积极 AI Logo 积极 AI

等边三角形特殊性质演示

等边三角形特殊性质演示
几何画板及绘图内容加载中，请稍等……
2016-07-04 05:49
测试改名0圆多边形角几何作图
所属专题 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
①本范例演示等边三角形的特殊性质与动态变化；②涉及核心数学概念包括角度、等边三角形构造、旋转、缩放、交点计算等；③构造过程中运用了Segment（线段）、Rotate（旋转）、Dilate（缩放）、Intersect（交点）等GeoGebra命令与对象；④适合高中数学教学，用于理解几何变换与多边形性质。

GeoGebra 命令及参数

  1. Segment(A, B) → l
  2. Point(l) → L
  3. Segment(L, B) → f_1
  4. Segment(A, L) → n
  5. Rotate(B, π / 3, A) → B'_2
  6. Segment(B'_2, L) → m
  7. Min(list1) → o
  8. Polygon(A, B, 3) → poly1, a, b, c, C
  9. Dilate(A, If[0 < d ≤ 1, 1 - d, 0], B) → A'
  10. Segment(A, A') → e
  11. Dilate(B, If[1 < d ≤ 2, 2 - d, 0], C) → B'
  12. Segment(B, B') → f
  13. Dilate(C, If[2 < d ≤ 3, 3 - d, 0], A) → C'
  14. Segment(C, C') → g
  15. Segment(A, B) → h
  16. Segment(A, C) → i
  17. Circle(A, (0.35 * o)) → k
  18. Segment(B, C) → j
  19. Intersect(k, i, 1) → D
  20. Intersect(k, h, 1) → E
  21. CircleSector(A, E, D) → p
  22. Rotate(A, If[3.5 < d ≤ 4.5, ((d - 3.5) * π / 3), 1.0471975511965976], A) → A'_1
  23. Rotate(A', If[3.5 < d ≤ 4.5, ((d - 3.5) * π / 3), 1.0471975511965976], A) → A''
  24. Segment(A'_1, A'') → e'
  25. Rotate(A, If[4.5 < d ≤ 5.5, ((-(d - 4.5)) * π / 3), -1.0471975511965976], B) → A'_2
  26. Rotate(A', If[4.5 < d ≤ 5.5, ((-(d - 4.5)) * π / 3), -1.0471975511965976], B) → A''_1
  27. Segment(A'_2, A''_1) → e'_1
  28. Dilate(A, If[6 < d ≤ 7, 7 - d, 0], B) → A'_3
  29. Vector(A, A'_3) → u
  30. Translate(p, u) → p'
  31. Rotate(p', If[7 < d ≤ 8, (((d - 7) * 2) * π / 3), 2.0943951023931953], B) → p''
  32. Circle(B, (0.15 * h)) → r
  33. Intersect(f, e'_1) → G
  34. Intersect(f, e'_1) → H
  35. Intersect(f, e'_1) → I
  36. Intersect(f, e'_1) → J
  37. Intersect(r, j, 1) → F
  38. Intersect(r, h, 1) → K
  39. Dilate(B, If[8 < d ≤ 9, 9 - d, 0], C) → B'_1
  40. Vector(B, B'_1) → v
  41. Translate(p'', v) → p'''
  42. Rotate(p''', If[9 < d ≤ 10, (((d - 9) * 2) * π / 3), 2.0943951023931953], C) → t
  43. Line(A, B) → g_1
  44. Point(g_1) → M
  45. Ray(B, M) → h_1
  46. Point(h_1) → N
  47. Ray(B, N) → i_1
  48. Sort(list1) → list2
  49. Circle(N, Element[list2, 2]) → c_1
  50. Circle(N, Element[list2, 1]) → d_1
  51. Dilate(B'_2, If[10 < d ≤ 11, 11 - d, 0], L) → Q
  52. Segment(B'_2, Q) → n_1
  53. Segment(A, L) → p_1
  54. Segment(L, B) → q_1
  55. Circle(N, Element[list2, 3]) → e_1
  56. Intersect(e_1, i_1, 1) → O
  57. Circle(N, p_1) → k_1
  58. Circle(O, q_1) → r_1
  59. Intersect(k_1, r_1, 1) → P
  60. Segment(N, P) → j_1
  61. Segment(P, O) → l_1
  62. Segment(O, N) → m_1
  63. Rotate(N, π / 3, P) → N'
  64. Angle(N, P, N') → α
  65. Ray(P, N') → s
  66. Dilate(L, If[11.5 < d ≤ 12.5, 12.5 - d, 0], N) → L'
  67. Vector(L, L') → w
  68. Translate(B'_2, w) → R
  69. Translate(Q, w) → Q'
  70. Segment(R, Q') → s_1
  71. Angle(B, L, B'_2) → β
  72. Rotate(R, If[11 < d ≤ 12, ((-(d - 11)) * β), (-β)], Q') → R'
  73. Rotate(Q', If[11 < d ≤ 12, ((-(d - 11)) * β), (-β)], Q') → Q''
  74. Rotate(R, If[11.5 < d ≤ 12.5, ((-(d - 11.5)) * β), (-β)], L') → R'_1
  75. Rotate(Q', If[11.5 < d ≤ 12.5, ((-(d - 11.5)) * β), (-β)], L') → Q''_1
  76. Segment(R'_1, Q''_1) → t_1
  77. Dilate(L, If[12.5 < d ≤ 13.5, 13.5 - d, 0], P) → L'_1
  78. Vector(L, L'_1) → u_1
  79. Translate(A, u_1) → A'_4
  80. Translate(L, u_1) → L'_2
  81. Segment(A'_4, L'_2) → a_1
  82. Line(P, N) → b_1
  83. Line(L, b_1) → f_2
  84. Point(f_2) → S
  85. Angle(A, L, S) → γ
  86. Rotate(A'_4, If[12.5 < d ≤ 13.5, ((d - 12.5) * γ), γ], L'_2) → T
  87. Rotate(L'_2, If[12.5 < d ≤ 13.5, ((d - 12.5) * γ), γ], L'_2) → U
  88. Segment(T, U) → g_2
  89. Dilate(B, If[13.5 < d ≤ 14.5, 14.5 - d, 0], P) → B'_3
  90. Vector(B, B'_3) → v_1
  91. Translate(L, v_1) → L'_3
  92. Translate(B, v_1) → B'_4
  93. Segment(L'_3, B'_4) → h_2
  94. Line(P, O) → i_2
  95. Line(B, i_2) → j_2
  96. Point(j_2) → V
  97. Angle(V, B, A) → δ
  98. Rotate(L'_3, If[13.5 < d ≤ 14.5, ((-(d - 13.5)) * δ), (-δ)], B'_4) → W
  99. Rotate(B'_4, If[13.5 < d ≤ 14.5, ((-(d - 13.5)) * δ), (-δ)], B'_4) → Z
  100. Segment(W, Z) → k_2
  101. Polygon(N, O, P) → poly2, p_2, n_2, o_1
  102. Dilate(B, If[15 < d ≤ 16, 16 - d, 0], P) → B'_5
  103. Vector(B, B'_5) → q
  104. Translate(p'', q) → p'''_1
  105. Line(B, s) → l_2
  106. Point(l_2) → A_1
  107. Angle(A_1, B, L) → ε
  108. Rotate(p'''_1, If[16 < d ≤ 17, ((-(d - 16)) * ε), (-ε)], B'_5) → c_2
  109. Angle(N, P, N') → ζ
  110. Dilate(B, If[17 < d ≤ 18, 18 - d, 0], P) → B'_6
  111. Vector(B, B'_6) → w_1
  112. Translate(p'', w_1) → p'''_2
  113. Rotate(p'''_2, If[18 < d ≤ 19, ((-(d - 18)) * (ε - π / 3)), (-(ε - π / 3))], P) → d_2
  114. Angle(N', P, O) → η
  115. Dilate(A, If[10 < d ≤ 11, 11 - d, 0], L) → A'_5
  116. Segment(A, A'_5) → m_2
  117. Dilate(B, If[10 < d ≤ 11, 11 - d, 0], L) → B'_7
  118. Segment(B, B'_7) → q_2