积极 AI Logo 积极 AI

探索平行线内错角

探索平行线内错角
几何画板及绘图内容加载中，请稍等……
2016-03-20 08:42
角几何作图滑块动画
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 Angle Congruence Intros
①本范例演示通过旋转角度180度，探究平行线内错角的相等关系；②涉及核心数学概念：平行线、内错角、旋转对称；③作图要点：使用GeoGebra命令如Point, Rotate, Angle, Line, Circle, Intersect, CircleSector, Dilate, Vector, Translate, CircleArc, Midpoint, Segment, Ray等构建图形；④适合初中及以上学生，用于理解平行线性质与几何变换。

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(t, u) → t'
  20. CircleArc(A, E, G) → c_1
  21. CircleArc(A, G, D) → f_1
  22. CircleArc(C, J, H) → h_1
  23. Vector(A, C) → v
  24. Midpoint(C, A) → L
  25. Rotate(q, (((-i) * 180))°, L) → q'
  26. Rotate(A, (((-i) * 180))°, L) → A'_1
  27. Segment(L, A'_1) → g
  28. Segment(C, L) → n
  29. Segment(L, A) → s
  30. Point(b) → M
  31. Point(b) → N
  32. Ray(C, M) → a_1
  33. Ray(A, N) → b_1
  34. Rotate(E, (((-i) * 180))°, L) → E'
  35. Ray(A'_1, E') → d_1
  36. Circle(A'_1, Distance[L, A'_1]) → e_1
  37. Intersect(e_1, d_1, 1) → O
  38. Segment(A'_1, O) → g_1
  39. Rotate(r, ((i * 180))°, L) → r'_2
  40. Rotate(A, ((i * 180))°, L) → A'_2
  41. Rotate(D, ((i * 180))°, L) → D'
  42. Segment(L, A'_2) → h
  43. Circle(A'_2, L) → k_1
  44. Ray(A'_2, D') → i_1
  45. Intersect(k_1, i_1) → P,
  46. Segment(A'_2, P) → j_1

AI 绘图提示语参考

画两条平行线，并在线上取一点，旋转该点180度得到另一点，连接这两点形成一条直线。以第一条线上的点为圆心画圆，与第二条线相交于两点。分别以这两点为圆心画圆，与第一条线相交于四点。连接这些点形成多个扇形，并旋转其中一个扇形180度，观察其与原扇形的关系。再以圆心为基点，将扇形按比例缩放，并画出对应的射线和圆弧，展示平行线和旋转对称的性质。
以上提示语为根据原始绘图命令整理而来，仅供参考。