探索AAS/SAA全等条件

探索AAS/SAA全等条件
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2018-11-01 06:06
①本范例演示了通过角-角-边(AAS)或角-角-角(SAA)条件判定三角形全等的几何现象;②涉及的核心数学概念包括全等三角形判定定理、角度测量、线段长度比较、动态几何交互;③作图要点提炼自构造摘要,使用了Circle(圆)、Rotate(旋转)、Ray(射线)、Point(点)、Intersect(交点)、DynamicCoordinates(动态坐标)、Angle(角度)、Segment(线段)、If(条件判断)等GeoGebra命令与对象;④适合高中数学学生学习和理解三角形全等判定定理,也可用于几何作图教学演示。

GeoGebra 命令及参数

  1. Circle(A_2, Side3) → c_1
  2. Circle(A_2, Side2) → d_1
  3. Rotate(A_2, (-Angle1), A_2) → J
  4. Rotate(G, (-Angle1), A_2) → G'
  5. Ray(J, G') → b_1
  6. Point(b_1) → InvC_3
  7. Intersect(d_1, b_1, 1) → C_3
  8. DynamicCoordinates(InvC_3, If[Distance[C_3, InvC_3] < Sticky, x(C_3), x(InvC_3)], If[Distance[C_3, InvC_3] < Sticky, y(C_3), y(InvC_3)]) → C_2''
  9. Ray(A_2, G) → a_1
  10. Intersect(c_1, a_1, 1) → B_4
  11. Point(a_1) → InvB_3
  12. DynamicCoordinates(InvB_3, If[Distance[B_4, InvB_3] < Sticky, x(B_4), x(InvB_3)], If[Distance[B_4, InvB_3] < Sticky, y(B_4), y(InvB_3)]) → B_2
  13. Circle(B_2, 0.1) → e_1
  14. Intersect(e_1, a_1) → K, L
  15. Rotate(K, Angle2, B_2) → K'
  16. Ray(B_2, K') → f_1
  17. Circle(B_2, NonIncSide) → g_1
  18. Intersect(g_1, f_1) → C_2',
  19. Ray(A_3, E) → k
  20. Point(k) → InvB_2
  21. Rotate(E, Angle1, A_3) → E'
  22. Rotate(A_3, Angle1, A_3) → F
  23. Ray(F, E') → k'
  24. Circle(A_3, WrongSide3) → q
  25. Intersect(q, k, 1) → B_5
  26. DynamicCoordinates(InvB_2, If[Distance[B_5, InvB_2] < Sticky, x(B_5), x(InvB_2)], If[Distance[B_5, InvB_2] < Sticky, y(B_5), y(InvB_2)]) → B_3
  27. Circle(B_3, 0.1) → r
  28. Intersect(r, k) → H, I
  29. Rotate(H, (-Angle2), B_3) → H'
  30. Ray(B_3, H') → m
  31. Point(m) → InvC_2
  32. Circle(B_3, WrongSide1) → s
  33. Intersect(s, m, 1) → C_2
  34. DynamicCoordinates(InvC_2, If[Distance[C_2, InvC_2] < Sticky, x(C_2), x(InvC_2)], If[Distance[C_2, InvC_2] < Sticky, y(C_2), y(InvC_2)]) → C_3'
  35. Circle(A_3, NonIncSide) → p
  36. Intersect(p, k', 1) → C_3''
  37. Ray(A_1, A) → a
  38. Circle(A_1, Side3) → c
  39. Intersect(c, a, 1) → B
  40. Point(a) → InvB
  41. DynamicCoordinates(InvB, If[Distance[B, InvB] < Sticky, x(B), x(InvB)], If[Distance[B, InvB] < Sticky, y(B), y(InvB)]) → B_1
  42. Rotate(A_1, Angle1, A_1) → C_1
  43. Rotate(A, Angle1, A_1) → A'
  44. Ray(C_1, A') → a'
  45. Circle(A_1, Side2) → d
  46. Intersect(d, a', 1) → C
  47. Point(a') → InvC
  48. DynamicCoordinates(InvC, If[Distance[C, InvC] < Sticky, x(C), x(InvC)], If[Distance[C, InvC] < Sticky, y(C), y(InvC)]) → C_1'
  49. Circle(B_1, NonIncSide) → e
  50. Angle(B_1, A_1, C_1') → α
  51. Segment(A_1, B_1) → f
  52. Segment(A_1, C_1') → g
  53. Point(f) → D
  54. Rotate(D, (-Angle2), B_1) → D'
  55. Ray(B_1, D') → b
  56. Circle(B_1, NonIncSide) → h
  57. Intersect(h, b, 1) → C_1''
  58. Segment(B_1, C_1'') → i
  59. Angle(C_1'', B_1, A_1) → β
  60. If(Distance[C_1', C_1''] < 0.2, Polygon[A_1, B, C]) → poly1
  61. If(Distance[C_3', C_3''] < 0.2, Polygon[A_3, B_5, C_3'']) → poly2
  62. Segment(A_3, C_3'') → l
  63. Angle(B_5, A_3, C_3'') → γ
  64. Angle(C_2, B_3, A_3) → δ
  65. Segment(A_3, B_3) → n
  66. Segment(B_3, C_3') → t
  67. Angle(C_3, A_2, B_4) → ε
  68. Angle(A_2, B_2, C_2') → ζ
  69. Segment(A_2, B_2) → h_1
  70. If(Distance[C_2', C_2''] < 0.2, Polygon[A_2, B_2, C_2'']) → poly3
  71. Segment(B_2, C_2') → i_1
  72. Segment(C_2'', A_2) → j_1

AI 绘图提示语参考

画两个三角形,展示 AAS 或 SAA 全等条件。首先画一个圆和一条线段,以其中一个顶点为圆心,线段为半径画圆。旋转其中一个角,得到第二个顶点。连接顶点,交点处画圆,再交点处画线段。动态显示交点坐标。重复此过程画第二个三角形,展示全等关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。