ᠲᠠᠪᠤᠳᠤᠭᠠᠷ ᠪᠥᠯᠥᠭ ᠣᠭᠲᠣᠯᠣᠯᠴᠠᠭᠰᠠᠨ ᠰᠢᠯᠤᠭᠤᠨ ᠪᠠ ᠵᠡᠷᠭᠡᠴᠡᠭᠡ ᠰᠢᠯᠤᠭᠤᠨ （ᠨᠢᠭᠡᠴᠢ ᠶᠢᠨ ᠪᠠᠢᠴᠠᠭᠠᠯᠲᠠ 2） .pdf

ᠲᠠᠪᠤᠳᠤ ᠭᠠᠷ ᠪᠥᠯ ᠥᠭ ᠦᠨ ᠪᠠᠢᠴ ᠠᠭᠠᠯ ᠲᠠ ᠠᠩᠭᠢ ᠪᠥᠯ ᠥᠭ᠄ ᠨᠡᠷ ᠡ᠄ ︵90 ᠮᠢᠨᠦ᠋ ᠲ᠂ ᠨᠠᠢᠲᠡ 12 0 ᠬ ᠤᠪᠢ ︶ ᠨᠢᠭᠡ᠂ ᠰᠤᠩᠭᠤᠬ ᠤ ᠰ ᠡᠲᠤᠪ᠃ ( ᠰᠡᠲᠤᠪ ᠪᠦᠷᠢ 3 ᠬᠤᠪᠢ᠂ ᠨᠠᠢᠲᠡ 30 ᠬᠤᠪᠢ ) 1.ᠳᠣᠣᠷ ᠠᠬᠢ ᠦᠵ ᠡᠭᠳᠡᠯ ᠡᠴᠡ ᠵᠡᠷ ᠭᠡᠴᠡᠭᠡ ᠰᠢᠯᠵ ᠢᠯᠲᠡ ᠪᠣᠯᠬᠤ ᠨᠢ᠄ （ ） A. ᠨᠢᠭᠡ ᠬᠠᠭ ᠤᠳᠠᠰᠤ ᠴᠠᠭ ᠠᠰᠤ ᠶᠢ ᠲᠡᠭ ᠦᠨ ᠦ ᠳᠤᠮᠳᠠ ᠱᠤᠭᠤᠮ ᠳᠠᠭ ᠠᠤ ᠨᠤᠭ ᠤᠯᠤᠨ ᠠ B. ᠨᠢᠰᠦ ᠭᠡ ᠫᠢ ᠯᠠ ᠶᠢᠨ ᠲᠦ᠋ᠷᠭᠡᠨ ᠡᠷᠭᠢᠯ ᠲᠡ C. ᠴᠠᠬᠢᠯ ᠭᠠᠨ ᠱᠠᠲᠤ ᠶᠢᠨ ᠳᠡᠭᠡ ᠭᠰᠢ ᠳᠣᠷ ᠣᠭᠰ ᠢ ᠰᠢᠯ ᠵᠢᠬᠦ D. ᠨᠣᠮ ᠳᠣᠲ ᠣᠷᠠᠬ ᠢ ᠬᠠᠭ ᠤᠳᠠᠰᠤ ᠪᠦᠷᠢ ᠶᠢ ᠤᠷᠪ ᠠᠭᠤᠯ ᠬᠤ 2. ᠳᠣᠣᠷ ᠠᠬᠢ ᠵᠢᠷᠤᠭ ᠤᠳ ᠲᠠ ᠬᠢ∠ 1 ᠪᠣᠯᠤᠨ ∠ 2 ᠨᠢ ᠬᠠᠷᠢᠯ ᠴᠠᠨ ᠵᠡᠷᠭᠡᠯ ᠡᠳᠡᠭᠡ ᠨᠥ ᠬᠥᠪᠦᠷᠢ ᠥᠨᠴᠥ ᠭ ᠪ ᠣᠯᠬᠤ ᠨᠢ᠄ ( ) A. B. C. D. 3. ᠵᠢᠷᠤᠭ 1 ᠮᠡ ᠲᠦ ᠂ ᠳᠣᠣᠷ ᠠᠬᠢ ᠮᠠᠭᠠᠳᠯ ᠠᠯ ᠪ ᠣᠶ ᠄ ᠵᠢᠷᠤᠭ ᠮᠡᠲᠦ᠂ ᠳᠤᠤᠷ ᠠᠬᠢ ᠬᠡᠯᠡᠯᠭᠡ ᠄ ①∠ 1 ᠪ ᠣᠯᠤᠨ ∠ 3 ᠨᠢ ᠮᠥᠷᠭᠥ ᠯᠳᠦᠭ ᠡ ᠦᠨᠴ ᠦᠭ ②∠ 1 ᠪ ᠣᠯᠤᠨ ∠ 4 ᠨᠢ ᠲᠣᠳᠣᠭᠠ ᠳᠣ ᠰᠣᠯᠪᠢᠭ ᠰᠠᠨ ᠦᠨᠴᠦ ᠭ ③ ∠ 1 ᠪ ᠣᠯᠤᠨ ∠ 2 ᠨᠢ ᠲᠣᠲᠤᠭᠠ ᠳᠤ ᠦᠷᠦᠭᠡᠯ ᠦᠨᠴᠦ ᠭ ④∠ 3 ᠪᠣᠯᠤᠨ ∠ 4 ᠨᠢ ᠲᠣᠬ ᠢᠷᠠᠭᠰᠠᠨ ᠦᠨᠴᠦ ᠭ᠂ ᠡᠭᠦ ᠨ ᠳ ᠦ ᠪᠤᠷᠤᠭ ᠤ ᠪᠣᠯᠬᠤ ᠨᠢ ᠄ ( ) A. ① B. ② C. ③ D. ④ 4. ᠵᠢᠷᠤᠭ 2 ᠮᠡᠲᠦ ᠂ ᠳᠣᠣᠷ ᠠᠬᠢ ᠨᠥᠬᠥ ᠴᠡᠯ ᠦ ᠳ ᠲᠦ ᠬᠣ ᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ AB , CD ᠤ ᠨ ᠵᠡ ᠷᠭᠡᠴᠡᠭᠡ ᠪᠣᠯᠬᠤ ᠶᠢ ᠮᠠ ᠭᠠᠳᠯ ᠠᠵᠤ ᠳᠡ ᠢᠯᠬᠦ ᠨᠢ᠄ ( ) A. ∠ 1= ∠ 2 B. ∠ 3= ∠ 4 C. ∠ 1= ∠ 5 D. ∠ 3= ∠ 5 5. ᠳᠣᠣᠷ ᠠᠬᠢ ᠦᠭ ᠦᠯᠡᠯ ᠳᠦ ᠵᠢᠩᠬ ᠢᠨᠢ ᠦᠭ ᠦᠯᠡᠯ ᠪᠣᠯ ᠬᠤ ᠨᠢ ᠄ ( ) A. ᠵᠡᠷ ᠭᠡᠯᠡᠳᠡ ᠭᠡ ᠨᠥᠬᠥ ᠪᠦᠷᠢ ᠥᠨᠴᠥ ᠭ ᠬᠠᠷ ᠢᠯᠴᠠᠨ ᠲᠡᠩ ᠴᠡᠭᠦᠦ B. ᠮᠥᠷᠭᠥ ᠯᠳᠦᠭᠡ ᠦᠨᠴ ᠦᠭ ᠬᠠᠷᠢᠯ ᠴᠠᠨ ᠲᠡᠩ ᠴᠡᠭᠦᠦ C. ᠲᠣᠳᠣᠭᠠ ᠳᠣ ᠰ ᠣᠯᠪᠢᠭ ᠰᠠᠨ ᠦᠨᠴᠦ ᠭ ᠬᠠᠷ ᠢᠯᠴᠠᠨ ᠲᠡᠩ ᠴᠡᠭᠦᠦ D. ᠲᠣᠬ ᠢᠷᠠᠭᠰᠠᠨ ᠦᠨᠴ ᠦᠭ ᠬᠠᠷᠢᠯ ᠴᠠᠨ ᠲᠡᠩ ᠴᠡᠭᠦᠦ 6. ᠵᠢᠷᠤᠭ 3 ᠮᠡ ᠲᠦ᠂ ᠰᠢᠯᠤᠭᠤᠨ 𝑎 , b ᠨᠢ ᠰᠢᠯᠤᠭᠤᠨ c ᠳᠤ ᠣᠭᠲᠣ ᠯᠣᠭᠳᠠᠵᠠᠢ᠂ ᠲᠡᠭᠡᠪ ᠡᠯ ∠ 1 ᠪ ᠣᠯᠤᠨ ∠ 2 ᠨᠢ ᠄ ( ) A. ᠲᠣᠬ ᠢᠷᠠᠭᠰᠠᠨ ᠦᠨᠴ ᠦᠭ B. ᠲᠣᠳᠣᠭᠠ ᠳᠣ ᠰ ᠣᠯᠪᠢᠭᠰᠠᠨ ᠦᠨᠴ ᠦᠭ C. ᠲᠣᠲᠤᠭᠠ ᠳᠤ ᠦᠷᠦ ᠭᠡᠯ ᠦ ᠨᠴᠦᠭ D. ᠵᠡᠷ ᠭᠡᠯᠡᠳᠡ ᠭᠡ ᠨᠥᠬᠥ ᠪᠦᠷᠢ ᠥᠨᠴᠥ ᠭ 7. ᠵᠢᠷᠤᠭ 4 ᠮᠡ ᠲᠦ ᠂ ᠴᠡᠭ P ᠡᠴᠡ ᠰᠢᠯ ᠤᠭᠤᠨ 𝑙 ᠬ ᠦᠷᠬᠦ ᠵᠠᠶ ᠨᠢ᠄ ( ) A. ᠬᠡᠷ ᠴᠢᠮ PA ᠦᠨ ᠤᠷᠲᠤ B. ᠬᠡᠷᠴᠢᠮ PB ᠦᠨ ᠤᠷᠲᠤ C. ᠬᠡᠷ ᠴᠢᠮ PC ᠦᠨ ᠤᠷᠲᠤ D. ᠬᠡᠷᠴᠢᠮ PD ᠦᠨ ᠤᠷᠲᠤ 8. ᠵᠢᠷᠤᠭ 5 ᠮᠡᠲᠦ᠂ BD // AC ᠂ BE ᠨᠢ ∠ AB D ᠶᠢ ᠲᠠᠯᠠᠯᠠᠨ ᠬᠤᠪᠢᠶ ᠠᠨ ᠠ᠂ AC ᠲᠠᠢ ᠴᠡᠭ E ᠳᠤ ᠤᠭᠲ ᠤᠯᠤᠯᠴᠠ ᠨ ᠠ᠃ ᠬᠡᠷᠪᠡ ∠ A= 50° ᠪᠣᠯ᠂ ∠ 1 ᠦ ᠨ ᠭᠷ ᠠᠳᠥ ᠰ ᠤᠨ ᠲᠣᠭ ᠠ ᠨᠢ ᠄ ( ) (1) (2) (3) (4) (5) A. 65° B. 60° C. 55° D. 50° 9. 𝑎 , b , c ᠨᠢ ᠢᠵᠢ ᠯᠢ ᠨᠢ ᠭᠡᠨ ᠬᠠᠪᠲᠠᠭ ᠠᠢ ᠳᠡ ᠭᠡᠷᠡᠬ ᠢ ᠭᠤᠷᠪ ᠠᠨ ᠰ ᠢᠯᠤᠭᠤᠨ᠂ ᠬᠡᠷᠪᠡ 𝑎 ᠪ ᠣᠯᠤᠨ b ᠨᠢ ᠵᠡ ᠷᠭᠡᠴᠡᠬ ᠦ ᠦᠭᠡᠢ ᠪᠣᠯ ᠂ b ᠪᠣᠯ ᠤᠨ c ᠨ ᠢ ᠵᠡ ᠷᠭᠡᠴᠡᠬ ᠦ ᠦᠭᠡᠢ᠂ ᠲᠡᠭᠡᠪ ᠡᠯ ᠳᠣᠣᠷ ᠠᠬᠢ ᠮᠠᠭᠠᠳᠯ ᠠᠯᠲᠠ ᠡᠴᠡ ᠵᠥ ᠪ ᠨᠢ᠄ ( ) A. 𝑎 ᠪᠣᠯᠤᠨ c ᠯᠠᠪ ᠵᠡᠷ ᠭᠡᠴᠡᠬ ᠦ ᠦᠭᠡᠢ B. 𝑎 ᠪᠣᠯᠤᠨ c ᠯᠠᠪ ᠵᠡᠷ ᠭᠡᠴᠡᠨ ᠡ C. 𝑎 ᠪᠣᠯᠤᠨ b ᠨᠢ ᠬᠠᠷᠢᠯ ᠴᠠᠨ ᠡᠭᠴᠡ D. 𝑎 ᠪᠣᠯᠤᠨ c ᠨᠢ ᠤᠭᠲᠤ ᠯᠤᠯᠴᠠᠬ ᠤ ᠪᠣᠶ ᠤ ᠵᠡ ᠷᠭᠡᠴᠡᠬ ᠦ ᠪᠣᠯ ᠤᠯᠴᠠᠭ ᠠ ᠲᠠ ᠢ 10. ᠦᠭ ᠭᠦᠭᠳᠡᠭᠰᠡ ᠨ ᠨᠢ ᠄ ᠵᠢᠷ ᠤᠭ 6 ᠮᠡ ᠲᠦ᠂ AB ∥CD ᠂ BC ᠨᠢ ∠ AB D ᠶᠢ ᠲᠠᠯᠠᠯᠠᠨ ᠬᠤᠪᠢᠶ ᠠᠨ ᠠ᠂ ∠ C= 40 °᠂ ᠲᠡᠭᠡᠪ ᠡᠯ∠ D ᠦᠨ ᠭᠷᠠᠳᠥ ᠰ ᠤᠨ ᠲᠣᠭ ᠠ ᠨᠢ ᠄ ( ) A. 40 ° B. 80 ° C. 90 ° D. 10 0° ᠬᠣᠶ ᠠᠷ᠂ ᠬᠠᠭ ᠠᠯᠲᠠ ᠳᠤ ᠲᠠᠭᠯ ᠠᠬᠤ ᠰᠡᠲᠤ ᠪ᠃ (ᠰᠡᠲᠤᠪ ᠪᠦᠷᠢ 2 ᠬ ᠤᠪᠢ᠂ ᠨᠠᠢᠲ ᠡ 18 ᠬᠤᠪᠢ ) 11. ᠵᠢᠷ ᠤᠭ 7 ᠮᠡ ᠲᠦ ᠂ ᠬᠣ ᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠣᠭᠲ ᠣᠯᠣᠯ ᠴᠠᠭᠠᠳ ᠳᠦ᠋ᠷᠪ ᠡᠨ ᠥᠨᠴᠥ ᠭ ᠡᠭᠦᠰᠬᠡᠨ ᠡ᠂ ᠦᠭ ᠭᠦᠭᠳᠡᠭᠰᠡᠨ ᠨᠢ ∠ 2 ＝3∠ 1᠂ ᠲᠡᠭᠡᠪ ᠡᠯ ∠ 4 ＝ __ __ _ 12. ᠳᠣᠣᠷ ᠠᠬᠢ ᠲᠠᠪᠤᠨ ᠨᠥᠬᠥ ᠴᠡᠯ ᠡᠴ ᠡ ᠬᠠᠷ ᠢᠯᠴᠠᠨ ᠡᠭᠴᠡ ᠪᠣᠯᠬᠤ ᠬᠤᠯ ᠪᠤᠭᠳᠠᠯ ᠢ ᠣᠯᠵ ᠤ ᠳᠡ ᠢᠯᠬᠦ ᠨᠢ᠄ __ __ __ __ ᠃ （ᠳᠤᠭᠠ ᠷ ᠢ ᠨᠢ ᠲᠠᠭᠯ ᠠ ） ① ᠮᠥᠷᠭᠥ ᠯᠳᠦᠭᠡ ᠦᠨ ᠴᠦᠭ ᠦᠨ ᠲᠠᠯᠠᠯᠠᠨ ᠬᠤᠪᠢ ᠶᠠᠭᠴᠢ ᠱᠤᠭᠤᠮ ②ᠵᠡᠷᠭ ᠡᠯᠡᠳᠡ ᠭᠡ ᠨᠥᠬᠥ ᠪᠦᠷᠢ ᠥᠨᠴ ᠥᠭ ᠤᠨ ᠲᠠᠯᠠᠯᠠᠨ ᠬᠤᠪᠢᠶ ᠠᠭᠴᠢ ᠱᠤᠭᠤ ᠮ ③ ᠵᠡᠷ ᠭᠡᠴᠡᠭᠡ ᠰᠢᠯ ᠤᠭᠤᠨ ᠤ ᠤᠭᠲᠤ ᠯᠤᠭᠳᠠᠭ ᠠᠳ ᠡᠭᠦᠰᠦᠭᠰᠡᠨ ᠨᠢ ᠭᠡ ᠪᠦᠯᠦ ᠭ ᠲᠣᠬ ᠢᠷᠠᠭᠰ ᠠᠨ ᠥᠨᠴ ᠥᠭ ᠦ ᠨ ᠲᠠ ᠯᠠᠯᠠᠨ ᠬᠤᠪᠢ ᠶᠠᠭᠴᠢ ᠱᠤᠭᠤ ᠮ ④ ᠵᠡ ᠷᠭᠡᠴᠡᠭᠡ ᠰᠢᠯᠤᠭᠤᠨ ᠤ ᠤᠭᠲᠤᠯᠤᠭᠳᠠ ᠭᠠᠳ ᠡᠭ ᠦᠰᠦᠭ ᠰᠡᠨ ᠨᠢ ᠭᠡ ᠪᠦᠯᠦ ᠭ ᠲᠣᠳ ᠣᠭᠠᠳᠣ ᠰᠣᠯ ᠪᠢᠭᠰᠠᠨ ᠦᠨᠴ ᠦᠭ ᠤᠨ ᠲᠠᠯᠠᠯᠠᠨ ᠬᠤᠪᠢᠶ ᠠᠭᠴᠢ ᠱᠤᠭᠤ ᠮ ⑤ ᠵᠡᠷ ᠭᠡᠴᠡᠭᠡ ᠰᠢᠯ ᠤᠭᠤᠨ ᠤ ᠤᠭᠲᠤᠯ ᠤᠭᠳᠠᠭ ᠠᠳ ᠡᠭᠦᠰ ᠦᠭᠰᠡᠨ ᠨᠢᠭᠡ ᠪᠦᠯᠦᠭ ᠲᠣᠲᠤᠭᠠ ᠳᠤ ᠦᠷᠦᠭᠡᠯ ᠦᠨᠴ ᠦᠭ ᠤᠨ ᠲᠠᠯ ᠠᠯᠠᠨ ᠬᠤᠪᠢᠶ ᠠᠭᠴᠢ ᠱᠤᠭᠤᠮ 13. ︽ ᠳᠣᠲᠣᠭᠠ ᠳᠤ ᠰ ᠣᠯᠪᠢᠭᠰᠠᠨ ᠥᠨᠴ ᠥᠭ ᠲᠡᠩ ᠴᠡᠭᠦᠦ ︾ ᠭᠡᠬᠦ ᠦᠭ ᠦᠯᠡᠯ ᠢ ︽ ᠬᠡ ᠷᠪᠡ ᠁ ᠪᠣᠯ ᠁ ︾ ᠭᠡᠬᠦ ᠬᠡᠯᠪᠡ ᠷᠢ ᠲᠠ ᠢ ᠪ ᠣᠯᠭᠠᠵᠤ ᠪᠢᠴᠢ᠄ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ 14. ᠵᠢᠷ ᠤᠭ 8 ᠮᠡᠲᠦ᠂ ᠭᠣᠣ ᠯ ᠦᠨ ᠤᠰᠤ ᠶᠢ ᠣᠰᠣ ᠨ ᠲᠠ ᠲᠠᠭᠠᠯ A ᠳᠦ ᠲᠠᠲᠠᠬᠤ ᠪᠠ ᠷ ᠲᠥᠯ ᠥᠪᠯᠡᠵ ᠦ ᠪ ᠠᠢᠨ ᠠ ᠂ ᠤᠷᠢᠳ ᠢᠶᠠ ᠷ AB ⊥ CD ᠡᠭ ᠴᠡ ᠶᠢᠨ ᠰᠠᠭ ᠤᠷᠢ ᠨᠢ B ᠶᠢ ᠪᠠᠢᠭ ᠤᠯᠵᠤ ᠂ ᠳᠠ ᠷᠠᠭ ᠠ ᠨᠢ A B ᠶᠢ ᠳᠠᠭ ᠠᠵᠤ ᠰᠤᠪᠠᠭ ᠨᠡᠭᠡᠭᠡᠪ ᠡᠯ ᠂ ᠨᠡᠭᠡᠭᠡᠭᠰ ᠡᠨ ᠵᠠ ᠮ ᠨᠢ ᠬᠠᠮ ᠤᠭ ᠣᠬ ᠣᠷ ᠪ ᠣᠯᠤᠨ ᠠ ᠂ ᠢᠩᠭ ᠢᠵᠦ ᠲᠥ ᠯᠥᠪᠯᠡ ᠭᠰᠡᠨ ᠦᠨ ᠳᠦᠰᠦᠯᠡᠯ ᠪᠣᠯ _ __ __ __ _ 15. ᠵᠢᠷ ᠤᠭ 9 ᠮᠡ ᠲᠦ᠂ ᠨᠢᠭᠡ ᡂᠢ ᠨᠢ ᠰᠢᠯᠤᠭᠤᠨ ᠳᠠᠭ ᠠᠤ ᠬᠤᠭ ᠤᠷᠠᠬ ᠤ ᠶᠢᠨ ᠬᠠᠮᠲᠤ ᠣᠷᠣᠨ ᠪᠠᠢᠷ ᠢ ᠨᠢ ᠵᠦ᠋ ᠷᠢᠵᠡᠢ ᠂ E ,D ,B ,F ᠨᠢ ᠨᠢᠭ ᠡ ᠰ ᠢᠯᠤᠭᠤᠨ ᠳᠡᠭᠡᠷ ᠡ ᠤᠷᠤᠰ ᠢᠨ ᠠ᠃ ᠬᠡᠷᠪᠡ ∠ DBC =50° ᠪᠣᠯ᠂ ∠ AD E ᠦ ᠨ ᠭᠷᠠᠳᠥ ᠰ ᠤᠨ ᠲᠣᠭ ᠠ ᠨᠢ ᠄ _ __ __ __ _ 16. ᠵᠢᠷ ᠤᠭ 10 ᠮᠡ ᠲᠦ᠂ ᠤᠷᠲᠤ ᠳᠥᠷᠪ ᠡᠯᠵᠢᠨ A BC D ᠳᠦ᠂ AB = 3᠂ BC = 4᠂ ᠵᠢᠷᠤᠭ ᠲᠠᠬᠢ ᠳᠥᠷᠪ ᠡᠨ ᠪᠠᠭ ᠠ ᠤᠷᠲᠤ ᠳᠥᠷᠪ ᠡᠯᠵᠢᠨ ᠦ ᠬᠦᠷ ᠢᠶᠠᠨ ᠤ ᠤᠷᠲᠤ ᠶᠢᠨ ᠨᠡᠢᠯ ᠡᠪᠦᠷᠢ ᠨᠢ᠄ __ __ __ (6) (7) (8) (9) (10) 17. ᠵᠢᠷ ᠤᠭ 11 ᠮᠡ ᠲᠦ᠂ ᠰᠣᠷᠣ ᠭᠣᠯ ᠢᠶᠠᠷ ᠲᠡ ᠮᠤᠷ ᠯᠤᠩᠬ ᠤ ᠲᠠ ᠢ ᠤᠮᠳ ᠠᠭᠠᠨ ᠢ ᠤᠤᠭᠤᠬᠤ ᠳᠤ ᠵᠢᠷᠤᠭ ᠲᠤ ᠦᠵ ᠡᠭᠦᠯᠦ ᠭᠰᠡᠨ ᠮᠡ ᠲᠦ᠂ ∠ 1= 110° ᠂ ᠲᠡᠭᠡᠪ ᠡᠯ ∠ 2= __ ___ ° （ ᠲᠡ ᠮᠦᠷ ᠯᠤᠩᠬ ᠤᠨ ᠤ ᠳᠡᠭᠡᠷ ᠡ ᠳᠣᠣᠷ ᠠ ᠲᠠ ᠯ ᠠ ᠨᠢ ᠬᠠᠷ ᠢᠯᠴᠠᠨ ᠵᠡᠷ ᠭᠡᠴᠡᠭᠡ ） 18. ᠵᠢᠷ ᠤᠭ 12 ᠮᠡᠲᠦ᠂ ᠦᠭ ᠭᠦᠭᠳᠡᠭ ᠰᠡᠨ ᠨᠢ ᠰ ᠢᠯᠤᠭᠤᠨ AB ᠶᠢ ᠵᠡᠷᠭᠡᠴᠡᠭᠡ ᠰᠢᠯᠵ ᠢᠭᠦᠯᠦ ᠭᠡᠳ ᠴᠡᠭ C ᠶᠢᠨ ᠪᠠᠢᠷ ᠢᠨ ᠳ ᠤ ᠬᠦᠷᠭᠡᠨ ᠡ᠃ ᠠᠷᠭ ᠠ 1᠄ AC ᠶᠢ ᠬᠤᠯᠪᠤᠨ ᠠ᠂ ᠳᠠᠷᠠᠭ ᠠ ᠨᠢ ᠴᠡᠭ B ᠶᠢ ᠳᠠᠭ ᠠᠷᠢᠭ ᠤᠯᠤᠨ ᠬᠡᠷᠴᠢᠮ BD ᠶᠢ ᠪᠠᠢᠭ ᠤᠯᠤᠨ ᠠ᠂ ᠬᠡᠷᠴᠢᠮ BD ᠨᠢ_ __ __ __ _ ᠶᠢ ᠬᠠᠩᠭ ᠠᠨ ᠠ᠃ CD ᠶᠢ ᠬᠣ ᠯᠪᠤᠨ ᠠ᠂ ᠲᠡᠭᠡᠪ ᠡᠯ CD ᠨᠢ ᠳᠠᠷᠦ ᠢ ᠪᠠᠢᠭ ᠤᠯᠬᠤ ᠵᠢᠷᠤᠭ ᠪᠣᠯᠤ ᠨ ᠠ᠃ ᠠᠷᠭ ᠠ 2 ᠄ ᠴᠡᠭ C ᠶᠢ ᠳᠠᠭ ᠠᠷᠢᠭ ᠤᠯᠤᠨ ᠬᠡᠷᠴᠢᠮ CD ᠶᠢ ᠪᠠᠢᠭ ᠤᠯᠤᠨ ᠠ᠂ ᠬᠡᠷᠴᠢ ᠮ CD ᠨᠢ_ __ __ __ _ᠪᠥ ᠭᠡᠳ __ __ ___ ᠶᠢ ᠬᠠᠩᠭ ᠠᠨ ᠠ᠂ ᠲᠡᠭᠡᠪ ᠡᠯ CD ᠨᠢ ᠳᠠᠷᠦ ᠢ ᠪᠠᠢᠭ ᠤᠯᠬᠤ ᠵᠢᠷ ᠤᠭ ᠪᠣᠯᠤᠨ ᠠ᠃ 19. ᠵᠢᠷ ᠤᠭ 13 ᠮᠡᠲᠦ᠂ ᠬᠡᠷ ᠪᠡ ∠ __ __ __ _ = ∠ __ __ __ _ ᠪᠣᠯ᠂ AD || BC ᠃ ᠭᠤᠷᠪ ᠠ᠂ ᠪᠣᠳᠣᠵ ᠤ ᠬᠠᠷ ᠢᠭᠤᠯ ᠬᠤ ᠰᠡ ᠲᠤᠪ᠃ ( ᠨᠠ ᠢᠲᠡ 72 ᠬᠤᠪᠢ ) 20. ( 8 ᠬᠤᠪᠢ ) ᠦᠭ ᠭᠦᠭᠳᠡᠭᠰᠡᠨ ᠨᠢ᠄ ᠵᠢᠷᠤᠭ ᠮᠡᠲᠦ᠂ BE // CD ᠂ ∠ A= ∠ 1᠃ ᠪᠠᠲᠤᠯ ᠠ᠄ ∠ C= ∠ E 21. (8 ᠬᠤᠪᠢ ) ᠵᠢᠷ ᠤᠭ ᠮᠡᠲᠦ ᠂ EF ∥CD ᠂ ∠ 1= ∠ 2᠂ ∠ ACB = 45° ᠃ ∠ DGC ᠦᠨ ᠭᠷᠠᠳᠥ ᠰ ᠤᠨ ᠲᠣᠭ ᠠ ᠶᠢ ᠣᠯ᠃ (11) (12) (13) 22. (8 ᠬᠤᠪᠢ ) ᠵᠢᠷ ᠤᠭ ᠮᠡᠲᠦ᠂ ᠦᠭ ᠭᠦᠭᠳᠡᠭᠰ ᠡᠨ ᠨᠢ ᠰᠢᠯ ᠤᠭᠤᠨ AB ᠪᠠ CD ᠨᠢ ᠴᠡᠭ O ᠳᠤ ᠤᠭᠲᠤᠯ ᠤᠯᠴᠠᠨ ᠠ᠃ ∠ CO E= 90° ᠂ OF ᠨᠢ ∠ AO E ᠶᠢ ᠲᠠᠯᠠ ᠯᠠᠨ ᠬᠤᠪᠢ ᠶᠠᠨ ᠠ᠂ ∠ CO F= 28° ᠃ ∠ BO D ᠦ ᠨ ᠭᠷ ᠠᠳᠥ ᠰ ᠤᠨ ᠲᠣᠭ ᠠ ᠶᠢ ᠣᠯ᠃ 23. (8 ᠬᠤᠪᠢ ) ᠦᠭ ᠭᠦᠭᠳᠡᠭᠰᠡ ᠨ ᠨ ᠢ᠄ ᠵᠢᠷᠤᠭ ᠮᠡᠲᠦ᠂ AB ∥CD ᠂ EF ᠨᠢ AB ᠲᠠᠢ ᠴᠡᠭ G ᠳᠤ ᠤᠭᠲᠤᠯᠤᠯ ᠴᠠᠵᠤ᠂ CD ᠲᠠᠢ ᠴᠡᠭ F ᠳᠤ ᠤᠭᠲᠤᠯ ᠤᠯᠴᠠᠨ ᠠ᠃ FH ᠨᠢ∠ EFD ᠶᠢ ᠲᠠᠯᠠᠯ ᠠᠨ ᠬᠤᠪᠢᠶ ᠠᠵᠤ᠂ AB ᠲᠠᠢ ᠴᠡᠭ H ᠲᠦ ᠤᠭᠲ ᠤᠯᠤᠯᠴᠠ ᠨ ᠠ᠃ ∠ AG E= 50° ᠂∠ BH F ᠦ ᠨ ᠭᠷᠠᠳᠥ ᠰ ᠤᠨ ᠲᠣᠭ ᠠ ᠶᠢ ᠣᠯ᠃ 24. (1 0 ᠬᠤᠪᠢ ) ᠵᠢᠷᠤᠭ ᠮᠡᠲᠦ᠂ AB ∥CD ᠂ ∠ 1= 30° ᠂ ∠ 2= 40° ᠂ ∠ EP F ᠦ ᠨ ᠶᠡᠬᠡ ᠪᠠ ᠭ ᠠ ᠶᠢ ᠣᠯ᠃ 25. (10 ᠬᠤᠪᠢ ) ᠵᠢᠷ ᠤᠭ ᠮᠡᠲᠦ᠂ ᠦᠭ ᠭᠦᠭᠳᠡᠭᠰᠡᠨ ᠨᠢ ᠄ ∠ 1= ∠ 2 ᠂ ∠ D = 50 °᠂ ∠ B ᠦ ᠨ ᠭᠷ ᠠᠳᠥ ᠰ ᠤᠨ ᠲᠣᠭ ᠠ ᠶᠢ ᠣᠯ᠃ 26. (10 ᠬᠤᠪᠢ ) ᠵᠢᠷ ᠤᠭ ᠮᠡᠲᠦ᠂ ᠨᠢᠭᠡᠨ ᠰᠠᠭ ᠤᠭᠠᠯ ᠢ ᠠ ᠷᠠᠳ ᠤᠨ ᠲᠣᠭᠣᠷ ᠢᠭ ᠲᠤ ᠨᠢᠭᠡ ᠤᠷ ᠳᠤ ᠳᠥᠷᠪ ᠡᠯᠵᠢᠨ ᠭᠠᠵᠠᠷ ᠲᠠ ᠶ ᠂ ᠰᠠᠭ ᠤᠭᠠᠯ ᠢ ᠠ ᠷᠠᠳ ᠤᠷ ᠳᠤ ᠳᠥᠷᠪ ᠡᠯᠵᠢᠨ ᠭᠠᠵᠠᠷ ᠳᠣᠲᠣᠷ ᠠ ᠠ ᠳᠠᠯᠢ ᠬᠠᠨ ᠥᠷᠭᠡ ᠨ ᠬᠣᠶ ᠠᠷ ᠵᠢᠵᠢᠭ ᠵᠠᠮ ᠵᠠᠰᠠ ᠬᠤ ᠰ ᠠᠨᠠᠭ ᠠ ᠲᠠᠶ ᠂ ᠦᠢ ᠯᠡᠳᠦ ᠭᠰᠡᠨ ᠬᠡᠰᠡᠭ ᠢ ᠨᠢ ᠨᠤᠭ ᠤᠷᠠᠭ ᠤᠯᠤᠨ ᠠ᠂ ᠵᠠᠮ ᠤ ᠨ ᠥᠷᠭᠡᠨ ᠨᠢ 2 ᠮᠧᠲᠷ ᠂ ᠨᠣᠭᠣᠭ ᠠᠷᠠᠭ ᠤᠯᠤᠭᠰ ᠠᠨ ᠲ ᠠᠯᠠᠪᠠ ᠢ ᠨᠢ ᠬᠡᠳ ᠦᠢ ᠪ ᠣᠶ︖ 27. (10 ᠬᠤᠪᠢ ) ᠵᠢᠷ ᠤᠭ ᠮᠡᠲᠦ᠂ ᠲᠡᠭ ᠰᠢ ᠳᠥᠷᠪ ᠡᠯᠵᠢᠨ ᠳᠥᠷᠪ ᠡᠯᠵᠢᠯ ᠡᠭᠡᠰᠦ ᠳᠣᠲᠣᠷ ᠠ ᠂ ᠵᠢᠵᠢᠭ ᠲᠡᠭᠰᠢ ᠳᠥᠷ ᠪᠡᠯᠵ ᠢᠨ ᠨᠢᠭᠡᠪᠦᠷ ᠢ ᠶᠢᠨ ᠲᠠᠯ ᠠ ᠶᠢᠨ ᠤᠷ ᠳᠤ ᠨᠢ ᠴᠥ ᠮ 1 ᠪᠣᠯ ᠤᠨ ᠠ ᠂ △ ABC ᠵᠢᠨ ᠭᠤᠷᠪ ᠠᠨ ᠣᠷᠣᠢ ᠶᠢᠨ ᠴᠡᠭ ᠤᠨ ᠪᠠᠢᠷ ᠢ ᠨᠢ ᠵᠢᠷ ᠤᠭ ᠮᠡᠲᠦ ᠂ △ AB C ᠶᠢ ᠨᠢᠭᠡ ᠤᠳᠠ ᠭ ᠠ ᠵᠡᠷ ᠭᠡᠴᠡᠭᠡ ᠰᠢᠯᠵ ᠢᠭᠦᠯᠦ ᠭᠰᠡᠨ ᠦ ᠳᠠ ᠷᠠᠭ ᠠ △ A′B ′C′ ᠶᠢ ᠣᠯᠤᠨ ᠠ ᠂ ᠵᠢᠷ ᠤᠭ ᠲᠤ B ᠴᠡᠭ ᠤᠨ ᠬᠠᠷᠠᠭ ᠠᠯᠵᠠᠭᠰᠠᠨ ᠴᠡᠭ B′ ᠶᠢ ᠲᠡᠮᠳᠡ ᠭᠯᠡᠭᠰᠡᠨ ᠪᠠᠢᠨ ᠠ ᠃ ᠳᠥᠷᠪ ᠡᠯᠵᠢᠯ ᠡᠭᠡᠰᠦ ᠲᠤ ᠵᠢᠷ ᠤᠭ ᠤᠨ ᠴᠡᠭ ᠢ ᠠ ᠰᠢᠭᠯ ᠠᠨ ᠵᠢᠷ ᠤᠭ ᠵᠢᠷᠤᠬ ᠤ ᠄ (1) ∆A′B ′C′ ᠶᠢ ᠵᠢᠷᠤᠨ ᠠ᠃ (2) AB ᠲᠠᠯ ᠠ ᠳᠡ ᠭᠡᠷᠡᠬ ᠢ ᠳᠤᠮ ᠳᠠ ᠱ ᠤᠭᠤᠮ CD ᠶᠢ ᠵᠢᠷᠤᠨ ᠠ᠃ (3) BC ᠲᠠᠯ ᠠ ᠳᠡ ᠭᠡᠷᠡᠬ ᠢ ᠦᠨᠳᠦ ᠷ AE ᠶᠢ ᠵᠢᠷᠤᠨ ᠠ᠃ (4) ∆A′B ′C′ ᠦᠨ ᠲᠠᠯ ᠠᠪᠠᠢ ᠨᠢ᠄ __ __ __ __ ᠃