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证明同角的补角相等——GeoGebra 动态几何演示

证明同角的补角相等——GeoGebra 动态几何演示
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2016-10-20 05:47
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 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2
本例通过 GeoGebra 动态几何软件演示了同角（或等角）的补角之间相等的几何性质。核心概念包括角的度量、补角定义以及等角关系。作图中运用了射线、旋转、角、圆、线、交点、LaTeX 文本、圆扇形、相似变换、平移、点、圆弧、垂线等命令，并利用了多个标签对象（如 A、B、α、B'、β 等）来构建并验证补角的等量关系。本例适合高中几何教学及数学证明课程使用。

GeoGebra 命令及参数

  1. Ray(A, B) → f
  2. Rotate(B, α, A) → B'
  3. Angle(B, A, B') → β
  4. Ray(A, B') → g
  5. Circle(A, 1) → c
  6. Line(B, A) → h
  7. Intersect(c, h, 2) → C
  8. Ray(A, C) → i
  9. Ray(D, E) → j
  10. Rotate(E, α, D) → E'
  11. Angle(E, D, E') → γ
  12. Ray(D, E') → k
  13. Line(E, D) → l
  14. Circle(D, 1) → d
  15. Intersect(d, l, 2) → F
  16. Ray(D, F) → m
  17. LaTeX(B', true, true) → text1
  18. Circle(D, 2) → e
  19. Intersect(e, j, 1) → G
  20. Intersect(e, k, 1) → H
  21. Line(D, i) → n
  22. CircleSector(D, G, H) → p
  23. Dilate(D, If[0 < a ≤ 1, 1 - a, 0], A) → D'
  24. Vector(D, D') → u
  25. Translate(p, u) → p'
  26. Point(n) → I
  27. Angle(I, D, E') → δ
  28. Line(D, g) → q
  29. Intersect(e, q, 2) → J
  30. Angle(H, D, J) → ε
  31. Rotate(p', If[0 < a ≤ 1, (a * ε), ε], D') → p''
  32. CircleArc(D, G, H) → r
  33. Intersect(e, m) → K,
  34. Dilate(D, If[2.75 < a ≤ 3.75, 3.75 - a, 0], A) → D'_1
  35. Vector(D, D'_1) → v
  36. CircleArc(D, H, K) → t
  37. OrthogonalLine(A, f) → b
  38. OrthogonalLine(D, j) → f_1
  39. Intersect(e, f_1) → L, M
  40. Angle(G, D, M) → ζ
  41. Ray(D, M) → s
  42. Line(D, b) → g_1
  43. Intersect(d, g_1, 2) → N
  44. Angle(M, D, N) → η
  45. CircleSector(D, H, M) → c_1
  46. Dilate(D, If[2.25 < a ≤ 3.25, 3.25 - a, 0], A) → D'_2
  47. Vector(D, D'_2) → w
  48. Translate(c_1, w) → d_1
  49. Rotate(d_1, If[2.25 < a ≤ 3.25, ((a - 2.25) * η), η], D'_2) → e_1
  50. Point(b) → O
  51. Angle(B, A, O) → θ
  52. CircleArc(D, H, M) → h_1
  53. Circle(A, 5) → k_1
  54. Intersect(k_1, b, 2) → Q
  55. Ray(A, Q) → i_1