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等边三角形的尺规作图

等边三角形的尺规作图
几何画板及绘图内容加载中，请稍等……
2017-02-18 03:18
测试改名0圆几何作图
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 Constructions (Dynamic Illustrations)
本示例演示如何使用圆规和直尺构造等边三角形。核心数学概念包括几何作图和变换。通过使用Dilate（缩放）、Segment（线段）、Circle（圆）、Rotate（旋转）等GeoGebra命令，可以动态地修改三角形的边长。适合初中及以上学生学习几何作图和变换。

GeoGebra 命令及参数

  1. Dilate(A, If[0 < b ≤ 1, 1 - b, 0], B) → A'
  2. Segment(A, A') → f
  3. Circle(A, B) → c
  4. Circle(B, A) → d
  5. Rotate(B, If[1 < b ≤ 2, (((b - 1) * 2) * π), (2 * π)], A) → B'
  6. CircleArc(A, B, B') → e
  7. Intersect(c, d, 1) → C
  8. Intersect(c, d, 2) → D
  9. Rotate(A, If[1 < b ≤ 2, (((b - 1) * 2) * π), (2 * π)], A) → A'_1
  10. Rotate(A', If[1 < b ≤ 2, (((b - 1) * 2) * π), (2 * π)], A) → A''
  11. Segment(A'_1, A'') → f'
  12. Rotate(A, If[2.5 < b ≤ 3.5, (((b - 2.5) * 2) * π), (2 * π)], B) → A'_2
  13. CircleArc(B, A, A'_2) → g
  14. Rotate(B, If[3.5 < b ≤ 4.5, ((b - 3.5) * π / 3), π / 3], A) → B'_1
  15. Rotate(A, If[3.5 < b ≤ 4.5, ((b - 3.5) * π / 3), π / 3], A) → A'_3
  16. Rotate(A', If[3.5 < b ≤ 4.5, ((b - 3.5) * π / 3), π / 3], A) → A''_1
  17. Segment(A'_3, A''_1) → f'_1
  18. Rotate(A, If[4.5 < b ≤ 5.5, ((-(b - 4.5)) * π / 3), ((-π)) / 3], B) → A'_4
  19. Rotate(A', If[4.5 < b ≤ 5.5, ((-(b - 4.5)) * π / 3), ((-π)) / 3], B) → A''_2
  20. Segment(A'_4, A''_2) → f'_2
  21. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  22. Rotate(A, If[2.5 < b ≤ 3.5, (((b - 2.5) * 2) * π), (2 * π)], B) → A'_5
  23. Rotate(A', If[2.5 < b ≤ 3.5, (((b - 2.5) * 2) * π), (2 * π)], B) → A''_3
  24. Segment(A'_5, A''_3) → f'_3