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动画演示：三角形的角平分线

动画演示：三角形的角平分线
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2016-06-16 07:48
测试改名0角变换几何作图滑块动画
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 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2
这个范例演示了三角形的角平分线。核心数学概念包括三角形的角平分线性质。通过使用GeoGebra命令如Ray, Point, Angle, Circle, Intersect等，可以构造出一个动态的三角形角平分线模型。适合初中及以上学生学习几何变换和三角形性质。

GeoGebra 命令及参数

  1. Ray(A, B) → a
  2. Ray(B, C) → b
  3. Ray(C, A) → c
  4. Point(a) → D_1
  5. Point(b) → E_1
  6. Point(c) → F_1
  7. Ray(A, F_1) → d
  8. Ray(B, D_1) → e
  9. Ray(C, E_1) → f
  10. Point(e) → D
  11. Point(f) → E
  12. Point(d) → F
  13. Angle(B, A, C) → α
  14. Angle(C, B, A) → β
  15. Angle(A, C, B) → γ
  16. Angle(F, A, B) → δ
  17. Angle(D, B, C) → ε
  18. Angle(E, C, A) → ζ
  19. Circle(A, 1.5) → g
  20. Circle(B, 1.5) → h
  21. Circle(C, 1.5) → k
  22. Intersect(g, c, 1) → G
  23. Intersect(g, a, 1) → H
  24. Intersect(g, c, 2) → I
  25. Intersect(h, b, 1) → J
  26. Intersect(h, a, 1) → K
  27. Intersect(h, a, 2) → L
  28. Intersect(k, b) → M, N
  29. Intersect(k, c) → O,
  30. CircleSector(A, H, G) → p
  31. CircleSector(B, J, K) → q
  32. CircleSector(C, O, M) → r
  33. CircleSector(C, N, O) → s
  34. CircleSector(B, L, J) → t
  35. CircleSector(A, I, H) → c_1
  36. Line(C, a) → i
  37. Vector(B, C) → u
  38. Vector(A, C) → v
  39. Translate(q, u) → q'
  40. Dilate(C, If[0 < j ≤ 1, j, 0], B) → C'
  41. Vector(B, C') → w
  42. Translate(q, w) → q'_1
  43. Mirror(q', C) → q''
  44. Dilate(A, If[2 < j ≤ 3, 3 - j, 0], C) → C'_1
  45. Vector(A, C'_1) → m
  46. Translate(p, m) → p'
  47. Dilate(C, If[0 < n ≤ 1, n, 0], B) → C'_2
  48. Dilate(A, If[1 < n ≤ 2, 2 - n, 0], C) → A'
  49. Vector(B, C'_2) → u_1
  50. Vector(A, A') → v_1
  51. If(0 < n ≤ 1, Translate[t, u_1], Translate[t, u]) → e_1
  52. If(1 < n ≤ 2, Translate[c_1, v_1], Translate[c_1, v]) → f_1
  53. Polygon(A, B, C) → poly1, c_2, a_2, b_1
  54. Line(A, B) → g_1
  55. Point(i) → P
  56. Point(i) → Q
  57. Angle(A, C, B) → η
  58. CircleSector(C, M, O) → p_1
  59. CircleSector(B, K, J) → q_1
  60. CircleSector(A, G, H) → r_1
  61. Translate(q_1, w) → s_1
  62. Translate(q_1, w) → t_1
  63. Vector(B, C) → w_1
  64. Translate(q_1, w_1) → e_2
  65. Rotate(e_2, 180°, C) → f_2
  66. Translate(r_1, m) → g_2
  67. CircleSector(C, O, N) → k_2
  68. CircleSector(B, J, L) → p_2
  69. CircleSector(A, H, I) → q_2
  70. Translate(p_2, u_1) → r_2
  71. Translate(p_2, u) → s_2
  72. Translate(q_2, v_1) → t_2
  73. Translate(q_1, u) → d_2
  74. Translate(q_1, w) → c_3
  75. Translate(A, w) → A'_1
  76. Translate(B, w) → B'
  77. Translate(C, w) → C'_3
  78. Polygon(A'_1, B', C'_3) → poly1', c'_3, a'_1, b'
  79. Translate(A, w_1) → A'_2
  80. Translate(B, w_1) → B'_1
  81. Translate(C, w_1) → C'_4
  82. Polygon(A'_2, B'_1, C'_4) → poly1'_1, c'_4, a'_2, b'_1
  83. Segment(C'_3, A'_1) → l
  84. Segment(A'_1, B') → l_1
  85. Segment(B', C'_3) → m_1
  86. Segment(C'_4, A'_2) → n_1
  87. Segment(A'_2, C'_3) → b_2
  88. Segment(C'_3, C'_4) → i_2
  89. Rotate(d_2, (((j - 1) * 180))°, C) → h_2
  90. Translate(r_1, m) → d_3
  91. Translate(A, m) → A'_3
  92. Translate(B, m) → B'_2
  93. Translate(C, m) → C'_5
  94. Polygon(A'_3, B'_2, C'_5) → poly1'_2, c'_5, a'_3, b'_2
  95. Segment(B'_2, C'_5) → i_1
  96. Segment(C'_5, A'_3) → j_1
  97. Segment(A'_3, B'_2) → k_1
  98. Line(A, C) → j_2
  99. Intersect(k, j_2) → R, S
  100. Rotate(S, (((j - 3) * 180))°, C) → S'
  101. CircleArc(C, S, S') → e_3
  102. Segment(A, B) → l_2
  103. Segment(B, C) → m_2
  104. Segment(A, C) → n_2
  105. Translate(q, w) → d_1
  106. Translate(q, u) → q'_2
  107. Rotate(q'_2, If[1 < j ≤ 2, (((-(j - 1)) * 180))°, 180°], C) → p''
  108. Translate(p, m) → p'_1
  109. Rotate(S, (((-(j - 3)) * 180))°, C) → S'_1
  110. CircleArc(C, S'_1, S) → f_3
  111. Ray(C, A) → a_3