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平行线与角的关系演示

平行线与角的关系演示
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2014-11-03 22:48
角变换几何作图
所属专题 PARCC Math I Unit 5 Lesson 5
①本范例演示平行线与角的关系，通过动态图形展示同位角、内错角相等；②涉及核心数学概念包括平行线性质、角度测量、几何变换；③作图要点：使用Point, Polygon, Segment, Line, Angle, Rotate, Intersect, TableText等GeoGebra命令构建平行线、角度和变换关系；④适合高中数学教学，用于理解平行线性质和角度关系。

GeoGebra 命令及参数

  1. Point(xAxis) → F
  2. Polygon((x(F), y(Corner[1])), Corner[2], Corner[3], (x(F), y(Corner[4]))) → poly1, c, d, e, f
  3. Segment(G, H) → g
  4. Point(g) → I
  5. Line(A, M) → a
  6. Line(N, D) → b
  7. Line(M, D) → h
  8. Line(A, N) → i
  9. Segment(A, M) → j
  10. Segment(N, D) → k
  11. Segment(M, D) → m
  12. Segment(A, N) → l
  13. Point(i) → E
  14. Angle(M, A, E) → α
  15. Angle(A, M, D) → β
  16. Angle(M, D, N) → γ
  17. Rotate(A, ε, M) → A'
  18. Angle(A, M, A') → ζ
  19. Rotate(D, (-ε), M) → D'
  20. Angle(D', M, D) → η
  21. Angle(A', M, D') → θ
  22. Rotate(D, 345*°, M) → D'_1
  23. Angle(D'_1, M, D) → ι
  24. Angle(D', M, D'_1) → κ
  25. Rotate(M, 9*°, A) → C'
  26. Angle(M, A, C') → λ
  27. Angle(C', A, E) → μ
  28. Rotate(C', ξ, A) → C''
  29. Angle(C', A, C'') → ο
  30. Rotate(C'', ξ, A) → C'''
  31. Angle(C'', A, C''') → ρ
  32. Rotate(C''', ξ, A) → J
  33. Angle(C''', A, J) → σ
  34. Rotate(J, ξ, A) → J'
  35. Angle(J, A, J') → τ
  36. Rotate(M, 55*°, D) → C'_1
  37. Angle(M, D, C'_1) → υ
  38. Angle(C'_1, D, N) → ϕ
  39. Rotate(C'_1, χ, D) → K
  40. Angle(C'_1, D, K) → ψ
  41. Angle(K, D, N) → ω
  42. Intersect(j, l) → L
  43. Line(G, H) → n
  44. Intersect(n, j) → O
  45. Point(l) → B
  46. Line(O, B) → p
  47. Line(B, D) → q
  48. Point(h) → C
  49. Line(D, C) → r
  50. Intersect(j, l) → P
  51. Line(M, P) → s
  52. Intersect(j, l) → Q
  53. Line(Q, N) → t
  54. TableText({{"\mathit{m}\angle 1 + \mathit{m} \angle 2", "=", 180}, {"3(\mathit{x}+15)+2\mathit{x}+55", "=", 180}, {"\mathit{x}", "=", 16}}, "rcl") → text3
  55. TableText({{"\angle 1", "\cong", "\angle 3"}, {"\mathit{m} \angle 1", "=", "\mathit{m} \angle 3"}}, "rcl") → text15
  56. TableText({{"\mathit{m} \angle 3", "=", "4 \mathit{y} + 9"}, {93, "=", "4\mathit{y} + 9"}, {21, "=", "\mathit{y}"}}, "rcl") → text16
  57. TableText({{"\angle 1", "\cong", "\angle 3"}, {"\mathit{m} \angle 1", "=", "\mathit{m} \angle 3"}, {β, "=", α}}, "rcl") → text17