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探索交错外角 by Tim Brzezinski

探索交错外角 by Tim Brzezinski
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2016-03-22 20:44
角变换几何作图
所属专题 Congruence (CO) Cluster Congruence (Vol 2) CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Parallel Lines & Related Angles Parallel Lines & Related Angles Logic and Parallel Lines Geometry: Parallel Lines & Related Angles Year 9 Mathematics Year 7 (Angles) Angle Congruence Intros
①本范例演示了当横截线与平行线相交时，交错外角是相等的几何现象；②涉及的核心数学概念包括角、平行线、横截线、几何证明；③作图要点——从下方『构造摘要』提炼用到了Point（点）、Line（线）、Circle（圆）、Intersect（交点）、Angle（角）等GeoGebra命令/对象；④适合高中数学教学或几何学习，用于直观理解平行线性质。

GeoGebra 命令及参数

  1. Point(a) → B
  2. Rotate(B, α, A) → B'
  3. Angle(B, A, B') → β
  4. Line(A, B') → b
  5. Circle(A, 1) → e
  6. Intersect(b, d) → C
  7. Circle(C, 1) → f
  8. Intersect(e, a) → D, E
  9. Intersect(e, b) → F, G
  10. Intersect(f, b) → H, I
  11. Intersect(f, d) → J, K
  12. CircleSector(C, J, H) → k
  13. CircleSector(C, H, K) → p
  14. CircleSector(A, F, E) → t
  15. Dilate(A, If[0 < i < 1, 1 - i], C) → A'
  16. Vector(A, A') → u
  17. Vector(A, C) → v
  18. Midpoint(C, A) → L
  19. Rotate(A, (((-i) * 180))°, L) → A'_1
  20. Segment(L, A'_1) → g
  21. Segment(C, L) → n
  22. Segment(L, A) → s
  23. Point(b) → M
  24. Point(b) → N
  25. Ray(C, M) → a_1
  26. Ray(A, N) → b_1
  27. Rotate(E, (((-i) * 180))°, L) → E'
  28. Ray(A'_1, E') → d_1
  29. Circle(A'_1, Distance[L, A'_1]) → e_1
  30. Intersect(e_1, d_1, 1) → O
  31. Rotate(A, ((i * 180))°, L) → A'_2
  32. Rotate(D, ((i * 180))°, L) → D'
  33. Circle(A'_2, L) → k_1
  34. Ray(A'_2, D') → i_1
  35. Intersect(k_1, i_1) → P,
  36. Segment(A'_2, P) → j_1
  37. Intersect(e, b, 1) → Q
  38. Intersect(f, n, 1) → R
  39. CircleSector(A, Q, E) → c_1
  40. Rotate(c_1, (((-i) * 180))°, L) → q
  41. Rotate(Q, (((-i) * 180))°, L) → Q'
  42. Circle(A, g) → g_1
  43. Intersect(g_1, b_1, 1) → S
  44. Intersect(g_1, a, 2) → T
  45. Segment(A, S) → h_1
  46. Rotate(A, (((-i) * 180))°, L) → A'_3
  47. Rotate(S, (((-i) * 180))°, L) → S'
  48. Segment(A'_3, S') → l_1
  49. Segment(A, T) → m_1
  50. Rotate(A, (((-i) * 180))°, L) → A'_4
  51. Rotate(T, (((-i) * 180))°, L) → T'
  52. Segment(A'_4, T') → n_1
  53. CircleArc(A, Q, E) → p_1
  54. Intersect(e_1, a, 1) → U
  55. Segment(A, U) → q_1
  56. Intersect(a, q_1) → V
  57. Intersect(a, q_1) → W
  58. Intersect(e, a, 1) → Z
  59. CircleSector(A, Z, Q) → r
  60. Rotate(A, ((i * 180))°, L) → A'_5
  61. Rotate(r, ((i * 180))°, L) → r'
  62. Rotate(A, ((i * 180))°, L) → A'_6
  63. Rotate(S, ((i * 180))°, L) → S'_1
  64. Segment(A'_6, S'_1) → h
  65. Segment(L, A'_5) → r_1
  66. CircleArc(A, Z, Q) → f_1

AI 绘图提示语参考

画两条平行线，然后画一条穿过它们的直线作为横截线。在横截线与平行线的外部，标记出一对对应的外角。旋转其中一个角，观察其对应角的大小保持不变。使用点、线、圆和交点等工具，逐步构建图形，展示外角相等的性质。
以上提示语为根据原始绘图命令整理而来，仅供参考。