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等腰三角形快速构造技巧

等腰三角形快速构造技巧
几何画板及绘图内容加载中，请稍等……
2017-02-17 21:41
测试改名0圆变换几何作图
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 Constructions (Dynamic Illustrations)
本范例演示如何通过尺规作图快速构造等腰三角形。涉及的核心数学概念包括圆、交点、旋转、相似变换等。作图要点提炼自 GeoGebra 命令：使用 Circle（圆）、Intersect（交点）、Rotate（旋转）、Dilate（缩放）等命令，结合 Point（点）、Segment（线段）、Angle（角）、Midpoint（中点）等对象。适合初中及以上学段，用于学习几何作图技巧和变换方法。

GeoGebra 命令及参数

  1. Circle(A, B) → c
  2. Intersect(c, q) → O, P
  3. CircleArc(A, O, P) → d
  4. Point(d) → C
  5. CircleArc(A, C, P) → e
  6. Point(e) → D
  7. Dilate(A, If[0 < j ≤ 1, 1 - j, 0], C) → A'
  8. Segment(A, A') → a
  9. Angle(C, A, D) → α
  10. Rotate(A, If[1 < j ≤ 2, ((j - 1) * α), α], A) → A'_1
  11. Rotate(A', If[1 < j ≤ 2, ((j - 1) * α), α], A) → A''
  12. Segment(A'_1, A'') → a'
  13. Segment(A, C) → b
  14. Segment(C, D) → f
  15. Segment(D, A) → g
  16. Midpoint(f) → E
  17. Segment(A, E) → h
  18. Midpoint(h) → F
  19. Segment(A, F) → i
  20. Segment(F, E) → k
  21. Circle(A, (0.35 * i)) → p
  22. Circle(E, (0.15 * Distance[D, E])) → r
  23. Intersect(r, f, 2) → G
  24. Intersect(r, h, 1) → H
  25. Intersect(r, f, 1) → I
  26. Intersect(p, b, 1) → J
  27. Intersect(p, h, 1) → K
  28. Intersect(p, g, 1) → L
  29. Circle(A, B) → c_1
  30. Dilate(C, If[2 < j ≤ 3, 3 - j, 0], D) → C'
  31. Segment(C, C') → l
  32. Polygon(C, D, A) → poly1, a_1, c_2, d_1
  33. Circle(C, (0.2 * Distance[D, E])) → e_1
  34. Intersect(e_1, b) → M,
  35. Intersect(e_1, f) → N,
  36. Dilate(A, If[3 < j ≤ 4, 4 - j, 0], F) → A'_2
  37. Dilate(F, If[5 < j ≤ 6, 6 - j, 0], E) → F'
  38. Dilate(E, If[6 < j ≤ 7, 7 - j, 0], D) → E'
  39. Rotate(E, If[7 < j ≤ 8, ((j - 7) * π), 3.141592653589793], E) → E'_1
  40. Rotate(E', If[7 < j ≤ 8, ((j - 7) * π), 3.141592653589793], E) → E''
  41. Dilate(C, If[9 < j ≤ 10, 10 - j, 0], D) → C'_1
  42. Vector(C, C'_1) → u
  43. Angle(E, C, A) → β
  44. CircleArc(A, C, A'') → s_1