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内错角定理演示 (V3)

内错角定理演示 (V3)
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2016-02-05 09:37
角向量变换几何作图
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 Geometry: Parallel Lines & Related Angles Angle Congruence Intros
① 本范例动态演示两条平行线被一条截线所截时形成的内错角相等的几何现象。② 核心概念包括内错角定理、平行线判别、角的度量与全等、向量平移与旋转变换。③ 作图使用了 Point、Line、Rotate、Translate、Dilate、Vector、Angle、Circle、Intersect、CircleSector、CircleArc 等命令，通过构造点 A、B、C 等对象并应用旋转、平移、缩放生成对应角与辅助圆弧。④ 适用于初中几何（八年级平行线与角）、高中解析几何复习以及 GeoGebra 教学演示与自主探究。

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, E, G) → q
  15. CircleSector(A, G, D) → r
  16. CircleSector(A, F, E) → t
  17. Dilate(A, If[0 < i < 1, 1 - i], C) → A'
  18. Vector(A, A') → u
  19. Translate(q, u) → q'
  20. Translate(r, u) → r'
  21. Translate(t, u) → t'
  22. CircleArc(A, E, G) → c_1
  23. CircleArc(A, G, D) → f_1
  24. CircleArc(C, J, H) → h_1
  25. CircleArc(C, H, K) → p_1
  26. Rotate(q', (((-i) * 180))°, A') → q''
  27. Rotate(r', (((-i) * 180))°, A') → r''