ᠠᠷᠪᠠᠨ ᠲᠤᠯᠤᠳᠤᠭᠠᠷ ᠪᠦᠯᠦᠭ ᠬᠤᠶᠠᠷ ᠡᠭᠴᠡ ᠲᠠᠯ᠎ᠠ ᠶᠢᠨ ᠪᠠᠳᠤᠶᠤᠰᠤ （ᠨᠢᠭᠡᠴᠢ ᠶᠢᠨ ᠪᠠᠢᠴᠠᠭᠠᠯᠲᠠ 1） .pdf

ᠠᠷᠪ ᠠᠨ ᠳ᠋᠊ ᠣᠯᠣᠳ ᠤᠭᠠᠷ ᠪᠥᠯ ᠥᠭ ᠦ ᠨ᠊ ᠪᠠ ᠢᠴᠠ ᠭᠠᠯᠲ ᠠ ᠠᠩᠭᠢ ᠪᠥᠯᠥᠭ᠄ ᠨᠡᠷ ᠡ᠄ ︵90 ᠮ᠊ ᠢᠨᠦ᠋ᠲ᠂ ᠨᠠᠢ ᠲᠡ 120 ᠬᠤ ᠪᠢ︶ ᠨᠢᠭᠡ᠂ ᠰ᠊ ᠤᠩᠭᠤ ᠬᠤ ᠰ᠊ ᠡᠲᠤᠪ᠃ ︵ᠰᠡᠲ ᠤᠪ ᠤ ᠦᠷᠢ 3 ᠬᠤᠪᠢ᠂ ᠨ᠊ ᠠᠢᠲ ᠡ 30 ᠬᠤ ᠪᠢ︶ 1. ᠳᠠᠷᠠᠭᠠᠬ ᠢ ᠡ ᠯ᠊ ᠡ ᠪᠦᠯᠦᠭ ᠲᠤᠭ ᠠ ᠳ᠋᠊ ᠥ᠂ ᠲᠡᠭᠰ ᠢ ᠦᠨᠴ ᠦᠭᠲᠤ ᠭᠤᠷᠪᠠ ᠯᠵᠢᠨ ᠤ ᠬ᠋᠊ ᠤᠷᠪᠠ ᠨ᠊ ᠲ᠊ ᠠᠯ ᠠ ᠶᠢᠨ ᠬᠤᠯ ᠪᠤᠭᠳ ᠠᠯ ᠢ ᠤ ᠦᠷᠢ ᠯᠳᠤᠭ ᠦᠯᠵᠤ ᠴᠢᠳ ᠠᠬᠤ ᠦᠭᠡᠢ ᠨᠢ ︵︶ A. 1. 5 , 2 , 2.5 B. 3 , 4 , 5 C. 5 , 12 , 3 D. 20 , 30 , 40 2. ᠬᠡᠷᠪᠡ ᠲᠡᠭᠰ ᠢ ᠦᠨᠴ ᠦᠭᠲᠤ ᠭᠤᠷᠪᠠ ᠯᠵᠢᠨ ᠤ ᠬ᠊ ᠤᠶᠠᠷ ᠡᠭᠴᠡ ᠲᠠᠯ ᠠ ᠶᠢ ᠴᠦ᠋ᠮ ᠤ ᠬ᠋᠊ ᠤᠨ 2 ᠲᠠᠬᠢ ᠨ᠊ ᠪᠤᠯᠲ ᠠᠯ ᠠ ᠶᠡᠭᠡᠰᠭᠡᠪᠡᠯ᠂ ᠵᠢᠰ ᠢᠭᠦᠦ ᠲᠠᠯ ᠠ ᠶᠢᠨ ᠤᠷ ᠲᠤ ᠨ᠊ ᠢ ᠤ ᠬ᠋᠊ ᠤᠨ ᠢᠶᠠᠨ ︵︶ ᠲᠠᠬ ᠶᠢᠨ ᠤ ᠤᠯᠳᠠᠯ ᠠ ᠶᠠᠬ ᠡᠰᠤᠨ ᠠ᠃ A. 2 B. 3 C. 4 D. 5 3. ᠬᠡᠷᠪᠡ ᠨᠢᠭᠡ ᠱᠠᠳ ᠤ ᠪᠠ ᠨ᠊ ᠪᠠ ᠷᠢᠯᠭ ᠠ ᠶᠢ ᠲᠦ᠋ ᠰᠢᠬᠦ ᠯᠵᠤ ᠲᠠᠯᠪᠢ ᠪᠠᠯ᠂ ᠱᠠᠲ ᠤ ᠶᠢ ᠨ᠊ ᠰ᠊ ᠠᠭᠤᠷᠢ ᠨᠢ ᠪᠠ ᠷᠢᠯᠭ ᠠ ᠶᠢᠨ ᠰ᠊ ᠠᠭᠤᠷᠢ ᠡᠴ ᠠ 5 ᠮ᠊ ᠧᠲᠷ ᠵᠶᠢᠲ ᠠᠢ ᠪᠤ ᠯ᠊᠂ 13 ᠮᠧᠲ ᠷ᠊ ᠤᠷ ᠲᠤ ᠱᠠ ᠲᠤ ᠨ᠊ ᠢ ᠪᠠ ᠷᠢᠯᠭ ᠠ ᠶᠢ ᠨ᠊ ︵︶ ᠮᠧᠲ ᠷ᠊ ᠦᠨᠳ ᠤᠷ ᠲ᠊ ᠤ ᠬᠦᠷ ᠴᠤ ᠴ᠊ ᠢᠳᠠᠨ ᠠ᠃ A. 12 B. 13 C. 14 D. 15 4. ᠳᠠᠷᠠᠭᠠᠬ ᠢ ᠡ ᠯ᠊ ᠡ ᠪᠦᠯᠦᠭ ᠲᠤ ᠬ᠋᠊ ᠠ᠄ ① 6 , 8 , 10 ② 13 , 5 , 12 ③ 1 , 2 , 3 ④ 9 , 40 , 41 ⑤ 3 12 , 4 12 , 5 12 ᠳ᠋᠊ ᠥ᠂ ᠭᠧᠤᠬ ᠦ᠋ ᠲ᠊ ᠤᠭ ᠠ ᠪᠤᠯ ᠵᠤ ᠪᠤᠯᠬᠤ ᠨᠢ ᠨ᠊ ᠢᠲ ᠠ ︵︶ ᠪᠦᠯ ᠦᠭ ᠤ ᠠᠢᠨ ᠠ᠃ A. 2 B. 3 C. 4 D. 5 5. ∆AB C ᠳᠤ᠂ ∠C ＝90°᠂ ᠬ᠊ ᠦᠷᠢ ᠶᠡᠨ ᠦ ᠤ ᠷᠲᠤ ᠨᠢ 60᠂ ᠵᠢᠰᠢ ᠭᠦᠦ ᠲᠠᠯ ᠠ ᠪᠤᠯᠤ ᠨ᠊ ᠨ᠊ ᠢᠭᠡ ᠡᠭᠴᠡ ᠲᠠᠯ ᠠ ᠶᠢ ᠨ᠊ ᠬ᠊ ᠠᠷᠢᠴ ᠠᠯ ᠨ᠊ ᠢ 13 ∶5 ᠪᠤᠯ᠂ ᠡᠨᠡ ᠲᠡᠭᠰ ᠢ ᠦᠨᠴ ᠦᠭᠲᠤ ᠭᠤᠷᠪᠠ ᠯᠵᠢᠨ ᠤ ᠬ᠋᠊ ᠤᠷᠪᠠ ᠨ᠊ ᠲ᠊ ᠠᠯ ᠠ ᠶᠢᠨ ᠤᠷᠲ ᠤ ᠨᠢ ᠲ᠊ ᠤᠰ ᠲᠤᠰ ︵︶ A. 5 ,4 ,3 B. 13 ,12 ,5 C. 10 ,8 ,6 D. 26 ,24 ,10 6. ∆AB C ᠳᠤ᠂ ᠦᠭ ᠭᠦᠭᠳ ᠡᠭᠰᠡᠨ ᠨᠢ AB = 12 cm , AC = 9cm , BC = 15 cm ᠲ᠊ ᠡᠭᠡᠪᠡᠯ ∆AB C ᠶᠢᠨ ᠲᠠᠯᠠᠪᠠ ᠢ ᠨᠢ ︵︶ A. 108 cm 2 B. 90 cm 2 C. 180 cm 2 D. 54 cm 2 7. ᠬᠠᠪᠲ ᠠᠭᠠᠢ ᠶᠢᠨ ᠲᠡᠭᠰ ᠢ ᠦᠨᠴ ᠦᠭᠲᠤ ᠪᠠᠢ ᠷᠢᠰᠢ ᠯ᠊ ᠤᠨ ᠰᠢᠰ ᠲᠧᠮ ᠳᠤ᠂ ᠴᠡᠭ P ︵－2,3︶ ᠡ ᠴᠠ ᠡᠬᠢᠨ ᠦ ᠴ᠊ ᠡᠭ ᠬ᠊ ᠦᠷᠬᠦ ᠵᠠᠢ ᠨᠢ ︵︶ A. √5 B. √11 C. √13 D. 2 8. ᠬᠡᠷᠪᠡ ᠲᠡᠭᠰ ᠢ ᠲ᠊ ᠦᠷᠪᠡᠯ ᠶᠢᠨ AB CD ᠶᠢᠨ ᠲᠠᠯᠠᠪᠠ ᠢ ᠨᠢ 29 ᠪᠤ ᠯ᠊᠂ ᠲ᠊ ᠠᠰᠢᠭᠤ ᠪᠴᠢ AC ᠶᠢᠨ ᠤᠷᠲ ᠤ ᠨᠢ ︵︶ A. 23 B. 49 C. √ 23 D. 29 9. ᠵᠢᠷᠤᠭ 1 ᠮᠡᠲ ᠤ᠂ AB = BC = CD = DE = 1 ᠪᠦᠭᠡᠳ BC ⊥ AB , CD ⊥ AC , DE ⊥ AD ᠲ᠊ ᠡᠭᠡᠪᠡᠯ ᠬᠡᠷᠴ ᠢᠮ A E ᠵ᠊ ᠶᠢᠨ ᠤᠷ ᠲᠤ ᠨ᠊ ᠢ ︵︶ A. 32 B. 2 C. 52 D. 3 ︵1︶ 10. ᠵᠢᠷᠤ ᠬ᠋᠊ 2 ᠮᠡᠲᠤ᠂ Rt ∆AB C ᠳ᠋᠊ ᠦ᠂ ∠C = 90°᠂ ᠴᠡᠭ D ᠨᠢ AC ᠲᠡᠭᠡᠷᠠᠬ ᠢ ᠨ᠊ ᠢᠭᠡ ᠴᠡᠭ ᠪᠦᠭᠡᠳ DA = DB = 5᠂ ᠪᠠᠰᠠ ∆D AB ᠶᠢ ᠨ᠊ ᠲ᠊ ᠠᠯᠠᠪᠠ ᠢ ᠨᠢ 10 ᠪᠤᠯ ᠤᠨ ᠠ᠂ ᠲ᠊ ᠡᠭᠡᠪᠡᠯ DC ᠶᠢᠨ ᠤ ᠷᠲᠤ ᠨᠢ ︵︶ A. 4 B. 3 C. 5 D. 4. 5 ᠬᠤᠶ ᠠᠷ᠂ ᠬᠠᠭᠠ ᠯᠲᠠ ᠳ᠋᠊ ᠤ ᠲ᠊ ᠠᠭᠯᠠᠬᠤ ᠰᠡᠲᠤ ᠪ᠊᠃ ︵ᠰᠡᠲ ᠤᠪ ᠤ ᠦᠷᠢ 3 ᠬᠤᠪᠢ᠂ ᠨ᠊ ᠠᠢᠲ ᠡ 24 ᠬᠤ ᠪᠢ︶ 11. ᠲᠡᠭ ᠰᠢ ᠦᠨᠴ ᠦᠭᠲᠤ ᠭᠤᠷᠪᠠ ᠯᠵᠢᠨ ᠤ ᠬᠤ ᠶᠠᠷ ᠡᠭᠴᠡ ᠲᠠᠯ ᠠ ᠶᠢ ᠨ᠊ ᠤᠷᠲ ᠤ ᠨᠢ ᠲ᠊ ᠤᠰ ᠲ᠊ ᠤᠰ 5 ᠪᠠ 12 ᠪᠤᠯᠤ ᠨ᠊ ᠠ᠂ ᠲ᠊ ᠡᠭᠡᠪᠡᠯ ᠵᠢᠰ ᠢᠭᠦᠦ ᠲᠠᠯ ᠠ ᠲ᠊ ᠡᠭᠡᠷᠠᠬ ᠢ ᠦᠨ ᠲᠤᠷ ᠨᠢ ᠪᠤᠯᠤ ᠨ᠊ ᠠ᠃ 12. ᠲᠡᠭ ᠰᠢ ᠦᠨᠴ ᠦᠭᠲᠤ ᠭᠤᠷᠪᠠ ᠯᠵᠢᠨ ᠤ ᠬ᠋᠊ ᠤᠷᠪᠠ ᠨ᠊ ᠲ᠊ ᠠᠯ ᠠ ᠶᠢᠨ ᠤᠷᠲ ᠤ ᠨᠢ ᠲᠠᠷᠠᠭᠠ ᠯᠠᠭᠰᠠᠨ ᠭᠤᠷᠪᠠ ᠨ᠊ ᠲ᠊ ᠡᠭᠰᠢ ᠲᠤᠭ ᠠ ᠪᠤ ᠯᠤᠨ ᠠ᠂ ᠲᠡᠭᠡᠪᠡᠯ ᠡᠨᠡ ᠭᠤᠷᠪᠠ ᠨ᠊ ᠲ᠊ ᠤᠭ ᠠ ᠨᠢ ᠲ᠊ ᠤᠰ ᠲᠤᠰ ᠪᠤ ᠯᠤᠨ ᠠ᠃ 13. ᠵᠢᠷᠤᠭ 3 ᠮᠡᠲᠤ᠂ ᠨᠢᠭᠡᠨ ᠰᠠᠭᠤ ᠷᠢ ᠮ᠊ ᠤᠳᠤ ᠨᠢ ᠬ᠋᠊ ᠠᠵᠠᠷ ᠠᠴᠠ 9 ᠮ᠊ ᠧᠲᠷ ᠵᠠᠢ ᠲᠠᠢ ᠬᠡᠰᠡᠭ ᠢᠶᠡᠷ ᠢᠶᠡᠨ ᠬᠤ ᠭᠤᠷᠠᠵ ᠤ᠂ ᠮ᠊ ᠤᠳᠤᠨ ᠤ ᠦᠵᠦ ᠭᠦᠷ ᠨᠢ ᠰ᠊ ᠠᠭᠤᠷᠢ ᠡᠴ ᠠ 12 ᠮᠧᠲ ᠷ᠊ ᠵᠠᠢ ᠲᠠᠢ ᠭᠠᠵᠠ ᠷ᠊ ᠲᠤ ᠤᠨᠠᠪᠠ᠂ ᠲ᠊ ᠡᠭᠡᠪᠡᠯ ᠮᠤᠳ ᠤ ᠬ᠊ ᠤᠭᠤᠷᠠᠬ ᠤ ᠡᠴ ᠠ ᠡ ᠮᠤᠨ ᠠ ᠦᠨ ᠲᠤᠷ ᠪᠠᠢ ᠵᠠᠢ᠃ 14. ᠬᠡᠷᠪᠡ ᠨᠢᠭᠡ ᠭᠤ ᠷᠪᠠᠯ ᠶᠢᠨ ᠤ ᠬ᠋᠊ ᠤᠷᠪᠠ ᠨ᠊ ᠲ᠊ ᠤᠳᠤᠭᠠᠲ ᠤ ᠦᠨᠴ ᠦᠭ ᠦᠨ ᠬᠠᠷᠢ ᠴᠠᠯ ᠨᠢ 1∶ 2∶ 3 ᠪᠦᠭᠡᠳ ᠬᠠᠮᠤᠭ ᠤᠨ ᠪᠠᠭ ᠠ ᠲᠠᠯ ᠠ ᠶᠢ ᠨ᠊ ᠤ ᠷᠲᠤ ᠨᠢ 8 ᠪᠤᠯ᠂ ᠬᠠᠮᠤᠭ ᠤᠨ ᠤᠷᠲ ᠤ ᠲ᠊ ᠠᠯ ᠠ ᠵ᠊ ᠶᠢᠨ ᠤᠷᠲ ᠤ ᠨᠢ ᠪᠤ ᠯᠤᠨ ᠠ᠃ 15. ᠶᠢ ᠷᠤᠭ 4 ᠮᠡᠲ ᠤ᠂ ᠠᠳᠠᠯ ᠢ ᠬ᠊ ᠠᠵᠠᠭᠤ ᠲᠤ △ AB C ᠶᠢᠨ ᠰᠠᠭᠤ ᠷᠢ BC = 16᠂ ᠦᠨ ᠲᠤᠷ AD = 6᠂ ᠲᠡᠭᠡᠪᠡᠯ ᠬ᠊ ᠠᠵᠠᠭᠤ AB ᠶᠢ ᠨ᠊ ᠤᠷᠲ ᠤ ᠨᠢ᠃ 16. ∆ AB C ᠳᠤ᠂ AB ＝8cm , BC ＝15 cm᠂ ᠬᠡᠷᠪᠡ ∠B ＝90° ᠪᠤᠯᠭᠠᠬᠤ ᠭᠡᠪᠡᠯ᠂ AC ᠶᠢᠨ ᠤᠷᠲ ᠤ ᠨᠢ ᠵ᠊ ᠠᠪᠡᠯ ______ cm ᠪᠠᠢ ᠬᠤ ᠬ᠊ ᠡᠷᠡᠭᠲ ᠢ᠃ 17. ᠨᠢ ᠭᠡᠨ ᠲᠡᠭᠰ ᠢ ᠦᠨᠴ ᠦᠭᠲᠤ ᠭᠤᠷᠪᠠ ᠯᠵᠢᠨ ᠤ ᠨ᠊ ᠢᠭᠡ ᠡᠭᠴᠠ ᠲᠠᠯ ᠠ ᠵ᠊ ᠶᠢᠨ ᠤᠷᠲ ᠤ ᠨᠢ 12 cm᠂ ᠵᠢᠰᠢ ᠭᠦᠦ ᠲᠠᠯ ᠠ ᠶᠢ ᠨ᠊ ᠤᠷᠲ ᠤ ᠨᠢ 13 cm᠂ ᠲᠡᠭᠡ ᠪᠡᠯ ᠡᠨᠡ ᠲ᠊ ᠡᠭᠰᠢ ᠦᠨᠴ ᠦᠭᠲᠤ ᠬ᠋᠊ ᠤᠷᠪᠠ ᠯᠵᠢᠨ ᠤ ᠲᠠᠯᠠᠪᠠ ᠢ ᠨᠢ ______᠃ 18. ᠵᠢᠷᠤᠭ 5 ᠮᠡᠲᠤ᠂ ᠨᠢ ᠭᠡᠨ ᠬᠦᠮᠦᠨ ᠭᠣ ᠣᠯ ᠤ ᠨ᠊ ᠡ ᠷᠭᠢ ᠳᠡᠭᠡ ᠷᠡᠬᠢ A ᠴᠡᠭ ᠠᠴᠠ ᠡᠬᠢ ᠯᠡᠵᠤ᠂ ᠭᠣ ᠣᠯ ᠤ ᠨ᠊ ᠡ ᠷᠬᠢᠮ ᠳᠤ ᠡᠭᠴᠡ ᠪᠣᠯᠬᠤ AB ᠱᠤᠭᠤ ᠮ᠊ ᠲ᠊ ᠠᠭᠠᠤ ᠤᠮᠪᠠ ᠨ᠊ B ᠴᠡᠭ ᠬᠦᠷᠬ ᠦ ᠭᠡᠪᠡ᠃ ᠬ᠋᠊ ᠡᠪᠡᠴ ᠤ ᠤ ᠰᠤᠨ ᠤ ᠤ ᠷᠤᠰᠬ ᠠᠯ ᠤ ᠨ᠊ ᠨ᠊ ᠥᠯᠥᠭᠡ ᠠᠴᠠ ᠪᠣᠯᠵᠤ ᠡᠩᠰ ᠡᠷᠡᠬᠦ ᠡᠷᠬ ᠢᠮ ᠳᠡᠭᠡᠷᠠᠬ ᠢ ᠵᠣ ᠷᠢᠭᠰᠠᠨ ᠴᠡᠭ B ᠡᠴ ᠠ 200 m ᠵᠶᠢᠲ ᠠᠢ C ᠴᠡᠭ ᠲᠤ ᠤ ᠮᠪᠠᠨ ᠭᠠᠷᠴᠤ᠂ ᠲᠡᠷᠠ ᠨᠠᠢ ᠲᠡ 520 m ᠤ ᠮᠪᠠᠭᠰᠠᠨ ᠪᠣᠯ᠂ ᠭᠤᠤ ᠯ᠊ ᠤᠨ ᠦᠷ ᠭᠡᠨ ᠨᠢ _______ _ m᠃ ᠭᠤᠷᠪᠠ᠂ ᠪᠣᠳ ᠣᠵᠤ ᠬᠠᠷᠢ ᠭᠤᠯᠬᠤ ᠰᠡᠲᠤ ᠪ᠊᠃ ︵ᠨᠠᠢ ᠲᠡ 66 ᠬᠤ ᠪᠢ︶ 19. ︵10 ᠬᠤᠪᠢ︶ ᠵᠢᠷᠤᠭ ᠮᠡᠲᠤ᠂ ᠲ᠊ ᠡᠮᠤᠷ ᠵᠠᠮ ᠵᠠᠰᠠᠬᠤ ᠶᠠᠪᠤᠴ ᠠ ᠳ᠋᠊ ᠥ᠂ ᠠᠭᠤ ᠯᠠ ᠶ᠊ ᠢ ᠨ᠊ ᠦᠬᠡᠯ ᠡᠵᠤ ᠨᠤᠬ ᠠ ᠵᠠᠮ AC ᠶᠢ ᠵᠠᠰᠠᠬᠤ ᠴᠢᠬᠤᠯ ᠠ ᠲ᠊ ᠠᠢ ᠤ ᠤᠯᠵᠠᠢ᠃ ᠬᠡᠮ ᠵᠢᠬᠦ ᠪᠠᠷ ᠲᠠᠮᠵᠢ ᠨ᠊ ∠A = 40° , ∠B ＝50 ° , AB ＝5km , BC = 4km ᠪᠣᠯ ᠬᠤ ᠶ᠊ ᠢ ᠮ᠊ ᠡᠳᠡᠪᠡ᠃ ᠬᠡᠷᠪᠡ ᠡᠳᠤ ᠷ᠊ ᠤ ᠦᠷᠢ 0.3 km ᠵᠠᠰᠠᠪᠡᠯ᠂ ᠬᠡᠳᠤ ᠨ᠊ ᠡ ᠲᠤᠷ ᠲᠤ ᠨᠤᠬ ᠠ ᠵ᠊ ᠠᠮ AC ᠶᠢ ᠵᠠᠰᠠ ᠵᠤ ᠲ᠊ ᠠᠭᠤᠰ ᠬᠤ ᠤ ᠤᠢ︖ ︵2︶ ︵3︶ ︵4︶ ︵5︶ 20. ︵10 ᠬᠤᠪᠢ︶ ᠵᠢᠷᠤᠭ ᠮᠡᠲᠤ᠂ △ AB C ᠳ᠋᠊ ᠥ᠂ AD ⊥ BC᠂ ᠡᠭᠴᠡ ᠶᠢᠨ ᠰᠠᠭᠤ ᠷᠢ ᠨ᠊ ᠢ D᠂ AB = 3 , BD = 2 , DC = 1᠂ AC ᠶᠢᠨ ᠤᠷ ᠲᠤ ᠶ᠊ ᠢ ᠤᠯ᠃ 21. ︵10 ᠬᠤᠪᠢ︶ ∆AB C ᠳᠤ᠂ CD ᠨᠢ AB ᠲᠡᠭᠡᠷᠠᠬ ᠢ ᠦ ᠨᠳᠤᠷ᠂ AC = 20 , BC = 15 , DB = 9᠃ ︵1︶ AD ᠶᠢᠨ ᠤᠷᠲ ᠤ ᠶᠢ ᠤᠯ᠃ ︵2︶ ∆AB C ᠨ᠊ ᠢ ᠲ᠊ ᠡᠭᠰᠢ ᠦᠨᠴ ᠦᠭᠲᠤ ᠭᠤᠷᠪᠠ ᠯᠵᠢᠨ ᠮᠦ᠋ ᠨ᠊ ᠤ ᠤ︖ ᠰᠢ ᠯᠲᠠᠭᠠᠨ ᠢ ᠨ᠊ ᠢ ᠲ᠊ ᠣᠳᠣᠷᠬ ᠠᠢᠯᠠ᠃ 22. ︵12 ᠬᠤᠪᠢ︶ ᠨᠢᠭᠡᠨ ᠲᠤ ᠨᠤᠭ ᠤᠨ ᠬᠡᠯᠪᠡᠷᠢ ᠲᠦ᠋ ᠷᠰᠤ ᠨᠢ ᠵᠢᠷᠤ ᠬ᠋᠊ ᠮ᠊ ᠡᠲᠤ᠂ ᠠᠵᠢ ᠯᠴᠢᠨ ᠠᠪᠠ ᠬ᠋᠊ ᠠ ᠲᠤᠰ ᠲᠤ ᠨᠤᠭ ᠤᠨ ᠡᠯ ᠡ ᠲᠠᠯ ᠠ ᠵ᠊ ᠶᠢᠨ ᠤᠷᠲ ᠤ ᠶᠢ ᠲᠤᠤ ᠷᠠᠬᠢ ᠮᠡᠲ ᠤ ᠲ᠊ ᠡᠮᠲᠡᠭᠯᠡ ᠪᠡ᠄ AB = 3 , AD = 4 , BC = 12 , CD = 13᠂ ᠪᠠᠰᠠ ∠D AB = 90° ᠲᠤ ᠰ᠊ ᠲ᠊ ᠤᠨᠤᠭ ᠤᠨ ᠲᠠᠯᠠᠪᠠ ᠢ ᠶᠢ ᠤᠯ᠃ 23 . ︵12 ᠬᠤᠪᠢ︶ ᠵᠢᠷᠤᠭ ᠮᠡᠲ ᠤ᠂ ᠨᠢᠭᠡᠨ ᠱᠠ ᠲᠤ ᠶ᠊ ᠶᠢᠨ ᠤᠷᠲ ᠤ ᠨᠢ 25 ᠮᠤᠲ ᠷ᠊᠂ ᠲ᠊ ᠡᠭᠦᠨ ᠢ ᠬᠡᠷᠡᠮ ᠲᠦ᠋ ᠰᠢᠭᠦ ᠯᠦᠨ ︵AC ᠶᠢᠨ ᠪᠠᠢ ᠷᠢᠨ ᠳᠤ︶ ᠲᠠᠯ ᠪᠢᠬᠤ ᠦᠶ ᠡᠰ᠂ ᠱᠠᠳᠤ ᠶᠢᠨ ᠰᠠᠭᠤ ᠷᠢ ᠨ᠊ ᠢ ᠬᠡᠷᠡᠮ ᠠᠴᠠ 7 ᠮ᠊ ᠸᠲᠷ ᠵ᠊ ᠠᠢ ᠲᠠᠢ ᠪᠠᠢ ᠪᠡ᠃ ︵1︶ ᠡᠨᠡ ᠦᠶ ᠡᠰ ᠱᠠᠳ ᠤ ᠶᠢ ᠨ᠊ ᠳᠡᠭᠡ ᠲᠤ ᠦᠵ ᠦᠭᠦᠷ ᠨᠢ ᠬ᠋᠊ ᠠᠵᠠᠷ ᠠᠴᠠ ᠬ᠊ ᠡᠳᠦᠢ ᠦᠨᠳ ᠤᠷ ᠤ ᠣᠢ︖ ︵2︶ ᠱᠠᠳ ᠤ ᠵ᠊ ᠶᠢᠨ ᠳᠡᠭᠡ ᠲᠤ ᠦᠵᠦ ᠭᠦᠷ 𝐴 ᠶ᠊ ᠢ 4 ᠮᠤᠲ ᠷ᠊ ᠳᠣ ᠷᠤᠭᠰ ᠢᠯᠠᠭᠤ ᠯᠵᠤ᠂ D ᠪᠠᠢ ᠷᠢᠨ ᠳᠤ ᠬᠦᠷᠭᠡᠪᠡ ᠯ᠊᠂ ᠳᠣ ᠣᠷᠠᠳ ᠤ ᠦᠵ ᠦᠬᠦᠷ C ᠨᠢ ᠭᠠᠳ ᠠᠭᠰᠢ ᠬᠡᠳᠦᠢ ᠮᠤᠲ ᠷ᠊ ᠰ᠊ ᠢᠯᠵᠢ ᠬᠦ ᠪᠤ ᠢ︖ 24 . ︵12 ᠬᠤᠪᠢ︶ ᠵᠢᠷᠤᠭ ᠮᠡᠲᠤ᠂ ᠲᠡᠭᠰ ᠢ ᠦᠨᠴ ᠦᠭᠲᠤ ᠶᠢᠨ ᠨᠢᠭᠡ ᠲ᠊ ᠠᠯ ᠠ AD ᠶᠢ ᠨᠤᠭᠤ ᠯᠤᠭᠠᠳ D ᠴᠡᠭ ᠢ BC ᠲᠡᠭᠡᠷᠠᠬ ᠢ F ᠴᠡᠭ ᠲᠤ ᠤᠨᠠᠭᠠᠨ ᠠ᠂ ᠦᠭ ᠭᠦᠭᠳ ᠡᠭᠰᠡᠨ ᠨᠢ AB = 8cm , BC = 10 cm᠂ ᠲ᠊ ᠡᠭᠡᠪᠡᠯ EC ᠶᠢᠨ ᠤᠷ ᠲᠤ ᠶ᠊ ᠢ ᠤᠯ᠃ A D CB F E B C A D E