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探究外错角

探究外错角
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2016-11-07 17:14
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 Parallel Lines & Related Angles Parallel Lines & Related Angles
当平行线被截线所截时，外错角相等。本范例通过动态几何软件GeoGebra，演示了外错角的性质。核心数学概念包括角的性质和几何作图。使用了Point, Line, Rotate, Angle, Circle, Intersect, Segment, Vector, Ray, CircleArc, CircleSector, Translate等命令。适合初中及以上学生学习几何。

GeoGebra 命令及参数

  1. Point(y = 0) → A
  2. Line(A, B) → f
  3. Rotate(B, α, A) → B'
  4. Angle(B, A, B') → γ
  5. Line(A, B') → g
  6. Rotate(B', β, A) → B''
  7. Angle(B', A, B'') → δ
  8. Line(A, B'') → h
  9. Circle(A, a) → c
  10. Intersect(c, h, 2) → C
  11. Line(C, g) → i
  12. Circle(C, A) → d
  13. Circle(A, C) → e
  14. Intersect(e, h, 2) → J
  15. Segment(A, C) → j
  16. Circle(A, (0.3 * j)) → k
  17. Circle(C, (0.3 * j)) → p
  18. Intersect(p, h) → N, O
  19. Intersect(k, h) → P, Q
  20. Intersect(k, g) → T, U
  21. Intersect(p, i, 2) → V
  22. Intersect(p, i, 1) → W
  23. Circle(C, j / 2) → g_1
  24. Circle(A, j / 2) → h_1
  25. Intersect(g_1, i, 2) → D
  26. Intersect(g_1, i, 1) → E
  27. Intersect(g_1, h, 2) → H
  28. Intersect(g_1, h) → I, Z
  29. Intersect(h_1, h) → A_1, B_1
  30. Intersect(h_1, g) → E_1, F_1
  31. Point(j) → G_1
  32. Vector(A, G_1) → u
  33. Segment(A, G_1) → l
  34. Ray(A, A_1) → m
  35. Ray(C, H) → n
  36. Vector(A, G_1) → v
  37. Segment(G_1, C) → s
  38. CircleArc(C, N, O) → r
  39. Point(r) → F
  40. Rotate(F, (-δ), C) → F'
  41. Angle(F', C, F) → ε
  42. Segment(A, C) → b
  43. CircleSector(A, P, U) → d_1
  44. Translate(d_1, v) → e_1
  45. CircleArc(C, W, V) → f_1
  46. Point(f_1) → G
  47. Rotate(G, (-(π - ε)), C) → G'
  48. Angle(G', C, G) → ζ
  49. CircleSector(C, G', G) → k_1
  50. CircleArc(A, P, U) → q
  51. Segment(A, C) → t

AI 绘图提示语参考

画两条平行线，一条横线穿过它们，形成外错角。用圆和交点标记角度，展示外错角相等。旋转和构造辅助线段，验证角度关系。添加弧线和扇形，强调几何性质。
以上提示语为根据原始绘图命令整理而来，仅供参考。