ᠠᠷᠪᠠᠨ ᠨᠢᠭᠡᠳᠤᠭᠡᠷ ᠪᠥᠯᠥᠭ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ （ᠨᠢᠭᠡᠴᠢ ᠶᠢᠨ ᠪᠠᠢᠴᠠᠭᠠᠯᠲᠠ 1） .pdf

ᠠᠷᠪ ᠠᠨ ᠨ ᠢᠭᠡᠳ ᠤᠭᠡᠷ 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.ᠲ ᠠᠷᠠᠭᠠ ᠬᠢ ᠡ ᠯ ᠡ ᠪᠦᠯᠦᠭ ᠲᠣᠭᠠᠨ ᠡᠴᠡ ᠭᠤᠷᠪᠠ ᠯᠵᠢᠨ ᠤ ᠭ ᠤᠷᠪᠠ ᠨ ᠲ ᠠᠯ ᠠ ᠶᠢ ᠪ ᠦᠷᠢ ᠯᠳᠦᠭ ᠦᠯᠵᠦ ᠲᠡᠢ ᠯᠬᠦ ᠨᠢ᠄ ( ) A. 1 , 1 , 2 B. 1 , 2 , 4 C. 2 , 3 , 4 D. 2 , 3 , 5 2. ∆O AB ᠳᠤ᠂ ∠O =90 °, ∠A = 35° ᠪᠣᠯ ∠B = ( ) A. 35° B. 55° C. 65° D. 145° 3. ᠲᠠᠷᠠᠭᠠ ᠬᠢ ᠵ ᠢᠷᠤᠭ ᠡᠴᠡ ᠭ ᠤᠷᠪᠠ ᠯᠵᠢᠨ ᠤ ᠲ ᠤᠭᠳ ᠠᠪᠤᠷᠢ ᠳᠤ ᠴ ᠢᠨᠠᠷ ᠢ ᠬᠡᠷᠡᠭᠯ ᠡᠭᠰᠡᠨ ᠦᠭᠡᠢ ᠨ ᠢ ( ) A. ᠭᠡᠷ ᠤ ᠨ ᠣᠷᠤᠢ ᠶᠢᠨ ᠵᠢᠶ ᠠᠰᠠ B. ᠳᠤ ᠭᠤᠢ ᠲ ᠡᠷᠭᠡᠨ ᠤ ᠲ ᠤᠯᠬᠤ ᠵᠢᠶᠠᠰ ᠠ C. ᠰᠤ ᠨᠵᠤ ᠠᠪᠴᠢ ᠬᠤ ᠡ ᠭᠦᠳᠡ D. ᠮᠣᠳ ᠤᠨ ᠡ ᠭᠦᠳᠡᠨ ᠲᠡᠭᠡᠷ ᠠ ᠨ ᠢᠭᠡ ᠮ ᠣᠳᠤᠨ ᠵᠦ᠋ ᠰᠦᠮ ᠬᠠᠳ ᠠᠬᠤ 4. ᠵᠢᠷᠤᠭ 1 ᠮ ᠡᠳᠤ᠂ 𝑎|| b᠂ c , d ᠨ ᠢ ᠲ ᠤᠰ ᠲᠤᠰ ᠤᠭᠳ ᠤᠯᠤᠭᠴ ᠢ ᠰᠢᠯᠤ ᠭᠤᠨ ᠪᠥᠭᠡ ᠳ ᠴᠡᠭ A ᠲᠤ ᠤᠭ ᠳᠤᠯᠤ ᠯᠴᠠᠨ ᠠ᠃ ᠬᠡᠷᠪᠡ ∠ 1= 60° , ∠2 = 100° ᠪᠣᠯ ∠A =( ) A. 40° B. 50° C. 60° D. 70° 5. ᠵᠢᠷᠤ ᠭ 2 ᠮᠡᠳᠤ᠂ BD ᠪᠣᠯ ∆AB C ᠶ ᠢᠨ ᠲ ᠤᠮᠳᠠ ᠱᠤᠭᠤ ᠮ᠂ AB = 5 , BC = 3 ᠪᠥᠭᠡ ᠳ ∆AB D ᠶᠢᠨ ᠬ ᠦᠷᠢ ᠶᠡᠨ ᠤᠷᠳ ᠤ ᠨᠢ 11 ᠲᠡᠭᠡᠪᠡ ᠯ ∆B CD ᠶᠢᠨ ᠬᠦᠷ ᠢᠶᠡᠨ ᠤ ᠤ ᠷᠳᠤ ᠨ ᠢ᠄ ( ) A. 9 B. 14 C. 16 D. ᠲᠤ ᠭᠳᠠᠭᠠᠵ ᠤ ᠴ ᠢᠳᠠᠬᠤ ᠦᠭᠡᠢ 6. ᠨᠢᠭᠡᠨ ᠣ ᠯᠠᠨ ᠦᠨᠴ ᠦᠭᠳᠤ ᠶᠢᠨ ᠨᠢᠭᠡ ᠣ ᠷᠤᠢ ᠶᠢᠨ ᠴᠡᠭ ᠡᠴᠡ 4 ᠲ ᠠᠰᠢᠭᠤ ᠪᠴᠢ ᠲᠠᠳ ᠠᠵᠤ ᠲᠡᠢ ᠯᠦᠨ ᠡ᠂ ᠲᠡᠭᠡᠪᠡᠯ ᠡᠨᠡ ᠤ ᠯᠠᠨ ᠦᠨᠴ ᠦᠭᠳᠤ ᠶᠢᠨ ᠲ ᠤᠳᠤᠭᠠᠳ ᠤ ᠥᠨ ᠴᠦᠭ ᠤᠨ ᠨ ᠡᠢᠯᠡᠪ ᠤᠷᠢ ᠨ ᠢ᠄ ( ) A. 72 0° B. 90 0° C. 180 0° D. 144 0° 7. ᠵᠢᠷᠤᠭ 3 ᠮᠡᠳᠦ᠂ ∆ AB C ᠳᠤ ∠A BC = 50° ᠂ ∠A CB = 70° ᠂ AD ᠨᠢ ∠B AC ᠶᠢ ᠲᠠᠯᠠᠯ ᠠᠨ ᠬᠤᠪᠢ ᠶᠠᠨ ᠠ ᠂ ᠴᠡᠭ D ᠶᠢ ᠲᠠᠭ ᠠᠷᠢᠭᠤ ᠯᠤᠨ DE ⊥ AB ᠪᠠᠷ ᠪᠠᠢ ᠭᠤᠯᠪᠠ ᠯ ᠡ ᠭᠴᠡ ᠶᠢᠨ ᠰᠠᠭᠤ ᠷᠢ ᠨ ᠢ E ᠲᠡᠭᠡᠪᠡᠯ ∠A DE ᠶᠢᠨ ᠭᠷᠠᠳ ᠦ᠋ᠰ ᠤᠨ ᠲᠣᠭ ᠠ ᠨ ᠢ ( ) A. 45° B. 50° C. 60° D. 70° 8. ᠨᠢᠭᠡᠨ ᠤ ᠯᠠᠨ ᠦᠨᠴ ᠦᠭᠳᠦ ᠶᠢᠨ ᠲᠤᠳ ᠤᠭᠠᠳ ᠤ ᠥᠨᠴ ᠦᠭ ᠤ ᠨ ᠨ ᠡᠢᠯᠡᠪ ᠦᠷᠢ ᠨᠢ 1080 ° ᠲ ᠡᠭᠡᠪᠡᠯ ᠡᠨᠡᠬᠦ ᠤᠯ ᠠᠨ ᠦᠨ ᠴᠦᠭᠳ ᠦ ᠨᠢ ᠄ ( ) A. ᠶᠢᠰ ᠦᠨ ᠦᠨᠴ ᠦᠭᠳᠦ B. ᠨᠠᠢ ᠮᠠᠨ ᠦᠨ ᠴᠦᠭᠳ ᠦ C. ᠲᠤ ᠯᠤᠭᠠᠨ ᠦᠨ ᠴᠦᠭᠳ ᠦ D. ᠵᠢᠷᠭᠤᠭᠠᠨ ᠦᠨᠴ ᠦᠭᠳᠦ 9. ᠵᠢᠷᠤ ᠭ 4 ᠮᠡᠳᠦ᠂ Rt ∆AB C ᠳᠤ᠂ ∠AB C= 90 °᠂ ∠A = 65° ᠂ BD ᠲᠠᠭᠠᠤ ᠨᠤᠭᠤ ᠯᠪᠠᠯ ᠴᠡᠭ A ᠨᠢ CB ᠲᠠᠯ ᠠ ᠲ ᠡᠭᠡᠷᠡᠬ ᠢ ᠴᠡᠭ A ′ᠲ ᠠᠢ ᠲ ᠠᠪᠬᠤᠴ ᠠᠨ ᠠ ᠃ ᠲ ᠡᠭᠡᠪᠡᠯ ∠ A ′DC = ( ) (1) (2) (3) (4) A. 40° B. 30° C. 25° D. 20° 10. ᠵᠢᠷᠤᠭ 5 ᠮᠡᠳᠤ᠂ ∆ AB C ᠳᠤ ∠A = 40° ᠂ ∠A BO = 20° ᠂ ∠A CO = 30° ᠪᠣᠯ ∠B OC = ( ) A. 80° B. 85° C. 90° D. ᠲᠤ ᠭᠳᠠᠭᠠᠵ ᠤ ᠲ ᠡᠢᠯᠬ ᠦ ᠦᠭᠡᠢ ᠬᠣᠶ ᠠᠷ᠂ ᠬᠠᠭᠠ ᠯᠲᠠ ᠳ ᠤ ᠲ ᠠᠭᠯᠠᠬᠤ ᠰᠡᠲᠤ ᠪ᠃ ︵ᠰᠡᠲ ᠤᠪ ᠪ ᠦᠷᠢ 3 ᠬᠤᠪᠢ ᠂ ᠨ ᠠᠢᠲ ᠡ 24 ᠬᠤᠪᠢ ︶ 11. ᠬᠡᠷᠪᠡ ᠨᠢᠭᠡᠨ ᠤᠯ ᠠᠨ ᠦᠨᠴ ᠦᠭᠳᠤ ᠶᠢᠨ ᠭᠠᠳ ᠠᠭᠠᠳ ᠤ ᠦᠨᠴ ᠦᠭ ᠪᠦᠷᠢ ᠨᠢ 30 ° ᠪᠣ ᠯ ᠡ ᠨᠡᠬᠦ ᠤᠯᠠᠨ ᠥᠨᠴ ᠥᠭᠳᠥ ᠶᠢᠨ ᠲᠠᠯ ᠠ ᠶᠢ ᠨ ᠲ ᠣᠭ ᠠ ᠨᠢ᠄ ___ _ 12. ᠵᠢ ᠷᠤᠭ 6 ᠮᠡᠳ ᠦ᠂ ∠A CD =13 0° ᠂ ∠B = ∠A ᠪᠣᠯ ∠A ᠶᠢᠨ ᠭᠷ ᠠᠳᠦ᠋ ᠰ ᠤᠨ ᠲᠣᠭ ᠠ ᠨ ᠢ᠄____ 13. ᠠ ᠳᠠᠯᠢ ᠬᠠᠵᠠ ᠭᠤᠳ ᠤ ᠭ ᠤᠷᠪᠠ ᠯᠵᠢᠨ ᠤ ᠲᠠᠯ ᠠ ᠶᠢᠨ ᠤ ᠷᠳᠤ ᠨᠢ ᠲᠤᠰ ᠪᠦᠷ ᠢ 5 ᠪᠠ 12 ᠪᠣᠯ ᠲᠡᠭᠦ ᠨ ᠤ ᠬᠦᠷ ᠢᠶᠡᠨ ᠤ ᠤᠷᠳ ᠤ ᠨᠢ᠄ ____ 14. ᠵᠢᠷᠤᠭ 7 ᠮᠡᠳᠦ ᠂ ᠲ ᠠᠪᠤᠨ ᠦᠨᠴ ᠦᠭᠳᠦ AB CD E ᠶ ᠢᠨ ᠲᠤᠳ ᠤᠭᠠᠳ ᠤ ᠥᠨᠴ ᠦᠭ ᠨᠢᠭᠡᠪ ᠤᠷᠢ ᠨᠢ ᠬ ᠠᠷᠢᠯᠴ ᠠᠨ ᠲ ᠡᠩᠴ ᠡᠭᠦᠦ DF ⊥ AB ᠲᠡᠭᠡᠪᠡᠯ ∠C DF =_______ 15. ᠬ ᠡᠷᠪᠡ 𝑎 , b , c ᠨᠢ ᠭᠤᠷᠪᠠ ᠯᠵᠢᠨ ᠤ ᠭᠤᠷᠪᠠ ᠨ ᠲᠠᠯ ᠠ ᠪᠥᠭᠡ ᠳ𝑎 , b ᠨᠢ √𝑎 − 10 + (b − 2) 2= 0 ᠢ ᠬ ᠠᠩᠭᠠᠨ ᠠ᠃ ᠭᠤ ᠷᠪᠠᠳ ᠤᠭᠠᠷ ᠲᠠᠯ ᠠ c ᠨᠢ ᠲ ᠡᠭᠰᠢ ᠲᠣᠭ ᠠ ᠪᠣᠯ c= __ ____ _ 16. ᠵᠢ ᠷᠤᠭ 8 ᠮᠡᠳ ᠦ᠂ ∆AB C ᠳᠤ᠂ AD ⊥ BC ᠡᠭᠴᠡ ᠶᠢᠨ ᠰ ᠠᠭᠤᠷᠢ ᠨᠢ D ᠂ AE ᠨᠢ ∠D AC ᠶᠢ ᠲᠠᠯᠠᠯ ᠠᠨ ᠬᠤᠪᠢ ᠶᠠᠨ ᠠ ᠂∠B AC = 80° ᠂∠B = 60° ᠲᠡᠭᠡᠪᠡᠯ ∠A EC =_______ 17. ᠵᠢᠷᠤᠭ 9 ᠮᠡᠳᠤ᠂ ᠭᠤᠷᠪᠠ ᠯᠵᠢᠨ ᠬᠠᠪᠳ ᠠᠰᠤ AB C ᠳᠤ ∠A = 75 ° ᠂ ∠B = 60° ᠂ ᠭ ᠤᠷᠪᠠ ᠯᠵᠢᠨ ᠬ ᠠᠪᠳᠠ ᠰᠤ ᠶ ᠢᠨ ᠨᠢᠭᠡ ᠥᠨᠴ ᠦᠭ ᠢ ᠨᠤᠭᠤ ᠯᠵᠤ ᠴᠡᠭ C ᠶᠢ ᠭ ᠤᠷᠪᠠ ᠯᠵᠢᠨ ᠤ ᠲ ᠤᠲᠤᠷ ᠠ ᠪᠠ ᠢᠯᠭᠠᠪᠠ ᠯ ∠α = 25 ° ᠪᠣ ᠯ ∠β =_______ 18. ᠵᠢᠷᠤᠭ 10 ᠮᠡᠳᠦ᠂ ∆AB C ᠳᠤ᠂ ∠C = 46 °,∆ AB C ᠶ ᠢ ᠰ ᠢᠯᠤᠭᠤ ᠨ𝑙 ᠲᠠᠭᠠᠤ ᠨᠤᠭᠤ ᠯᠪᠠᠯ ᠴᠡᠭ C ᠨᠢ ᠴᠡᠭ D ᠲᠤ ᠤᠨᠠᠨ ᠠ᠂ ᠲ ᠡᠭᠡᠪᠡᠯ ∠1 − ∠2 =________ ᠭᠤᠷᠪᠠ᠂ ᠪᠣᠳ ᠣᠵᠤ ᠬᠠᠷᠢ ᠭᠤᠯᠬᠤ ᠰᠡᠲᠤ ᠪ᠃ (ᠨᠠᠢ ᠲᠡ 66 ᠬᠤ ᠪᠢ ) 19. ( 8 ᠬᠤ ᠪᠢ) ᠵᠢᠷᠤᠭ ᠮᠡᠳ ᠤ ∆ AB C ᠦᠭ ᠬᠦᠭᠳ ᠡᠪᠡ᠃ ︵1 ︶BC ᠲᠠᠯ ᠠ ᠲ ᠡᠭᠡᠷᠡᠬ ᠢ ᠲ ᠤᠮᠳᠠ ᠱ ᠤᠭᠤᠮ AD ᠶᠢ ᠪᠠ ᠢᠭᠤ ᠯ᠃ ︵2 ︶∆AD C ᠶᠢᠨ ᠲ ᠠᠯ ᠠ AD ᠲᠡᠭᠡᠷᠡᠬ ᠢ ᠥᠨᠳ ᠦᠷ CF ᠶᠢ ᠪᠠ ᠢᠭᠤ ᠯ᠃ ︵3 ︶ ᠬᠡᠷᠪᠡ AD = 6 , CF = 4 ᠪ ᠣᠯ ∆ AB C ᠶ ᠢᠨ ᠲ ᠠᠯᠠᠪᠠ ᠢ ᠶᠢ ᠣ ᠯ᠃ (5) (6) (8) (7) (9) (10) 20. ( 8 ᠬᠤᠪᠢ ) ᠵᠢ ᠷᠤᠭ ᠮᠡᠲᠦ᠂ ∆AB C ᠳ ᠤ᠂∠B AC = 90° ᠂ BD ᠨᠢ ∠A BC ᠶᠢ ᠲᠠᠯᠠᠯ ᠠᠨ ᠬᠤ ᠪᠢᠶᠠᠨ ᠠ᠂ CD || AB , ∠D = 29° ᠂ ∠1 ᠶᠢ ᠣ ᠯ᠃ 21. (10 ᠬᠤᠪᠢ ) ᠵ ᠢᠷᠤᠭ ᠮᠡᠲ ᠦ᠂ ∆ AB C ᠳ ᠤ᠂ ∠A = 30° , ∠B = 62° CE ᠨᠢ ∠A CB ᠲᠠᠯ ᠠᠯᠠᠨ ᠬᠤ ᠪᠢᠶᠠᠨ ᠠ᠂ ︵1 ︶∠A CE ᠭᠷᠠᠳ ᠦ᠋ᠰ ᠤᠨ ᠲᠣᠭ ᠠ ᠶᠢ ᠣᠯ᠃ ︵2 ︶ᠬᠡᠷᠪᠡ CD ⊥ AB ᠂ ᠡᠭᠴᠡ ᠶᠢᠨ ᠰ ᠠᠭᠤᠷᠢ ᠨᠢD ᠂ ∠C DF = 74° ᠪᠣᠯ ∆C FD ᠨᠢ ᠲ ᠡᠭᠰᠢ ᠦᠨᠴ ᠦᠭᠳᠦ ᠭᠤ ᠷᠪᠠᠯ ᠵᠢᠨ ᠪᠣᠯ ᠬᠤ ᠶ ᠢ ᠪᠠ ᠳᠤᠯᠠ᠃ 22. (10 ᠬᠤᠪᠢ ) ᠵ ᠢᠷᠤᠭ ᠮ ᠡᠳᠦ᠂ ᠵᠢᠷᠭᠤᠭᠠᠨ ᠦᠨᠴ ᠦᠭᠳᠦ AB CD EF ᠶᠢᠨ ᠲᠤ ᠳᠤᠭᠠᠳ ᠤ ᠥᠨᠴ ᠦᠭ ᠨ ᠢ ᠴᠥ ᠮ ᠬᠠᠷᠢ ᠯᠴᠠᠨ ᠲᠡᠩ ᠴᠡᠭᠦ ᠦ᠂ CF || AB ᠃ (1) ∠F CD ᠶᠢ ᠣ ᠯ᠃ (2) ᠪᠠ ᠳᠤᠯᠠᠭᠳ ᠠᠬᠤ ᠨ ᠢ᠄ AF || CD 23. (10 ᠬᠤᠪᠢ ) ∆ AB C ᠳ ᠤ᠂ ∠A = 50° ᠥᠨ ᠳᠦᠷ BD ᠪᠠ ᠥᠨᠳ ᠦᠷ CE ᠶᠢᠨ ᠤᠷᠤᠰᠢ ᠬᠤ ᠰ ᠢᠯᠤᠭᠤ ᠨ ᠨ ᠢ ᠴᠡᠭ P ᠳᠤ ᠤᠭ ᠳᠤᠯᠤ ᠯᠴᠠᠨ ᠠ᠂ ᠵ ᠢᠷᠤᠭ ᠢ ᠨ ᠢ ᠵᠢ ᠷᠤᠵᠤ ∠B PC ᠶᠢ ᠣ ᠯ᠃ 24. (10 ᠬᠤᠪᠢ ) ᠵ ᠢᠷᠤᠭ ᠮᠡᠲ ᠦ᠂ ∆ AB C ᠳ ᠤ᠂ AD , BE ᠨᠢ ᠲᠤᠰ ᠪᠤᠷᠢ ∠B AC , ∠A BC ᠶᠢ ᠲᠠᠯᠠᠯ ᠠᠨ ᠬᠤ ᠪᠢᠶᠠᠨ ᠠ᠃ (1) ᠬᠡᠷᠪᠡ ∠C = 70° , ∠B AC = 60° ᠪᠣᠯ ∠B ED ᠶᠢ ᠣᠯ᠃ ᠬᠡᠷᠪᠡ ∠B ED = 50° ᠪᠣᠯ ∠C ᠶᠢ ᠣ ᠯ᠃ (2) ∠B ED ᠪᠠ ∠C ᠲ ᠣᠭ ᠠ ᠬᠡᠮ ᠵᠢᠭᠳ ᠡᠬᠦᠨ ᠤ ᠬ ᠣᠯᠪᠤ ᠭᠳᠠᠯ ᠢ ᠪᠢᠴ ᠢᠵᠦ᠂ ᠴᠢᠨᠤ ᠳᠦ᠋ᠩ ᠨᠡᠯᠲᠡ ᠪᠠᠨ ᠪ ᠠᠳᠤᠯ ᠠ᠃