ᠴᠢᠪᠠᠭ᠎ᠠ ᠮᠤᠩᠭᠤᠯ ᠲᠤᠮᠳᠠᠳᠤ ᠰᠤᠷᠭᠠᠭᠤᠯᠢ — ᠲᠤᠭᠠᠨ ᠤ ᠤᠬᠠᠭᠠᠨ — ᠨᠠᠢᠮᠠ ᠤᠨ — ᠲᠤᠤᠷᠠᠳᠤ — ᠦᠷᠴᠠᠶᠢᠬᠤ — 18.2.2🎬 ‍ᠤᠮᠪ （1） .pptx

ᠵᠢᠰᠢᠬᠦᠯᠵᠢᠨ ᠤᠤ ︖,ᠲᠠᠢ ᠪᠤᠢ ︖ ᠶᠠᠮᠠᠷ ᠬᠤᠯᠪᠤᠠᠠᠳ᠋ᠠᠯ ᠲᠠᠯ᠎ᠠ ᠨᠢ,ᠨᠠᠢ᠍ᠮᠠᠳᠤᠭᠠᠷ ᠣᠨ （ ᠲᠤᠤᠷᠠᠳᠤ ᠲᠡᠪᠳᠡᠷ ）,ᠠᠯᠪᠠᠨ ᠵᠢᠷᠤᠮ ᠤᠨ ᠰᠤᠷᠭᠠᠨ ᠭᠦᠮᠦᠵᠢᠯ ᠦᠨ ᠰᠤᠷᠬᠤ ᠪᠢᠴᠢᠭ᠌,ᠲᠣᠭᠠᠨ ᠤ ᠤᠬᠠᠭᠠᠨ,ᠠᠷᠤ ᠬᠣᠷᠴᠢᠨ ᠬᠣᠰᠢᠭᠤᠨ ‍ᠣ ᠴᠢᠪᠠᠭ᠎ᠠ ᠮᠣᠩᠭᠤᠯ ᠦᠨᠳᠦᠰᠦᠲᠡᠨ ‍ᠣ ᠳᠤᠮᠳᠠᠳᠤ ᠰᠤᠷᠭᠠᠭᠤᠯᠢ ᠦᠷᠴᠠᠢᠬᠤ,18.2 ᠤᠨᠴᠠᠭᠠᠢ ᠵᠢᠰᠢᠭᠦᠯᠵᠢᠨ,18.2.2 ᠷᠤᠮᠪ (1),,ᠵᠢᠰᠢᠭᠦᠯᠵᠢᠨ,,ᠷᠣᠮᠪ,,ᠷᠤᠮᠪ ᠤᠨ ᠲᠤᠳᠤᠷᠬᠠᠶᠢᠯᠠᠯᠲᠠ,1.ᠷᠤᠮᠪ ᠲᠦ ᠶᠠᠮᠠᠷ ᠶᠠᠮᠠᠷ ᠲᠡᠨᠭᠴᠡᠭᠦᠦ ᠬᠡᠷᠴᠢᠮ ᠪᠠᠢᠢᠬᠤ ᠪᠤᠢ ︖ 2.ᠷᠤᠮᠪ ᠲᠦ ᠶᠠᠮᠠᠷ ᠶᠠᠮᠠᠷ ᠲᠡᠨᠭᠴᠡᠭᠦᠦ ᠦᠨᠴᠦᠭ ᠪᠠᠢᠢᠬᠤ ᠪᠤᠢ ︖ 3.ᠷᠤᠮᠪ ᠦᠨ ᠲᠠᠰᠢᠭᠤᠪᠴᠢ ᠨᠢ ᠶᠠᠮᠠᠷ ᠤᠨᠴᠠᠭᠠᠢ ᠬᠤᠯᠪᠤᠠᠠᠳᠠᠯ ᠲᠠᠢ ᠪᠤᠢ ︖ 4.ᠷᠤᠮᠪ ᠲᠡᠩᠭᠡᠯᠢᠭ ᠲᠦ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠳᠡᠢ ᠵᠢᠷᠤᠭ ᠲᠦᠷᠰᠦ ᠤᠤ︖ ᠲᠡᠭᠦᠨ ᠦ ᠲᠡᠭᠰᠢ ᠬᠡᠮ ᠦᠨ ᠲᠡᠩᠭᠡᠯᠢᠭ ᠨᠢ ︖,1.AB=CD=AD=BC OA=OC , OB=OD,2.∠DAB=∠BCD , ∠ABC =∠CDA, ∠1=∠2=∠3=∠4, ∠5=∠6=∠7=∠8,3.𝐴𝐶⊥𝐵𝐷 AO=CO,BO=DO,4.ᠲᠡᠩᠭᠡᠯᠢᠭ ᠲᠦ ᠲᠡᠭᠰᠢ ᠬᠡᠮᠳᠡᠢ ᠵᠢᠷᠤᠭ ᠲᠦᠷᠰᠦ ᠮᠦᠨ ᠃ ᠬᠤᠶᠠᠷ ᠲᠠᠰᠢᠭᠤᠪᠴᠢ ᠶᠢᠨ ᠤᠷᠤᠰᠢᠵᠤ ᠪᠠᠢᠢᠭ᠎ᠠ ᠰᠢᠯᠤᠭᠤᠨ,,,1. ᠷᠣᠮᠪ ᠤᠨ ᠲᠦᠷᠪᠡᠨ ᠲᠠᠯ᠎ᠠ ᠨᠢ ᠴᠦᠮ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠃ 2. ᠷᠣᠮᠪ ᠤᠨ ᠬᠣᠶᠠᠷ ᠲᠠᠰᠢᠭᠣᠪᠴᠢ ᠨᠢ ᠬᠠᠷᠢᠯᠴᠠᠨ ᠡᠭᠴᠡ ᠪᠣᠯᠬᠣ ᠪᠦᠭᠡᠳ ᠲᠠᠰᠢᠭᠣᠪᠴᠢ ᠨᠢᠭᠡ ᠪᠦᠷᠢ ᠨᠢ ᠨᠢᠭᠡ ᠬᠣᠣᠰ ᠡᠰᠡᠷᠭᠦ ᠦᠨᠴᠦᠭ ᠶᠢᠡᠨ ᠲᠠᠯᠠᠯᠠᠨ ᠬᠣᠪᠢᠶᠠᠨ᠎ᠠ ᠃,𝐴𝐵∥𝐶𝐷,𝐴𝐷∥𝐵𝐶 AB=𝐶𝐷,𝐴𝐷=𝐵𝐶,∠𝐴=∠𝐶,∠𝐵=∠𝐷 ∠𝐴+∠𝐷= 180 ° , ∠𝐴+∠= 180 °,𝑂𝐴=𝑂𝐶, 𝑂𝐵=𝑂𝐷,ᠷᠤᠮᠪ ᠤᠨ ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ,𝐴𝐶⊥𝐵𝐷 AO=CO,BO=DO,∠DAB=∠BCD ∠ABC=∠CDA ∠1=∠2=∠3=∠4 ∠5=∠6=∠7=∠8,𝐴𝐵∥𝐶𝐷,𝐴𝐷∥𝐵𝐶 AB=CD=AD=BC,1. ᠷᠣᠮᠪ ᠤᠨ ᠲᠦᠷᠪᠡᠨ ᠲᠠᠯ᠎ᠠ ᠨᠢ ᠴᠦᠮ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠃ 2. ᠷᠣᠮᠪ ᠤᠨ ᠬᠣᠶᠠᠷ ᠲᠠᠰᠢᠭᠣᠪᠴᠢ ᠨᠢ ᠬᠠᠷᠢᠯᠴᠠᠨ ᠡᠭᠴᠡ ᠪᠣᠯᠬᠣ ᠪᠦᠭᠡᠳ ᠲᠠᠰᠢᠭᠣᠪᠴᠢ ᠨᠢᠭᠡ ᠪᠦᠷᠢ ᠨᠢ ᠨᠢᠭᠡ ᠬᠣᠣᠰ ᠡᠰᠡᠷᠭᠦ ᠦᠨᠴᠦᠭ ᠶᠢᠡᠨ ᠲᠠᠯᠠᠯᠠᠨ ᠬᠣᠪᠢᠶᠠᠨ᠎ᠠ ᠃,ᠷᠤᠮᠪ ᠤᠨ ᠲᠠᠯᠠᠪᠠᠢ,S = 1 2 BD∙ AC,ᠬᠠᠭᠠᠰ ᠲᠠᠢ ᠲᠡᠩᠴᠡᠨ᠎᠎ᠡ ᠃ ᠲᠠᠰᠢᠭᠤᠪᠴᠢ ᠶᠢᠨ ᠦᠷᠡᠵᠢᠪᠦᠷᠢ ᠶᠢᠨ ᠷᠤᠮᠪ ᠤᠨ ᠲᠠᠯᠠᠪᠠᠢ ᠨᠢ ᠬᠤᠶᠠᠷ,= 1 2 BD∙AO+ 1 2 BD∙CO,= 1 2 BD∙(AO+CO),= 1 2 BD∙AC,ᠪᠠᠳ᠋ᠤᠳᠬᠠᠯ ᠄,∠BAC= ᠭᠷᠠᠳᠦ᠋ᠰ ᠃ 2. ᠷᠤᠮᠪABCD ᠳ᠋ᠤ ∠ABC=60° ᠪᠤᠯ ᠲᠡᠭᠡᠪᠡᠯ ᠲᠡᠭᠦᠨ ᠦ ᠲᠠᠯ᠎ᠠ ᠶᠢᠨ ᠤᠷᠳᠤ ᠨᠢ cm᠃ 1.ᠨᠢᠬᠡ ᠷᠤᠮᠪ ᠤᠨ ᠬᠦᠷᠢᠶᠡᠨ ᠦ ᠤᠷᠳᠤ ᠨᠢ 12cm,,ᠤᠷᠳᠤ ᠨᠢ , ᠲᠤᠰ 6cm ᠪᠠ 8cm ᠪᠣᠯ ᠲᠡᠭᠦᠨ ᠦ ᠲᠠᠯ᠎ᠠ ᠶᠢᠨ 3.ᠨᠢᠬᠡ ᠷᠤᠮᠪ ᠤᠨ ᠬᠤᠶᠠᠷ ᠲᠠᠰᠢᠭᠤᠪᠴᠢ ᠶᠢᠨ ᠤᠷᠳᠤ ᠨᠢ ᠲᠤᠰ,A.10cm B.7cm C. 5cm D.4cm,3cm,60,C,3,4,ᠵᠢᠱᠢᠶ᠎ᠡ ᠄ ᠵᠢᠷᠤᠭ ᠮᠡᠳᠦ ᠂ ᠷᠤᠮᠪ ᠬᠡᠯᠪᠡᠷᠢᠳᠡᠢ ᠴᠡᠴᠡᠭᠯᠢᠭABCD ᠶᠢᠨ ᠲᠠᠯ᠎ᠠ ᠶᠢᠨ ᠤᠷᠳᠤ ᠨᠢ 20m, ∠ABC=60°ᠷᠤᠮᠪ ᠤᠨ ᠲᠠᠰᠢᠭᠤᠪᠴᠢ ᠲᠠᠭᠠᠤ ᠬᠤᠶᠠᠷ ᠵᠦᠷᠢᠭ AC ᠪᠠ BD ᠵᠠᠰᠠᠪᠠ ᠃ ᠬᠤᠶᠠᠷ ᠵᠦᠷᠢᠭ ᠦᠨ ᠤᠷᠳᠤ ᠪᠠ ᠴᠢᠴᠢᠭᠯᠢᠭ ᠦᠨ ᠲᠠᠯᠠᠪᠠᠢ ᠶᠢ ᠤᠯ ᠃( ᠳ᠋ᠦᠩ ᠦᠨ ᠠᠷᠪᠠᠳᠤ ᠶᠢᠨ ᠪᠤᠲᠠᠷᠬᠠᠢ ᠶᠢᠨ ᠴᠡᠭ ᠦᠨ ᠠᠷᠤ ᠳᠤ ᠨᠢᠭᠡ ᠤᠷᠤᠨ ᠦᠯᠡᠳᠡᠭᠡ),ᠪᠤᠳᠤᠬᠤ ᠨᠢ ᠄,∴ AC⊥BD, ∠ABO = 1 2 ∠ABC = 1 2 ×60°=30°,BO= 𝐴𝐵 2 − 𝐴𝑂 2 = 20 2 − 10 2 =10 3 （m）,ᠡᠢᠮᠦ ᠡᠴᠡ᠄ ᠴᠡᠴᠡᠭᠯᠢᠭ ᠤᠨ ᠬᠤᠶᠠᠷ ᠵᠦᠷᠢᠭ ᠦᠨ ᠤᠷᠳᠤ ᠨᠢ ᠲᠤᠰ ᠲᠤᠰ,ᠴᠡᠴᠡᠭᠯᠢᠭ ᠤᠨ ᠲᠠᠯᠠᠪᠠᠢ ᠨᠢ,AC=2AO=20m,BD=2OB=20 3 ≈20×1 .732 ≈34.64 m,ᠪᠠᠳ᠋ᠤᠳᠬᠠᠯ ᠄,(3) ᠷᠤᠮᠪ ᠦᠨ ᠲᠠᠯᠠᠪᠠᠢ ᠶᠢ ᠤᠯ ᠃ (2) ᠲᠠᠰᠢᠭᠤᠪᠴᠢ AC,BD ᠤᠷᠳᠤ ᠶᠢ ᠤᠯ ᠃ (1)∠𝐴𝐵𝐶 ᠶᠢᠨ ᠭᠷᠠᠳᠦ᠋ᠰ ᠦᠨ ᠲᠣᠭ᠎ᠠ ᠶᠢ ᠤᠯ ᠃ ᠴᠡᠭ ᠂ DE⊥AB,AE=2; ᠤᠯᠬᠤ ᠨᠢ᠄ 4. ᠷᠤᠮᠪ ABCD ᠳᠤ ᠂ E ᠪᠤᠯ AB ᠶᠢᠨ ᠲᠤᠮᠳᠠ,ᠪᠤᠳᠤᠬᠤ ᠨᠢ ᠄,(1),∴AD=AB=BD,∴ ∠DBA= 60 ° ∴ ∠ABC=120 °,(2),2,∵AE=2， ∴ AB=4 ∴ BD=AB=4,AO= 𝐴𝐵 2 − 𝐵𝑂 2 = 4 2 − 2 2 =2 3,∴ AC=4 3,(3),ᠷᠤᠮᠪ ᠤᠨ ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ ᠄,ᠲᠠᠯ᠎ᠠ,,ᠦᠨᠴᠦᠭ,ᠵᠡᠷᠭᠡᠴᠡᠭᠡ ᠲᠠᠯ᠎ᠠ ᠨᠢ ᠡᠰᠡᠷᠭᠦ,ᠲᠡᠨᠭᠴᠡᠭᠦᠦ ᠲᠠᠯ᠎ᠠ ᠨᠢ ᠲᠦᠷᠪᠡᠨ,ᠲᠡᠨᠭᠴᠡᠭᠦᠦ ᠦᠨᠴᠦᠭ ᠨᠢ ᠡᠰᠡᠷᠭᠦ,,ᠨᠦᠬᠦᠪᠦᠷᠢ ᠦᠨᠴᠦᠭ ᠨᠢ ᠵᠡᠷᠭᠡᠯᠡᠳᠡᠭᠡ,ᠲᠠᠰᠢᠭᠤᠪᠴᠢ,,ᠬᠤᠪᠢᠶᠠᠨ᠎ᠠ ᠲᠠᠯᠠᠯᠠᠨ ᠡᠭᠴᠡ ᠬᠠᠷᠢᠯᠴᠠᠨ,ᠬᠤᠪᠢᠶᠠᠨ᠎ᠠ ᠲᠠᠯᠠᠯᠠᠨ ᠦᠨᠴᠦᠭ ᠢᠶᠡᠨ ᠡᠰᠡᠷᠭᠦ ᠨᠢᠬᠡᠪᠦᠷᠢ ᠨᠢ ᠲᠠᠰᠢᠭᠤᠪᠴᠢ,ᠬᠤᠶᠠᠷ ᠲᠠᠰᠢᠭᠤᠪᠴᠢ ᠶᠢᠨ ᠦᠷᠡᠵᠢᠪᠦᠷᠢ ᠶᠢᠨ ᠬᠠᠭᠠᠰ ᠰᠠᠭᠤᠷᠢ × ᠦᠨᠳᠦᠷ = ᠷᠤᠮᠪ ᠤᠨ ᠲᠠᠯᠠᠪᠠᠢ ᠄,,ᠪᠤᠯᠪᠠᠰᠤᠷᠠᠯ ᠄ ᠲᠡᠪᠲᠡᠷ ᠦᠨ 68 ᠨᠢᠭᠤᠷ ᠤᠨ1,2 ᠳ᠋ᠤᠭᠠᠷ ᠰᠡᠳᠦᠪ ᠲᠠᠰᠬᠠᠯ ᠄ᠲᠡᠪᠲᠡᠷ ᠦᠨ ᠤ72 ᠨᠢᠭᠤᠷ ᠤᠨ5,11 ᠳ᠋ᠤᠭᠠᠷ ᠰᠡᠳᠦᠪ,