ᠴᠢᠪᠠᠭ᠎ᠠ ᠮᠤᠩᠭᠤᠯ ᠦᠨᠳᠦᠰᠦᠲᠡᠨ ᠤ ᠲᠤᠮᠳᠠᠳᠤ ᠰᠤᠷᠭᠠᠭᠤᠯᠢ — ᠲᠤᠭᠠᠨ ᠪ᠊ ᠤᠬᠠᠭᠠᠨ — ᠨᠠᠢᠮᠠᠨ ᠤᠨ — ᠳᠤᠤᠷᠠᠳᠤ — — ᠦᠷᠴᠠᠶᠢᠬᠤ — ᠲᠡᠭᠰᠢ ᠳᠦᠷᠪᠡᠯᠵᠢᠨ

ᠨᠠᠢ᠍ᠮᠠᠳᠤᠭᠠᠷ ᠣᠨ （ ᠲᠤᠤᠷᠠᠳᠤ ᠲᠡᠪᠳᠡᠷ ）,ᠠᠯᠪᠠᠨ ᠵᠢᠷᠤᠮ ᠤᠨ ᠰᠤᠷᠭᠠᠨ ᠭᠦᠮᠦᠵᠢᠯ ᠦᠨ ᠰᠤᠷᠬᠤ ᠪᠢᠴᠢᠭ᠌,ᠲᠣᠭᠠᠨ ᠤ ᠤᠬᠠᠭᠠᠨ,ᠠᠷᠤ ᠬᠣᠷᠴᠢᠨ ᠬᠣᠰᠢᠭᠤᠨ ᠤ᠋ ᠴᠢᠪᠠᠭ᠎ᠠ ᠮᠣᠩᠭᠤᠯ ᠦᠨᠳᠦᠰᠦᠲᠡᠨ ᠤ᠋ ᠳᠤᠮᠳᠠᠳᠤ ᠰᠤᠷᠭᠠᠭᠤᠯᠢ ᠦᠷᠴᠠᠢᠬᠤ,ᠲᠡᠭᠰᠢ ᠲᠦᠷᠪᠡᠯᠵᠢᠨ,18.2.3,,,ᠲᠦᠷᠪᠡᠯᠵᠢᠨ ᠲᠡᠭᠰᠢ,,〃,〃,,〃,〃,,,ᠲᠡᠨᠭᠴᠡᠭᠦᠦ ᠲᠠᠯ᠎ᠠ ᠨᠢ ᠵᠡᠷᠭᠡᠯᠡᠳᠡᠭᠡ,ᠨᠢ 𝟗𝟎° ᠨᠢᠬᠡ ᠦᠨᠴᠦᠭ,ᠲᠡᠭᠰᠢ ᠳᠦᠷᠪᠡᠯᠵᠢᠨ ‍ ‍ᠣ ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ ᠄,𝐴𝐵=𝐴𝐷=𝐵𝐶=𝐷𝐶,ᠠᠳᠠᠯᠢ ᠬᠠᠵᠠᠭᠤᠳᠤ ᠲᠡᠭᠰᠢ ᠦᠨᠴᠦᠭᠳᠦ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ,ᠲᠠᠯ᠎ᠠ,ᠦᠨᠴᠦᠭ,ᠳᠠᠰᠢᠭᠤᠪᠴᠢ,𝐴𝐶=𝐵𝐷, 𝐴𝐶⊥𝐵𝐷, AO=BO=CO=DO,∠𝐴𝐵𝐶=∠𝐵𝐶𝐷 =∠𝐶𝐷𝐴=∠𝐷𝐴𝐵= 90 °,2.ᠲᠡᠭᠰᠢ ᠬᠡᠮᠳᠦ ᠴᠢᠨᠠᠷ ᠄,(A),(B),(C),(D),,,,,ᠲᠡᠩᠭᠡᠯᠢᠭ ᠲᠦ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠳᠦ ᠵᠢᠷᠤᠭ ᠲᠦᠷᠰᠦ ᠮᠦᠨ ᠃,ᠲᠦᠷᠪᠡᠨ ᠵᠤᠷᠪᠤᠰ ᠲᠡᠭᠰᠢ ᠬᠡᠮ ᠦᠨ ᠲᠡᠩᠭᠡᠯᠢᠭ᠌ ᠲᠠᠢ ᠃,,,,ᠵᠢᠰᠢᠬᠦᠯᠵᠢᠨ,ᠦᠨᠴᠦᠭᠳᠦ ᠲᠡᠭᠰᠢ,ᠷᠤᠮᠪ,ᠵᠢᠰᠢᠬᠦᠯᠵᠢᠨ ᠶᠠᠮᠠᠷ ᠬᠤᠯᠪᠤᠠᠠᠳᠠᠯ ᠲᠠᠢ ᠪᠤᠢ ︖ ᠲᠡᠭᠰᠢ ᠲᠦᠷᠪᠡᠯᠵᠢᠨ ᠂ ᠷᠤᠮᠪ ᠂ ᠲᠡᠭᠰᠢ ᠦᠨᠴᠦᠭᠳᠦ ᠂,ᠲᠦᠷᠪᠡᠯᠵᠢᠨ ᠲᠡᠭᠰᠢ,ᠷᠤᠮᠪ ᠪᠦᠬᠡᠳ ᠲᠡᠭᠰᠢ ᠦᠨᠴᠦᠭᠳᠦ,,ᠵᠡᠷᠭᠡᠴᠡᠭᠡ ᠨᠢ ᠲᠤᠰ ᠲᠤᠰ ᠡᠰᠡᠷᠭᠦ ᠲᠠᠯ᠎ᠠ ᠬᠤᠶᠠᠷ ᠬᠤᠤᠰ,,,ᠲᠡᠨᠭᠴᠡᠭᠦᠦ ᠲᠠᠯ᠎ᠠ ᠨᠢ ᠵᠡᠷᠭᠡᠯᠡᠳᠡᠭᠡ ᠨᠢᠬᠡ ᠬᠤᠤᠰ,,,ᠲᠦᠷᠪᠡᠯᠵᠢᠨ ᠲᠡᠭᠰᠢ,ᠨᠢᠬᠡ ᠦᠨᠴᠦᠭ ᠨᠢ ᠲᠡᠭᠰᠢ ᠦᠨᠴᠦᠭ,,ᠲᠡᠨᠭᠴᠡᠭᠦᠦ ᠲᠠᠯ᠎ᠠ ᠨᠢ ᠵᠡᠷᠭᠡᠯᠡᠳᠡᠭᠡ,ᠨᠢᠬᠡ ᠦᠨᠴᠦᠭ ᠨᠢ ᠲᠡᠭᠰᠢ ᠦᠨᠴᠦᠭ,ᠲᠡᠭᠰᠢ ᠳᠦᠷᠪᠡᠯᠵᠢᠨ ‍ᠣ ᠮᠠᠭᠠᠳᠯᠠᠯᠲᠠ,ᠬᠤᠪᠢᠶᠠᠨ᠎ᠠ ᠃ ᠲᠦᠷᠪᠡᠨ ᠪᠦᠷᠢᠨ ᠲᠡᠨᠭᠴᠡᠭᠦᠦ ᠠᠳᠠᠯᠢ ᠬᠠᠵᠠᠭᠤᠳᠤ ᠲᠡᠭᠰᠢ ᠦᠨᠴᠦᠭᠳᠦ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᠪᠤᠯᠭᠠᠨ ᠪᠠᠲᠤᠯᠠ ᠄ ᠲᠡᠭᠰᠢ ᠲᠦᠷᠪᠡᠯᠵᠢᠨ ᠦ ᠬᠤᠶᠠᠷ ᠲᠠᠰᠢᠭᠤᠪᠴᠢ ᠨᠢᠡᠨᠡ ᠲᠡᠭᠰᠢ ᠲᠦᠷᠪᠡᠯᠵᠢᠨ ᠢ,ᠵᠢᠱᠢᠶ᠎ᠡ5:,,A,D,C,B,,,O,ᠨᠢ O ᠳᠦ ᠤᠠᠠᠳᠤᠯᠤᠯᠴᠠᠨ᠎ᠠ᠂ ABCD ᠂ ᠲᠠᠰᠢᠭᠤᠪᠴᠢ AC,BD ᠦᠭ᠍ᠬᠦᠭ᠍ᠳ᠋ᠡᠭ᠍ᠰᠡᠨ ᠨᠢ ᠄ ᠲᠡᠭᠰᠢ ᠲᠦᠷᠪᠡᠯᠵᠢᠨ,ᠠᠳᠠᠯᠢ ᠬᠠᠵᠠᠭᠤᠳᠤ ᠲᠡᠭᠰᠢ ᠦᠨᠴᠦᠭᠳᠦ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ∆CDO,∆∆DAO ᠪᠦᠷᠢᠨ ᠲᠡᠨᠭᠴᠡᠭᠦᠦ ᠪᠠᠳᠤᠯᠠᠠᠠᠳᠠᠬᠤ ᠨᠢ ᠄ ∆ABO,∆BCO,,ᠪᠠᠳᠤᠯᠠᠬᠤ ᠨᠢ ᠄,∴𝐴𝐶=𝐵𝐷, 𝐴𝐶⊥𝐵𝐷, AO=BO=CO=DO,∆ABO, ∆BCO, ∆CDO, ∆∆DAO ᠪᠦᠷᠢᠨ ᠲᠡᠨᠭᠴᠡᠭᠦᠦ ᠠᠳᠠᠯᠢ ᠬᠠᠵᠠᠭᠤᠳᠤ ᠲᠡᠭᠰᠢ ᠦᠨᠴᠦᠭᠳᠦ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ,∆ABO≅∆BCO ≅∆CDO≅∆DAO,A,B,D,,,E,,〃,〃,,∟,F,,ᠬᠠᠢᠴᠢᠯᠠᠨ᠎ᠠ,,E,ᠪᠠᠳᠤᠳᠬᠠᠯ᠄,ᠴᠠᠭᠠᠰᠤ ᠶᠢ ᠡᠰᠭᠡᠭᠡᠳ ᠭᠠᠷᠭᠠᠴᠢᠬᠠᠨ᠎ᠠ ᠂ ᠶᠠᠭᠠᠬᠢᠭᠠᠳ ︖ ᠦᠵᠡᠭᠦᠯᠦᠭᠰᠡᠨ ᠮᠡᠳᠦ ᠪᠡᠷ ᠨᠤᠭᠤᠯᠪᠠᠯ ᠂ᠲᠡᠭᠰᠢ ᠲᠦᠷᠪᠡᠯᠵᠢᠨ 1. (1) ᠨᠢᠬᠡᠨ ᠤᠷᠳᠤ ᠲᠦᠷᠪᠡᠯᠵᠢᠨ ᠴᠠᠭᠠᠰᠤ ᠶᠢ ᠵᠢᠷᠤᠭ ᠲᠤ,ᠦᠨᠴᠦᠭᠳᠦ ᠲᠡᠭᠰᠢ ᠪᠤᠯᠬᠤ ᠲᠡᠨᠭᠴᠡᠭᠦᠦ ᠲᠠᠯ᠎ᠠ ᠨᠢ ᠵᠡᠷᠭᠡᠯᠡᠳᠡᠭᠡ,ᠬᠠᠪᠳᠠᠰᠤ ᠶᠢ ᠬᠡᠷᠭᠢᠨ ᠤᠠᠠᠳᠤᠯᠵᠤ ᠤᠯᠬᠤ ᠪᠤᠢ ︖ ᠡᠴᠡ ᠨᠢᠬᠡᠨ ᠬᠠᠮᠤᠭ ᠦᠨ ᠶᠡᠭᠡ ᠲᠡᠭᠰᠢ ᠲᠦᠷᠪᠡᠯᠵᠢᠨ ᠮᠤᠳᠤᠨ (2) ᠨᠢᠬᠡᠨ ᠤᠷᠳᠤ ᠲᠦᠷᠪᠡᠯᠵᠢᠨ ᠮᠤᠳᠤᠨ ᠬᠠᠪᠳᠠᠰᠤ,E,,,D,C,B,∟,,∟,A,ᠪᠤᠢ ︖ ᠦᠨ ᠲᠠᠯᠠᠪᠠᠢ ᠪᠠ ᠲᠠᠰᠢᠭᠤᠪᠴᠢ ᠶᠢᠨ ᠤᠷᠳᠤ ᠨᠢ ᠲᠤᠰ ᠲᠤᠰ ᠭᠡᠳᠦᠢ EB=10m ᠪᠤᠯᠬᠤ ᠶᠢ ᠬᠡᠮᠵᠢᠵᠤ ᠤᠯᠪᠠ ᠃ ᠡᠨᠡ ᠲᠠᠯᠠᠪᠤᠷ ᠲᠠᠯ᠎ᠠ ᠳᠡᠭᠡᠷ᠎ᠡ ᠨᠢᠬᠡᠨ ᠴᠡᠭ E ᠶᠢ ᠠᠪᠤᠭᠠᠳ ᠂ EC=30m ᠬᠡᠯᠪᠡᠷᠢ ᠲᠠᠢ ᠲᠠᠯᠠᠪᠤᠷ ᠪᠣᠯᠤᠨ᠎ᠠ ᠂ ᠰᠡᠷᠭᠦᠯᠡᠩ ᠪᠤᠯᠤᠨ ᠨᠠᠷᠠᠨ AB 2. ᠵᠢᠷᠤᠭ ᠮᠡᠳᠦ ᠂ ABCD ᠨᠢ ᠨᠢᠬᠡᠨ ᠲᠡᠭᠰᠢ ᠲᠦᠷᠪᠡᠯᠵᠢᠨ,ᠲᠡᠭᠰᠢ ᠲᠦᠷᠪᠡᠯᠵᠢᠨ ᠮᠦᠨ ᠦᠦ ︖ ᠶᠠᠭᠠᠬᠢᠭᠠᠳ ︖ 2. ᠲᠤᠤᠷᠠᠭᠢ ᠨᠦᠬᠦᠴᠡᠯ ᠨᠤᠭᠤᠳ ᠢ ᠬᠠᠨᠭᠭᠠᠬᠤ ᠲᠦᠷᠪᠡᠯᠵᠢᠨ ᠨᠢ,ᠲᠡᠨᠭᠴᠡᠭᠦᠦ ᠪᠤᠯᠬᠤ ᠲᠦᠷᠪᠡᠯᠵᠢᠨ ᠃ (4) ᠲᠠᠰᠢᠭᠤᠪᠴᠢ ᠨᠢ ᠬᠠᠷᠢᠯᠴᠠᠨ ᠡᠭᠴᠡ ᠲᠠᠯᠠᠯᠠᠨ ᠬᠤᠪᠢᠶᠠᠬᠤ ᠪᠦᠬᠡᠳ (3) ᠲᠠᠰᠢᠭᠤᠪᠴᠢ ᠨᠢ ᠲᠡᠨᠭᠴᠡᠭᠦᠦ ᠪᠤᠯᠬᠤ ᠷᠤᠮᠪ ᠃ (2) ᠲᠠᠰᠢᠭᠤᠪᠴᠢ ᠨᠢ ᠬᠠᠷᠢᠯᠴᠠᠨ ᠡᠭᠴᠡ ᠪᠤᠯᠬᠤ ᠲᠡᠭᠰᠢ ᠦᠨᠴᠦᠭᠳᠦ ᠃ ᠵᠢᠰᠢᠬᠦᠯᠵᠢᠨ ᠃ (1)ᠲᠠᠰᠢᠭᠤᠪᠴᠢ ᠨᠢ ᠬᠠᠷᠢᠯᠴᠠᠨ ᠡᠭᠴᠡ ᠪᠦᠬᠡᠳ ᠲᠡᠨᠭᠴᠡᠭᠦᠦ ᠪᠤᠯᠬᠤ,ᠦᠷᠭᠡᠳᠭᠡᠯ ᠪᠤᠯᠪᠠᠰᠤᠷᠠᠯ ᠄,ᠬᠠᠮᠤᠭ ᠪᠠᠭ᠎ᠠ ᠬᠡᠮᠵᠢᠭᠳᠡᠯ ᠢ ᠤᠯ ᠃ P ᠪᠤᠯ AC ᠲᠡᠭᠡᠷᠡᠭᠢ ᠬᠦᠳᠡᠯᠬᠦ ᠴᠡᠭ ᠂ PE+PB ᠶᠢᠨ E ᠪᠤᠯ ᠲᠠᠯ᠎ᠠ BC ᠲᠡᠭᠡᠷᠡᠭᠢ ᠨᠢᠬᠡ ᠴᠡᠭ ᠂ BE=1, ᠲᠡᠭᠰᠢ ᠲᠦᠷᠪᠡᠯᠵᠢᠨ ABCD ᠶᠢᠨ ᠲᠠᠯ᠎ᠠ ᠶᠢᠨ ᠤᠷᠳᠤ ᠨᠢ 4,,P,∵𝐴𝐶⊥𝐵𝐷, BO=DO,O,∴𝑃𝐵=𝑃𝐷,PE+PB =PE+PD =DE,ᠳ᠋ᠦ᠋ᠩᠨ᠋ᠡᠯᠳ᠋ᠡ ᠄,1. ᠲᠡᠭᠰᠢ ᠲᠦᠷᠪᠡᠯᠵᠢᠨ ᠦ ᠲᠤᠳᠤᠷᠬᠠᠢᠢᠯᠳᠠ ᠄,ᠭᠡᠨ᠎ᠡ ᠃ ᠦᠨᠴᠦᠭ ᠨᠢ 90° ᠪᠤᠯᠬᠤ ᠵᠢᠰᠢᠬᠦᠯᠵᠢᠨ ᠢ ᠲᠡᠭᠰᠢ ᠲᠦᠷᠪᠡᠯᠵᠢᠨ ᠨᠢᠬᠡ ᠬᠤᠤᠰ ᠵᠡᠷᠭᠡᠯᠡᠳᠡᠭᠡ ᠲᠠᠯ᠎ᠠ ᠨᠢ ᠲᠡᠨᠭᠴᠡᠭᠦᠦ ᠪᠦᠬᠡᠳ ᠨᠢᠬᠡ,2.ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ ᠄,ᠡᠰᠡᠷᠭᠦ ᠲᠠᠯ᠎ᠠ ᠨᠢ ᠵᠡᠷᠭᠡᠴᠡᠭᠡ ᠂ ᠲᠦᠷᠪᠡᠨ ᠲᠠᠯ᠎ᠠ ᠨᠢ ᠲᠡᠨᠭᠴᠡᠭᠦᠦ ᠃,ᠡᠰᠡᠷᠭᠦ ᠦᠨᠴᠦᠭ ᠨᠢ ᠲᠡᠭᠰᠢ ᠦᠨᠴᠦᠭ ᠃,ᠬᠤᠪᠢᠶᠠᠬᠤ ᠪᠦᠬᠡᠳ ᠡᠰᠡᠷᠭᠦ ᠦᠨᠴᠦᠭ ᠢᠡᠨ ᠲᠠᠯᠠᠯᠠᠨ ᠬᠤᠪᠢᠶᠠᠨ᠎ᠠ ᠃ ᠲᠠᠰᠢᠭᠤᠪᠴᠢ ᠨᠢ ᠲᠡᠨᠭᠴᠡᠭᠦᠦ ᠂ ᠬᠠᠷᠢᠯᠴᠠᠨ ᠡᠭᠴᠡ ᠲᠠᠯᠠᠯᠠᠨ,