤᠭᠠᠳ ᠤ ᠦᠨᠴ ᠦᠭ ᠦᠨ ᠨᠡᠢ ᠯᠡᠪᠦᠷᠢ ᠨᠢ ᠭ ᠠᠳᠠᠭᠠᠳ ᠤ ᠦᠨᠴ ᠦᠭ ᠦ ᠨ ᠨ ᠡᠢᠯᠡᠪ ᠦᠷᠢ ᠲᠡᠢ ᠲᠡᠨᠭ ᠴᠡᠭᠦ ᠦ᠂ ᠲᠡᠭᠡ ᠪᠡᠯ ᠡᠨᠡ ᠤᠯᠠᠨ ᠦᠨ ᠴᠦᠭᠳ ᠤ ᠳᠤ ᠨ ᠡᠢᠳ ᠡ ____ ᠲᠠᠰ ᠢᠭᠤᠪᠴᠢ ᠲᠠᠢ᠃ 16. ᠵᠢ ᠷᠤᠭ 10 ᠮᠡᠳ ᠤ᠂ ∠B DC = 142 0, ∠ B = 34 0 , ∠ C= 28 0 ᠲ ᠡᠭᠡᠪᠡᠯ ∠A = ___ ___ 17. ᠵᠢᠷᠤᠭ 11 ᠮᠡᠳ ᠤ᠂∆ AB C ᠳ ᠦ ᠂ B D ᠨᠢ ∆ AB C ᠶᠢᠨ ᠲᠤᠳ ᠤᠭᠠᠳ ᠤ ᠦᠨᠴ ᠦᠭ ᠦᠨ ᠲᠠᠯᠠᠯ ᠠᠨ ᠬᠤᠪᠢ ᠶᠠᠭᠴ ᠢ᠂ CE ᠨᠢ ∆AB C ᠶᠢᠨ ᠭᠠᠳ ᠠᠭᠠᠳ ᠤ ᠦᠨᠴ ᠦᠭ ᠦᠨ ᠲ ᠠᠯᠠᠯᠠᠨ ᠬᠤᠪᠢ ᠶᠠᠭᠴ ᠢ᠂ ᠡᠡᠷᠪ ∠B DC = 130 0, ∠E = 50 0᠂ ᠲᠡᠭᠡᠪᠡᠯ ∠B AC ᠶᠢᠨ ᠭᠷᠠ ᠳᠦ᠋ᠰ ᠦᠨ ᠲᠤᠭ ᠠ ᠨᠢ ___ ____ 18. ᠰᠢᠯᠤ ᠭᠤᠨ ᠳᠡᠭᠡ ᠷ ᠡ ᠲᠠᠷᠠᠭᠠ ᠯᠠᠭᠰᠠᠨ ᠲ ᠦ᠋ᠷᠪᠡᠨ ᠴᠡᠭ A , B , C , D ᠪᠤᠢ᠂ AD = 7 , AB = 2 ᠂ ᠡᠡ ᠷᠪ AB , BC , CD ᠨᠢ BC ᠪᠡᠷ ᠬᠠᠵ ᠠᠭᠤ ᠪᠤᠯᠭᠠᠭ ᠰᠠᠨ ᠠᠳᠠᠯ ᠢ ᠬᠠᠵᠠᠭᠤ ᠳᠤ ᠭᠤ ᠷᠪᠠᠯ ᠵᠢᠨ ᠦ ᠭᠤ ᠷᠪᠠᠨ ᠲᠠᠯ ᠠ ᠪᠤ ᠯ᠂ BC ᠶᠢ ᠨ ᠤᠷ ᠳᠤ ᠨ ᠢ ______ (7) (8) (9) (10) (11) ᠭᠤᠷᠪᠠ᠂ ᠪᠤᠳ ᠤᠵᠤ ᠬᠠᠷᠢ ᠭᠤᠯᠬᠤ ᠰᠡᠳᠤ ᠪ (ᠨ ᠡᠢᠳ ᠡ 6 ᠪᠠᠭ ᠠ ᠰ ᠡᠳᠤᠪ ᠲᠡᠢ᠂ ᠨᠠᠢ ᠲᠡ 46 ᠬᠤ ᠪᠢ ) 19. (10 ᠬᠤ ᠪᠢ) ᠵᠢᠷᠤᠭ ᠮᠡᠳ ᠤ᠂ AD ᠪᠤᠯ ∆ AB C ᠶᠢᠨ BC ᠲᠠᠯ ᠠ ᠲ ᠡᠭᠡᠷᠡᠬ ᠢ ᠦᠨᠳ ᠦᠷ᠂ BE ᠪᠤᠯ ∆ AB C ᠶᠢᠨ ᠦᠨᠴ ᠦᠭ ᠦᠨ ᠲᠠᠯ ᠠᠯᠠᠨ ᠬᠤ ᠪᠢᠶᠠᠭᠴ ᠢ᠂ ∠E BA = 34 0 , ∠AE B = 80 0 , ∠C AD ᠶᠢᠨ ᠭᠷᠠᠳ ᠦ᠋ᠰ ᠦᠨ ᠲ ᠤᠭ ᠠ ᠶᠢ ᠤᠯ᠃ 20. ( 10 ᠬ ᠤᠪᠢ ) ᠦᠭ ᠭᠦᠭᠳ ᠡᠭᠰᠡᠨ ᠨᠢ 𝑛 ᠦᠨᠴ ᠦᠭᠳᠤ ᠶᠢᠨ ᠲᠤᠳ ᠤᠭᠠᠳ ᠤ ᠦᠨᠴ ᠦᠭ ᠦᠨ ᠨᠡᠢ ᠯᠡᠪᠦᠷᠢ ᠨᠢ θ = (𝑛 − 2) × 180 0 (1) ᠠ ᠰᠤ ᠷᠤᠭᠴ ᠢ ᠡᠡᠯ ᠡᠬᠦ ᠳ ᠦ ᠪᠡᠨ ᠂ θ ᠶᠢᠨ ᠡᠡᠮ ᠵᠢᠭᠳ ᠡᠯ ᠢ 900 0 ᠢᠶ ᠡᠷ ᠠ ᠪᠴᠤ ᠪᠤᠯᠤ ᠨ ᠠ᠂ ᠡ ᠰᠤᠷᠤᠭ ᠴᠢ ᠡᠡᠯᠡᠬ ᠦ ᠳᠦ ᠪᠡᠨ᠂ θ ᠶᠢᠨ ᠡᠡᠮᠵ ᠢᠭᠳᠡᠯ ᠢ 800 0 ᠢ ᠶᠡᠷ ᠠᠪᠴᠤ ᠪᠤ ᠯᠤᠨ ᠠ᠂ ᠠ ᠡ ᠬᠤᠶ ᠠᠷ ᠰᠤᠷᠤᠭ ᠴᠢ ᠶ ᠢᠨ ᠡ ᠡᠯᠡᠬᠦ ᠨᠢ ᠵ ᠦ᠋ᠪ ᠤᠤ ︖ ᠡᠡᠷᠪ ᠵᠦ᠋ᠪ ᠪᠤᠯ n ᠦ ᠡᠡᠮᠵ ᠢᠭᠳᠡᠯ ᠢ ᠪᠤ ᠳᠤᠵᠤ ᠭᠠᠷᠭ ᠠ᠂ ᠡᠡᠷᠪ ᠪ ᠤᠷᠤᠭᠤ ᠪᠤᠯ ᠰ ᠢᠯᠳᠠᠭᠠᠨ ᠢ ᠨ ᠢ ᠲ ᠣᠳᠤᠷᠬ ᠠᠢᠯᠠ᠃ (2) ᠡᠡᠷᠪ n ᠤ ᠯᠠᠨ ᠦᠨᠴ ᠦᠭᠳᠤ ᠨᠢ ᠬ ᠤᠪᠢᠷᠠᠭᠠᠳ (𝑛 + 𝑥) ᠦᠨᠴ ᠦᠭᠳᠤ ᠪᠤᠯᠪᠠ ᠯ᠂ ᠲ ᠤᠳᠤᠭᠠᠳ ᠤ ᠦᠨᠴ ᠦᠭ ᠦᠨ ᠨᠡᠢ ᠯᠡᠪᠦᠷᠢ ᠨᠢ 540 0 ᠨ ᠡᠮᠡᠭᠳ ᠡᠨ ᠡ ᠂ ᠲ ᠡᠭᠰᠢ ᠳᠬᠡᠯ ᠪᠠᠢ ᠭᠤᠯᠬᠤ ᠠᠷᠭ ᠠ ᠪᠠ ᠷ 𝑥 ᠦᠨ ᠡ ᠡᠮᠵᠢᠭ ᠳᠡᠯ ᠢ ᠤᠯ᠃ 21. (10 ᠬᠤ ᠪᠢ) ᠵᠢᠷᠤᠭ ᠮᠡᠳ ᠤ᠂ Rt ∆AB C ᠳᠦ᠂ ∠A CB = 90 0᠃ (1) ᠡᠡᠷᠪ CD ᠪᠤᠯ AB ᠲᠡᠭᠡᠷᠡᠬ ᠢ ᠦᠨ ᠳᠦᠷ᠂ ∠A = 60 0᠂ ᠲᠡᠭᠡᠪᠡᠯ ∠B CD ᠶᠢᠨ ᠭᠷᠠᠳ ᠦ᠋ᠰ ᠦᠨ ᠲᠤᠭ ᠠ ᠨᠢ ____ ___᠂ ᠡᠡᠷᠪ ∠A = 43 0 ᠂ ᠲᠡᠭᠡᠪᠡᠯ ∠B CD ᠶ ᠢᠨ ᠭᠷᠠᠳ ᠦ᠋ᠰ ᠦᠨ ᠲᠤᠭ ᠠ ᠨᠢ _______᠂ ᠴᠢ ᠶᠠᠭᠤ ᠶᠢ ᠤᠯᠵᠤ ᠢᠯᠡᠷᠡᠭᠦ ᠯᠪ ︖ᠰᠢᠯ ᠳᠠᠭᠠᠨ ᠢ ᠨ ᠢ ᠲᠤᠳ ᠤᠷᠬᠠ ᠢᠯᠠ᠃ (2) ᠡᠡᠷᠪ ( 1) ᠳᠡᠬᠢ ᠳᠦ᠋ ᠨᠭᠨᠡᠯ ᠳᠡ ᠪᠡᠷ ᠨᠦ᠋ᠬ ᠦᠴᠡᠯ ᠪᠤᠯᠭᠠᠪᠠ ᠯ᠂ CD ᠪᠠ AB ᠨᠢ ᠶᠠᠮᠠᠷ ᠪᠠᠢ ᠷᠢ ᠶ ᠢᠨ ᠬᠤ ᠯᠪᠤᠭᠳ ᠠᠯ ᠲ ᠠᠢ ᠪᠤ ᠯᠬᠤ ᠪ ᠤᠢ ︖ ᠰᠢ ᠯᠳᠠᠭᠠᠨ ᠢ ᠨ ᠢ ᠲ ᠣᠳᠤᠷᠬ ᠠᠢᠯᠠ᠃ 22. (12 ᠬᠤ ᠪᠢ ) ᠵᠢ ᠷᠤᠭ ᠮᠡᠳ ᠤ᠂ CA ᠨᠢ ∠D CE ᠶᠢ ᠲᠠᠯ ᠠᠯᠠᠨ ᠬᠤ ᠪᠢᠶᠠᠬᠤ ᠪᠦᠭᠡ ᠳ BE ᠶᠢᠨ ᠦᠷ ᠭᠦᠯᠵ ᠢᠯᠡᠯ ᠱᠤ ᠭᠤᠮ ᠲᠠᠢ ᠴᠡᠭ A ᠳᠦ ᠤᠭ ᠳᠤᠯᠤ ᠯᠴᠠᠨ ᠠ᠃ (1) ∠A = 35 0, ∠ 𝐵 = 30 0 ᠂ ᠲᠡᠭᠡᠪᠡᠯ ∠B EC = ___ ___ __ 0 (ᠰᠢ ᠭᠤᠳ ᠳᠦ᠋ ᠩ ᠢ ᠨᠢ ᠪᠢᠴ ᠢ᠃) (2) ᠡᠡᠷᠡᠯ ᠳᠤ ∠A , ∠𝐵 ᠶᠢᠨ ᠭᠷᠠ ᠳᠦ᠋ᠰ ᠦᠨ ᠲᠤᠭ ᠠ ᠶᠢ ᠨᠢ ᠠᠷᠪᠢᠨ ᠤ ᠳᠠᠭ ᠠ ᠬ ᠤᠪᠢᠷᠠᠭᠠᠨ ᠪᠤᠳᠤ ᠬᠤ ᠪᠠ ᠷ ᠲ ᠠᠮᠵᠢᠨ ∠A , ∠ B, ∠ BE C ᠶ ᠢᠨ ᠬᠤᠭᠤ ᠷᠤᠨᠳ ᠤ ᠲ ᠤᠭᠳ ᠠᠭᠰᠠᠨ ᠲᠤ ᠭ ᠠ ᠡᠡᠮᠵ ᠢᠭᠳᠡ ᠭᠦᠨ ᠦ ᠬᠤᠯ ᠪᠤᠭᠳ ᠠᠯ ᠪ ᠠᠢᠬᠤ ᠶᠢ ᠢᠯ ᠡᠷᠡᠭᠦ ᠯᠪ ᠂ ᠴᠢ ᠡ ᠨᠡᠬᠦ ᠬᠤ ᠯᠪᠤᠭᠳ ᠠᠯ ᠢ ᠲ ᠡᠨᠭᠴᠡᠳ ᠬᠡᠯ ᠢ ᠶᠡᠷ ᠢᠯ ᠡᠷᠬᠡᠢ ᠯᠡᠵᠦ ᠦᠵᠡ᠂ ᠪᠠᠰ ᠠ ᠳᠦ᠋ᠨᠭ ᠨᠡᠯᠳᠡ ᠪ ᠠᠨ ᠪ ᠠᠳᠤᠯ ᠠ᠃ 23. (12 ᠬᠤ ᠪᠢ) ᠵᠢᠷᠤᠭ ᠮᠡᠳᠤ᠂ ᠲᠦ᠋ ᠷᠪᠡᠯ ᠵᠢᠨ AB CD ᠳᠦ᠂ ∠B + ∠A DC = 180 0 , CE ᠨᠢ ∠B CD ᠶᠢ ᠲᠠᠯᠠᠯ ᠠᠨ ᠬ ᠤᠪᠢᠶ ᠠᠵᠤ AB ᠲᠠᠢ ᠴᠡᠭ E ᠳᠦ ᠣᠭᠲᠤᠯ ᠤᠯᠴᠠᠨ ᠠ᠂ D E ᠶᠢ ᠬᠤ ᠯᠪᠤᠨ ᠠ᠃ (1) ᠡᠡᠷ ᠪ ∠A = 50 0, ∠𝐵 = 85 0 ᠲ ᠡᠭᠡᠪᠡᠯ ∠B EC ᠶᠢᠨ ᠭᠷ ᠠᠳᠦ᠋ ᠰ ᠦᠨ ᠲᠤᠭ ᠠ ᠶᠢ ᠤᠯ ᠃ (2) ∠A = ∠1 ᠃ ᠪᠠᠳᠤ ᠯᠠ᠄ ∠C DE = ∠D CE 24. (1 2 ᠬ ᠤᠪᠢ ) ∆ AB C ᠳᠦ᠂ ∠A ᠶᠢᠨ ᠲᠠᠯ ᠠᠯᠠᠨ ᠬᠤ ᠪᠢᠶᠠᠭᠴ ᠢ ᠶ ᠢᠨ ᠤ ᠷᠤᠰᠢ ᠬᠤ ᠰ ᠢᠯᠤᠭᠤ ᠨ ᠪᠠ ∠A BC ᠶᠢ ᠨ ᠭᠠᠳ ᠠᠭᠠᠳ ᠤ ᠦᠨᠴ ᠦᠭ ᠦᠨ ᠲᠠᠯᠠᠯ ᠠᠨ ᠬᠤᠪᠢ ᠶᠠᠭᠴ ᠢ ᠶᠢᠨ ᠤ ᠷᠤᠰᠢ ᠬᠤ ᠰᠢᠯᠤ ᠭᠤᠨ ᠦ ᠬᠠᠪᠴᠢ ᠭᠰᠠᠨ ᠬᠤ ᠷᠴᠠ ᠦ ᠨᠴᠦᠭ ∠A PB ᠶᠢ ∠C ᠶᠢᠨ ᠲᠠᠭᠠᠯ ᠳᠠ ᠦᠨᠴ ᠦᠭ ᠡᠡᠵᠦ ᠲᠣᠭᠲᠠᠭᠠ ᠶ ᠠ᠃ (1) ᠵᠢᠷᠤ ᠭ ① ᠮᠡ ᠳᠤ᠂ ∆AB C ᠳᠦ᠂ ∠C = 90 0, ∠𝐵𝐴 𝐶 = 60 0 ᠲ ᠡᠭᠡᠪᠡᠯ ∠C ᠶᠢᠨ ᠲᠠᠭᠠᠯ ᠳᠠ ᠦᠨᠴ ᠦᠭ ∠A PB ᠦᠨ ᠭᠷᠠᠳ ᠦ᠋ᠰ ᠦᠨ ᠲᠤᠭ ᠠ ᠨᠢ ___ ___ __ 0 (2) ᠭᠡᠷᠡᠯ ᠳᠤ ᠳᠤᠷ ᠠ ᠶᠢ ᠨ ᠭᠤᠷᠪᠠ ᠯᠵᠢᠨ ∆ AB C ᠳᠦ᠂ ∠C ᠪᠠ ᠲ ᠡᠭᠦᠨ ᠦ ᠲᠠᠭᠠ ᠯᠳᠠ ᠦᠨᠴ ᠦᠭ ∠A PB ᠦᠨ ᠭᠷᠠᠳ ᠦ᠋ᠰ ᠦᠨ ᠲᠤᠭᠠᠨ ᠤ ᠬ ᠤᠭᠤᠷᠤᠳ ᠤᠬᠢ ᠬᠤᠯ ᠪᠤᠭᠳ ᠠᠯ ᠢ ᠰᠦ᠋ᠪᠡᠭᠴᠢ ᠯᠡᠬᠦ ᠶᠢᠨ ᠲᠦ᠋ ᠯᠦᠭᠡ ᠂ ∠C ᠶᠢ ᠲᠤᠰ ᠲ ᠤᠰ ᠬᠤᠷᠴᠠ ᠦᠨᠴ ᠦᠭ᠂ ᠲ ᠡᠭᠰᠢ ᠦᠨᠴ ᠦᠭ᠂ᠮ ᠤᠭᠤᠬᠤ ᠦᠨᠴ ᠦᠭ ᠪᠤᠯᠭᠠᠨ ᠭ ᠤᠷᠪᠠ ᠯᠵᠢᠨ ᠪᠠᠢ ᠭᠤᠯᠪᠠ ᠂ ᠵᠢᠷᠤ ᠭ ②~ ④ᠮᠡᠳ ᠤ᠂ ᠤᠷᠢ ᠳᠠᠪᠠ ᠷ ᠦᠨᠴ ᠦᠭ ᠢ ᠡᠡᠮ ᠵᠢᠵᠦ᠂ ᠳᠦ᠋ ᠨᠭᠨᠡᠯ ᠳᠡ ᠶ ᠢ ᠲ ᠠᠭᠠᠮᠠᠭᠯ ᠠᠵᠤ᠂ ᠲᠠᠬᠢ ᠨ ᠪ ᠠᠳᠤᠯ ᠠᠬᠤ ᠰᠠᠨᠠᠭᠠᠳ ᠠᠢ᠃ ᠴᠢ ᠵᠢᠷᠤᠭ ᠲᠠᠬ ᠢ ᠦᠨ ᠴᠦᠭ ᠢ ᠡ ᠡᠮᠵᠢᠨ ᠲᠠᠷᠠᠭᠠ ᠬᠢ ᠬᠦᠰ ᠦᠨᠦᠭ ᠢ ᠲ ᠠᠭᠯᠠ᠃ ᠬᠦᠰ ᠦᠨᠦᠭ ᠳᠤ ᠳ ᠠᠬᠢ ᠲᠤᠭ ᠠ ᠡ ᠡᠮᠵᠢᠭ ᠳᠡᠯ ᠢ ᠦᠨ ᠳᠦᠰ ᠦᠯᠡᠨ ᠂ ᠭᠡᠷᠡᠯ ᠳᠤ ᠶ ᠢᠨ ᠤᠯᠤ ᠭᠰᠠᠨ ᠲᠠᠭᠠᠮᠠᠭᠯ ᠠᠯ ᠢ ᠪᠢᠴᠢ ᠪᠡᠯ ᠂ ∠C ᠪᠠ ᠲᠡᠭᠦ ᠨ ᠦ ᠲᠠᠭᠠᠯ ᠳᠠ ᠦᠨᠴ ᠦᠭ ∠A PB ᠦᠨ ᠭᠷᠠᠳ ᠦ᠋ᠰ ᠦᠨ ᠲᠤᠭᠠᠨ ᠤ ᠬ ᠣᠭᠣᠷᠣᠨᠳ ᠣᠬᠢ ᠬᠤᠯ ᠪᠤᠭᠳ ᠠᠯ ᠨ ᠢ ______ ______ ____᠃ (3) ∠C ᠨ ᠢ ᠬ ᠤᠷᠴᠠ ᠥᠨᠴ ᠥᠭ ᠪᠤᠶᠤ ᠮᠤ ᠬᠤᠭᠤ ᠥᠨᠴ ᠥᠭ ᠪᠣᠯᠬᠤ ᠭᠤᠷ ᠪᠠᠯᠵᠢ ᠨ ᠠ ᠴᠠ ᠨᠢᠭᠡ ᠶᠢ ᠰᠤᠩ ᠭᠤᠵᠤ᠂ ᠡᠡᠷᠡᠯ ᠳᠤ ᠶ ᠢ ᠬᠠᠪ ᠰᠤᠷᠤᠨ ᠲᠠᠮᠠ ᠭᠠᠯᠠᠯ ᠢ ᠨᠢ ᠪᠠᠲ ᠤᠯᠠ᠃ ∠C ᠶᠢᠨ ᠭᠷᠠᠳᠦ᠋ ᠰ ᠤᠨ ᠲᠣᠭ ᠠ ∠ A PB ᠶᠢᠨ ᠭᠷᠠᠳᠦ᠋ ᠰ ᠤᠨ ᠲᠣᠭ ᠠ ② 90° ______ ③ _______ _______ ④ _______ _______