ᠲᠣᠭᠠᠨ ᠤ ᠤᠬᠠᠭᠠᠨ ᠤ ᠶᠢᠰᠦᠳᠦᠭᠡᠷ ᠣᠨ ᠤ 23.2.1 ᠲᠥᠪ ᠲᠤ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠳᠤ 中心对称.pptx
23.2.1 ᠲᠦᠪ ᠲᠤ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠳᠦ ,,,,, ᠡᠷᠬᠢᠯᠲᠠ ᠶᠢᠨ ᠬᠠᠮᠢᠶᠠ ᠪᠦᠬᠦᠢ ᠤᠬᠠᠭᠳᠠᠬᠤᠨ ,,, ᠬᠠᠷᠠᠭᠠᠯᠵᠠᠭᠰᠠᠨ ᠴᠡᠭ ᠠᠴᠠ ᠡᠷᠭᠢᠯᠲᠡ ᠶᠢᠨ ᠲᠥᠪ ᠬᠦᠷᠬᠦ ᠵᠠᠢ ᠨᠢ ᠬᠠᠷᠢᠯᠴᠠᠨ ᠲᠡᠩᠴᠡᠭᠦᠦ᠃ , ᠬᠠᠷᠠᠭᠠᠯᠵᠠᠭᠰᠠᠨ ᠴᠡᠭ ᠪᠤᠯᠤᠨ ᠡᠷᠭᠢᠯᠲᠡ ᠶᠢᠨ ᠲᠥᠪ ᠢ ᠬᠤᠯᠪᠤᠭᠰᠠᠨ ᠬᠡᠷᠴᠢᠮ ᠦᠨ ᠬᠠᠪᠴᠢᠭᠰᠠᠨ ᠥᠨᠴᠦᠭ ᠨᠢ ᠡᠷᠭᠢᠯᠲᠡ ᠶᠢᠨ ᠥᠨᠴᠦᠭ ᠲᠠᠢ ᠲᠡᠩᠴᠡᠭᠦᠦ᠃ ,23.1 ᠵᠢᠷᠤᠭ ᠳᠦᠷᠰᠤ ᠶᠢᠨ ᠡᠷᠬᠢᠯᠲᠠ , ᠡᠷᠬᠢᠯᠲᠠ ᠶᠢᠨ ᠲᠥᠪ , ᠡᠷᠬᠢᠯᠲᠠ ᠶᠢᠨ ᠥᠨᠴᠦᠭ ,, ᠬᠠᠷᠭᠠᠯᠵᠡᠬᠰᠡ ᠴᠡᠭ , ᠡᠷᠬᠢᠯᠲᠠ ᠶᠢᠨ ᠰᠢᠡᠵᠢ ᠴᠢᠨᠠᠷ , ᠡᠷᠭᠢᠯᠲᠡ ᠠᠴᠠ ᠡᠮᠦᠨᠡᠬᠢ ᠬᠤᠢᠨᠠᠬᠢ ᠵᠢᠷᠤᠭ ᠳᠦᠷᠰᠦ ᠨᠢ ᠪᠦᠷᠢᠨ ᠲᠡᠩᠴᠡᠭᠦᠦ᠃ , ᠡᠷᠭᠢᠯᠲᠡ ᠶᠢᠨ ᠦᠨᠳᠦᠰᠤᠨ ᠨᠥᠬᠦᠴᠡᠯ ,,,, ᠡᠷᠬᠢᠯᠲᠠ ᠶᠢᠨ ᠥᠨᠴᠦᠭ , ᠡᠷᠬᠢᠯᠲᠠ ᠶᠢᠨ ᠲᠥᠪ , ᠡᠷᠭᠢᠯᠲᠡ ᠶᠢᠨ ᠴᠢᠭᠡᠯᠯ , ᠡᠷᠭᠢᠴᠡᠭᠦᠯᠦᠯ᠄ , ᠡᠷᠭᠢᠯᠲᠡ᠄ ᠨᠢᠭᠡᠨ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠶᠢᠨ ᠵᠢᠷᠤᠭ ᠳᠦᠷᠰᠦ ᠶᠢ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠳᠡᠭᠡᠷᠡᠬᠢ ᠨᠢᠭᠡᠨ ᠴᠡᠭ ᠢ ᠲᠣᠭᠤᠷᠢᠭᠤᠯᠤᠨ ᠨᠢᠭᠡᠨ ᠥᠨᠴᠦᠭ ᠡᠷᠭᠢᠭᠦᠯᠬᠦ ᠶᠢ ᠵᠢᠷᠤᠭ ᠳᠦᠷᠰᠦ ᠶᠢᠨ ᠡᠷᠭᠢᠯᠲᠡ ᠭᠡᠨᠡ᠃ , ᠰᠤᠷᠬᠤ ᠬᠠᠷᠠᠯᠲᠠ᠄ 1. ᠲᠦ᠋ᠪ ᠲᠣ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠳᠤ ᠶᠢᠨ ᠤᠬᠠᠭᠳᠠᠬᠤᠨ ᠪᠠ ᠲᠦ᠋ᠪ ᠲᠣ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠲᠦ ᠶᠢᠨ ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ ᠢ ᠡᠵᠡᠮᠰᠢᠨᠡ᠃ 2. ᠦᠭᠭᠦᠭᠳᠡᠭᠰᠡᠨ ᠵᠢᠷᠤᠭ ᠲᠦ᠋ᠷᠰᠦ ᠶᠢᠨ ᠦᠭᠭᠦᠭᠳᠡᠭᠰᠡᠨ ᠴᠡᠭ ᠤᠨ ᠬᠤᠪᠢ ᠳᠠᠬᠢ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠲᠦ ᠵᠢᠷᠤᠭ ᠲᠦ᠋ᠷᠰᠦ ᠶᠢ ᠪᠠᠢᠭᠤᠯᠵᠦ ᠴᠢᠳᠠᠨᠠ᠃ ,,𝑨 𝟏,𝑨 ∙,,B,∙,𝑪,D,,∙,𝑪 𝟏,∙,,𝑫 𝟏,●,,O,,B,𝐶,𝐷,𝐸,𝐹,𝐺, ᠳᠣᠣᠷᠠᠬᠢ ᠵᠢᠷᠤᠭ ᠳᠦ᠋ᠷᠰᠦ ᠶᠢ ᠴᠡᠭ 𝑂 ᠶᠢ ᠲᠣᠭᠤᠷᠢᠭᠤᠯᠣᠨ 180 0 ᠡᠷᠭᠢᠭᠦᠯᠬᠦ ᠲᠤ ᠲᠠ ᠶᠠᠭᠤ ᠣᠯᠵᠦ ᠮᠡᠳᠡᠬᠦ ᠪᠣᠢ︖ ,, ︵1︶ ᠵᠢᠷᠤᠭ ᠮᠡᠳᠤ᠂ ᠲᠡᠬᠦᠨ ᠳᠠᠬᠢ ᠨᠢᠭᠡ ᠬᠡ ᠵᠢᠷᠤᠭ ᠢ ᠴᠡᠭ O ᠶᠢ ᠲᠤᠭᠤᠷᠢᠭᠤᠯᠤᠨ 1800 ᠡᠷᠬᠢᠬᠦᠯᠪᠡᠯ᠂ ᠲᠠ ᠶᠠᠭᠤ ᠶᠢ ᠤᠯᠵᠦ ᠮᠡᠳᠡᠬᠦ ᠪᠤᠢ︖ ,O, ᠬᠤᠶᠠᠷ ᠵᠢᠷᠤᠭ ᠲᠦᠷᠰᠦ ᠨᠢ ᠪᠦᠷᠢᠮᠦᠰᠦᠨ ᠲᠠᠪᠬᠤᠴᠠᠨᠠ , ᠰᠡᠳᠭᠢᠬᠦ 1᠄ ,,,A,B,D,C,O, ︵2︶ ᠵᠢᠷᠤᠭ ᠮᠡᠳᠤ᠂ ᠬᠡᠷᠴᠢᠮ 𝐴𝐶,𝐵𝐷 ᠨᠢ ᠴᠡᠭ O ᠲᠤ ᠤᠭᠳᠤᠯᠤᠯᠴᠠᠨᠠ᠂ 𝑂𝐴=𝑂𝐶,𝑂𝐵=𝑂𝐷. ∆𝐶𝑂𝐷 ᠶᠢ ᠴᠡᠭ O ᠶᠢ ᠲᠤᠭᠤᠷᠢᠭᠤᠯᠤᠨ 180° ᠡᠷᠬᠢᠬᠦᠯᠪᠡᠯ᠂ ᠲᠠ ᠶᠠᠭᠤ ᠤᠯᠵᠤ ᠮᠡᠳᠡᠬᠦ ᠪᠤᠢ︖ ,∆𝐴𝑂𝐵≅∆𝐶𝑂𝐷, ᠤᠨᠴᠠᠭᠠᠢ ᠡᠷᠬᠢᠯᠳᠡ , ᠬᠤᠶᠠᠷ ᠵᠢᠷᠤᠭ ᠲᠦᠷᠰᠦ ᠨᠢ ᠪᠦᠷᠢᠮᠦᠰᠦᠨ ᠲᠠᠪᠬᠤᠴᠠᠨᠠ , ︵ᠴᠡᠭ O︶ , ︵1800︶ , ︵ᠳᠠᠪᠬᠤᠴᠠᠨᠠ︶ , ᠲᠡᠭᠡᠷᠡᠬᠢ ᠬᠤᠶᠠᠷ ᠡᠷᠭᠢᠯᠳᠡ ᠲᠠᠬᠢ ᠨᠡᠢᠲᠡᠯᠢᠭ ᠲᠠᠯᠠ ᠶᠢ ᠮᠡᠳᠡᠨᠡ ᠤᠤ︖ ᠵᠢᠷᠤᠭ ᠲᠦᠷᠰᠤ ᠲᠠᠬᠢ ᠡᠷᠬᠢᠯᠳᠡ ᠶᠢᠨ ᠲᠦᠪ ᠨᠢ ᠠᠯᠢ ᠴᠡᠭ ᠪᠤᠢ︖ ︵2︶ ᠡᠷᠭᠢᠯᠳᠡ ᠶᠢᠨ ᠦᠨᠴᠦᠭ ᠨᠢ ᠬᠡᠳᠦᠢ ᠶᠡᠭᠡ ᠪᠤᠢ︖ ︵3︶ ᠡᠷᠭᠢᠭᠰᠡᠨ ᠦ ᠰᠡᠭᠦᠯᠡᠷ ᠬᠤᠶᠠᠷ ᠵᠢᠷᠤᠭ ᠲᠦᠷᠰᠤ ᠨᠢ ᠶᠠᠮᠠᠷ ᠬᠤᠯᠪᠤᠭᠳᠠᠯ ᠲᠠᠢ ᠪᠤᠢ︖ , ᠨᠢᠭᠡ ᠵᠢᠷᠤᠭ ᠲᠦᠷᠰᠤ ᠶᠢ ᠨᠢᠭᠡᠨ ᠴᠡᠭ ᠢ ᠲᠤᠭᠤᠷᠢᠭᠤᠯᠤᠨ 1800 ᠡᠷᠭᠢᠭᠦᠯᠬᠦ ᠲᠤ ᠬᠡᠷᠪᠡ ᠲᠡᠷᠡ ᠨᠢ ᠨᠦᠬᠦᠭᠡ ᠨᠢᠭᠡ ᠵᠢᠷᠤᠭ ᠲᠦᠷᠰᠤ ᠲᠠᠢ ᠪᠠᠨ ᠲᠠᠪᠬᠤᠴᠠᠪᠠᠯ᠂ ᠡᠨᠡ ᠬᠤᠶᠠᠷ ᠵᠢᠷᠤᠭ ᠲᠦᠷᠰᠤ ᠶᠢ ᠡᠨᠡ ᠴᠡᠭ ᠦᠨ ᠬᠤᠪᠢ ᠲᠤ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠳᠡᠢ ᠪᠤᠶᠤ ᠲᠦᠪ ᠲᠤ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠳᠤ ᠭᠡᠵᠤ᠂ ᠡᠨᠡ ᠴᠡᠭ ᠢ ᠲᠡᠭᠰᠢ ᠬᠡᠮ ᠤᠨ ᠲᠦᠪ ᠭᠡᠨᠡ᠃ ᠡᠨᠡ ᠬᠤᠶᠠᠷ ᠵᠢᠷᠤᠭ ᠲᠦᠷᠰᠤ ᠶᠢ ᠡᠷᠭᠢᠬᠦᠯᠦᠭᠰᠡᠨ ᠦ ᠳᠠᠷᠠᠭᠠ ᠲᠠᠪᠬᠤᠴᠠᠬᠤ ᠬᠠᠷᠠᠭᠠᠯᠵᠠᠭᠰᠠᠨ ᠴᠡᠭ ᠢ ᠲᠡᠭᠰᠢ ᠭᠡᠮ ᠦᠨ ᠲᠥᠪ ᠦᠨ ᠬᠤᠪᠢ ᠲᠠᠬᠢ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠳᠤ ᠴᠡᠭ ᠭᠡᠨᠡ᠃ ,1. ᠲᠦᠪ ᠲᠣ ᠲᠡᠭᠰᠢ ᠭᠡᠮᠲᠦ ᠶᠢᠨ ᠲᠤᠳᠤᠷᠬᠠᠢᠯᠠᠯᠳᠠ :, ᠪᠣᠯᠪᠠᠰᠤᠷᠠᠯ᠄ ,⑴ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ABC ᠶᠢ ᠵᠢᠷᠤᠨᠠ᠃ ,C,A,B,C＇,A′,B′,O, ᠵᠢᠷᠤᠭ ᠮᠡᠳᠤ᠂ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᡂᠢ ᠶᠢᠨ ᠨᠢᠭᠡ ᠣᠷᠤᠢ ᠶᠢᠨ ᠴᠡᠭ ᠨᠢ O, ᠴᠡᠭ O ᠪᠠᠷ ᠲᠥᠪ ᠪᠣᠯᠭᠠᠵᠤ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᡂᠢ ᠶᠢ ᠡᠷᠭᠢᠭᠦᠯᠪᠡᠯ᠂ ᠴᠡᠭ O ᠶᠢᠨ ᠬᠤᠪᠢ ᠲᠤ ᠲᠥᠪ ᠲᠤ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠳᠠᠢ ᠬᠤᠶᠠᠷ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᠢ ᠵᠢᠷᠤᠵᠤ ᠲᠡᠢᠯᠤᠨᠡ᠄ , ᠰᠡᠳᠭᠢᠬᠦ 2᠄ ,⑵ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᡂᠢ ᠶᠢᠨ ᠨᠢᠭᠡ ᠣᠷᠤᠢ ᠶᠢᠨ ᠴᠡᠭ O ᠪᠠᠷ ᠲᠥᠪ ᠪᠣᠯᠭᠠᠵᠤ᠂ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᡂᠢ ᠶᠢ 18 0 0 ᠡᠷᠭᠢᠭᠦᠯᠵᠦ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ A`B`C` ᠢ ᠵᠢᠷᠤᠨᠠ᠃ ,⑶ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᡂᠢ ᠪᠠᠨ ᠰᠢᠯᠵᠢᠭᠦᠯᠦᠨᠡ᠃ , ︵1︶ ᠲᠦᠪ ᠲᠤ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠳᠤ ᠪᠤᠯᠬᠤ ᠬᠤᠶᠠᠷ ᠵᠢᠷᠤᠭ ᠲᠦᠷᠰᠤ ᠶᠢᠨ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠳᠤ ᠴᠡᠭ ᠢ ᠬᠤᠯᠪᠤᠭᠰᠠᠨ ᠬᠡᠷᠴᠢᠮ ᠨᠢ ᠴᠦᠮ ᠲᠡᠭᠰᠢ ᠬᠡᠮ ᠦᠨ ᠲᠦᠪ ᠢ ᠲᠠᠭᠠᠷᠢᠬᠤ ᠪᠦᠭᠡᠳ ᠲᠡᠭᠰᠢ ᠬᠡᠮ ᠦᠨ ᠲᠦᠪ ᠲᠤ ᠲᠠᠯᠠᠯᠠᠨ ᠬᠤᠪᠢᠶᠠᠭᠳᠠᠨᠠ᠃ ,2. ᠲᠦᠪ ᠲᠣ ᠲᠡᠭᠰᠢ ᠭᠡᠮᠲᠦ ᠶᠢᠨ ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ :, ︵2︶ ᠲᠦᠪ ᠲᠤ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠳᠤ ᠪᠤᠯᠬᠤ ᠬᠤᠶᠠᠷ ᠵᠢᠷᠤᠭ ᠲᠦᠷᠰᠤ ᠪᠤᠯ ᠪᠦᠷᠢᠨ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠵᠢᠷᠤᠭ ᠲᠦᠷᠰᠤ ᠮᠦᠨ᠃ , ᠲᠦᠪ ᠲᠤ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠳᠤ ᠨᠢ ᠨᠢᠭᠡ ᠵᠦᠢᠯ ᠦᠨ ᠣᠨᠴᠠᠭᠠᠢ ᠡᠷᠬᠢᠯᠳᠡ᠂ ᠢᠮᠤ ᠠᠴᠠ ᠡᠷᠬᠢᠯᠳᠡ ᠶᠢᠨ ᠪᠤᠢ ᠪᠦᠬᠦᠢ ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ ᠪᠦᠷ ᠪᠠᠢᠨᠠ᠃ , ᠵᠢᠷᠤᠭ ᠮᠡᠳᠤ᠂ ᠥᠭᠭᠦᠭᠳᠡᠭᠰᠡᠨ 𝐴,𝐵,𝑂 ᠭᠤᠷᠪᠠᠨ ᠴᠡᠭ ᠨᠢ ᠶᠡᠷᠦᠩᠬᠡᠢ ᠰᠢᠯᠤᠭᠤᠨ ᠲᠡᠭᠡᠷᠠ ᠤᠷᠤᠰᠢᠬᠤ ᠦᠭᠡᠢ᠂ ᠴᠡᠭ 𝐴 , 𝐴 1 ᠨᠢ ᠴᠡᠭ 𝑂 ᠤᠨ ᠬᠤᠪᠢ ᠲᠤ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠳᠡᠢ᠂ ᠴᠡᠭ 𝐵, 𝐵 1 ᠨᠢ ᠴᠡᠭ 𝑂 ᠤᠨ ᠬᠤᠪᠢ ᠲᠤ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠳᠡᠢ᠂ ᠲᠡᠭᠡᠪᠡᠯ ᠬᠡᠷᠴᠢᠮ 𝐴𝐵 ᠪᠠ 𝐴 1 𝐵 1 ᠤᠨ ᠬᠤᠯᠪᠤᠭᠳᠠᠯ ᠨᠢ ︵︶ , ᠵᠡᠷᠭᠡᠴᠡᠭᠡ ᠪᠥᠭᠡᠳ ᠲᠡᠩᠴᠡᠭᠦᠤ , ᠪᠣᠯᠪᠠᠰᠤᠷᠠᠯ᠄ , ᠵᠢᠷᠤᠭ ᠮᠡᠳᠤ᠂ ᠦᠭᠭᠦᠭᠳᠡᠭᠰᠡᠨ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ 𝐴𝐵𝐶 ᠪᠤᠯᠤᠨ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ 𝐷𝐸𝐹 ᠨᠢ ᠲᠦᠪ ᠲᠤ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠳᠤ᠂ ᠴᠡᠭ 𝐴 ᠪᠤᠯᠤᠨ ᠴᠡᠭ 𝐷 ᠨᠢ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠳᠤ ᠴᠡᠭ ᠪᠣᠯᠤᠨᠠ᠃ ᠲᠡᠭᠡᠪᠡᠯ ᠲᠡᠭᠰᠢ ᠬᠡᠮ ᠦᠨ ᠲᠦᠪ 𝑂 ᠶᠢ ᠤᠯ᠃ , ᠰᠡᠳᠭᠢᠬᠦ 3᠄ , ᠠᠷᠭᠠ 2᠄ ,3. ᠲᠡᠭᠰᠢ ᠬᠡᠮ ᠦᠨ ᠲᠥᠪ ᠢ ᠤᠯᠬᠤ ᠠᠷᠭᠠ᠄ , ᠠᠷᠭᠠ 1᠄ , ᠬᠤᠶᠠᠷ ᠬᠤᠣᠰ ᠬᠠᠷᠠᠭᠠᠯᠵᠠᠭᠰᠠᠨ ᠴᠡᠭ ᠤᠨ ᠬᠤᠯᠪᠤᠭᠴᠢ ᠬᠡᠷᠴᠢᠮ ᠦᠨ ᠤᠭᠳᠤᠯᠤᠯᠴᠠᠯ ᠤᠨ ᠴᠡᠭ ᠨᠢ ᠪᠣᠯᠤᠨᠠ᠃ , ᠨᠢᠭᠡ ᠬᠤᠣᠰ ᠬᠠᠷᠠᠭᠠᠯᠵᠠᠭᠰᠠᠠᠨ ᠴᠡᠭ ᠤᠨ ᠬᠤᠯᠪᠤᠭᠴᠢ ᠬᠡᠷᠴᠢᠮ ᠦᠨ ᠲᠤᠮᠳᠠ ᠴᠡᠭ ᠨᠢ ᠪᠣᠯᠤᠨᠠ᠃ , ᠲᠦᠪ ᠲᠤ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠳᠤ ᠪᠠ ᠡᠷᠭᠢᠯᠳᠡ ᠶᠢᠨ ᠬᠤᠯᠪᠤᠭᠳᠠᠯ ᠪᠤᠯᠤᠨ ᠢᠯᠭᠠᠭᠠ ᠨᠢ︖ , ᠬᠤᠯᠪᠤᠭᠳᠠᠯ᠄ ᠲᠦᠪ ᠲᠤ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠳᠤ ᠪᠠ ᠡᠷᠭᠢᠯᠳᠡ ᠨᠢ ᠴᠦᠮ ᠨᠢᠭᠡᠨ ᠲᠤᠭᠳᠠᠭᠰᠠᠨ ᠴᠡᠭ ᠢ ᠲᠤᠭᠤᠷᠢᠨ ᠡᠷᠭᠢᠨᠡ᠃ , ᠢᠯᠭᠠᠭᠠ᠄ ᠲᠦᠪ ᠲᠤ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠳᠤ ᠶᠢᠨ ᠡᠷᠭᠢᠯᠳᠡ ᠶᠢᠨ ᠦᠨᠴᠦᠭ ᠨᠢ ᠴᠦᠮ 1800᠂ ᠡᠷᠭᠢᠯᠳᠡ ᠶᠢᠨ ᠦᠨᠴᠦᠭ ᠦᠨ ᠶᠡᠭᠡ ᠪᠠᠭᠠ ᠨᠢ ᠲᠤᠭᠳᠠᠮᠠᠯ ᠪᠢᠰᠢ᠂ ᠲᠦᠪ ᠲᠤ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠳᠤ ᠪᠤᠯ ᠤᠨᠴᠠᠭᠠᠢ ᠡᠷᠭᠢᠯᠳᠡ ᠪᠣᠯᠤᠨᠠ᠃ , ᠰᠡᠳᠭᠢᠬᠦ 4᠄ , ᠪᠣᠯᠪᠠᠰᠤᠷᠠᠯ᠄ ,1. ᠲᠠᠷᠠᠭᠠᠬᠢ ᠵᠢᠷᠤᠭ ᠲᠦᠷᠰᠤ ᠨᠦᠭᠦᠳ ᠦᠨ ᠴᠡᠭ O ᠶᠢᠨ ᠬᠤᠪᠢ ᠲᠤ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠳᠤ ᠵᠢᠷᠤᠭ ᠲᠦᠷᠰᠤ ᠶᠢ ᠲᠤᠰ ᠲᠤᠰ ᠵᠢᠷᠤ᠃ ,,,2. ᠵᠢᠷᠤᠭ ᠲᠠᠬᠢ ᠬᠤᠶᠡᠷ ᠲᠦᠷᠪᠡᠯᠵᠢᠨ ᠨᠢ ᠶᠠᠮᠠᠷ ᠨᠢᠭᠡᠨ ᠴᠡᠭ ᠦᠨ ᠬᠤᠪᠢ ᠲᠤ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠳᠠᠢ᠂ ᠲᠡᠳᠡᠭᠡᠷ ᠦᠨ ᠲᠡᠭᠰᠢ ᠬᠡᠮ ᠦᠨ ᠲᠥᠪ ᠢ ᠤᠯ᠃ , ᠳ᠋ᠦᠩᠨᠡᠯᠲᠡ᠄ ,1. ᠲᠦᠪ ᠲᠣ ᠲᠡᠭᠰᠢ ᠭᠡᠮᠲᠦ ᠶᠢᠨ ᠲᠤᠳᠤᠷᠬᠠᠢᠯᠠᠯᠳᠠ :,2. ᠲᠦᠪ ᠲᠣ ᠲᠡᠭᠰᠢ ᠭᠡᠮᠲᠦ ᠶᠢᠨ ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ :,3. ᠲᠡᠭᠰᠢ ᠬᠡᠮ ᠦᠨ ᠲᠥᠪ ᠢ ᠤᠯᠬᠤ ᠠᠷᠭᠠ᠄ , ᠲᠠᠰᠬᠠᠯ᠄ , ᠢᠵᠢᠯᠢ ᠠᠯᠬᠤᠮᠳᠤ ᠱᠠᠳᠤᠴᠢᠯᠠᠭᠰᠠᠨ ᠪᠣᠯᠪᠠᠰᠤᠷᠠᠯ ,
ᠮᠣᠩᠭᠣᠯ ᠳ᠋ᠣᠺ ᠤᠨ ᠬᠥᠮᠥᠷᠭᠡ