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Dynamic Parallelogram & Special Points Demo

Dynamic Parallelogram & Special Points Demo
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2019-10-11 01:17
VectorTrigonometryCoordinate GeometryGeometric Construction
This example dynamically demonstrates the positional relationships and properties of special points within a parallelogram, involving core math concepts like parallelograms, cosine rule, special points (e.g., intersection of diagonals, circumcenter), and probability & statistics (boxplot). Construction utilizes commands such as Rotate, Angle, Ray, Line, Point, Intersect, Segment, Min, Circle, Dilate, CircleSector, Vector, Translate, Polygon, OrthogonalLine, Max, Mirror. Suitable for high school mathematics teaching to explore geometric transformations and dynamic variations of special points in parallelograms.

GeoGebra Commands & Parameters

  1. Rotate(B, a°, A) → B'
  2. Angle(B, A, B') → α
  3. Ray(A, B) → f
  4. Ray(A, B') → g
  5. Line(B, g) → h
  6. Point(g) → C
  7. Line(C, f) → i
  8. Intersect(h, i) → D
  9. Segment(C, D) → j
  10. Segment(A, B) → k
  11. Segment(B, D) → l
  12. Segment(A, C) → m
  13. Min(m, k) → b
  14. Circle(C, (0.2 * b)) → d
  15. Circle(A, (0.2 * b)) → e
  16. Circle(B, (0.2 * b)) → p
  17. Circle(D, (0.2 * b)) → c
  18. Intersect(e, k, 1) → E
  19. Intersect(e, m, 1) → F
  20. Intersect(p, k, 1) → G
  21. Intersect(p, l, 1) → H
  22. Intersect(d, g, 2) → I
  23. Ray(C, I) → q
  24. Intersect(c, h, 2) → J
  25. Ray(D, J) → r
  26. Intersect(c, i, 2) → K
  27. Ray(D, K) → s
  28. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], B) → A'
  29. Segment(A, A') → t
  30. Rotate(E, If[1 < o ≤ 2, ((o - 1) * α), α], A) → E'
  31. CircleSector(A, E, E') → c_1
  32. Dilate(A, If[2 < o ≤ 3, 3 - o, 0], C) → A'_1
  33. Vector(A, A'_1) → u
  34. Translate(c_1, u) → d_1
  35. Segment(A, A'_1) → f_1
  36. Dilate(C, If[3 < o ≤ 4, 4 - o, 0], D) → C'
  37. Vector(C, C') → v
  38. Translate(d_1, v) → e_1
  39. Segment(C, C') → g_1
  40. Dilate(D, If[4 < o ≤ 5, 5 - o, 0], B) → D'
  41. Segment(D, D') → h_1
  42. Polygon(A, B, D, C) → poly1, a_1, b_1, d_2, c_2
  43. Dilate(A, If[5.5 < o ≤ 6.5, 6.5 - o, 0], C) → A'_2
  44. Vector(A, A'_2) → w
  45. Translate(A, w) → A'_3
  46. Translate(A', w) → A''
  47. Dilate(A, If[6.5 < o ≤ 7.5, 7.5 - o, 0], B) → A'_4
  48. Vector(A, A'_4) → u_1
  49. Translate(A, u_1) → A'_5
  50. Translate(A'_1, u_1) → L
  51. Intersect(d, i) → M, N
  52. Intersect(d, g) → O, P
  53. Angle(A, C, N) → β
  54. Rotate(N, If[6.5 < o ≤ 7.5, ((-(o - 6.5)) * β), (-β)], C) → N'
  55. Dilate(C, If[7.5 < o ≤ 8.5, 8.5 - o, 0], B) → C'_1
  56. Vector(C, C'_1) → v_1
  57. Line(B, Q) → i_1
  58. OrthogonalLine(C, i_1) → j_1
  59. OrthogonalLine(D, i_1) → l_1
  60. OrthogonalLine(A, i_1) → m_1
  61. Intersect(i_1, m_1) → R
  62. Intersect(i_1, j_1) → S
  63. Intersect(i_1, l_1) → T
  64. Segment(A, R) → n_1
  65. Segment(C, S) → s_1
  66. Segment(D, T) → t_1
  67. Max({n_1, s_1, t_1}) → k_1
  68. Dilate(C, If[7 < o ≤ 8, 8 - o, 0], S) → C'_2
  69. Angle(C, S, R) → γ
  70. Angle(Q, T, D) → ε
  71. Mirror(S, R) → S'
  72. Angle(A, R, S') → δ
  73. Segment(C, C'_2) → p_1
  74. Dilate(A, If[7 < o ≤ 8, 8 - o, 0], R) → A'_6
  75. Segment(A, A'_6) → q_1
  76. Dilate(D, If[7 < o ≤ 8, 8 - o, 0], T) → D'_1
  77. Segment(D, D'_1) → r_1
  78. Dilate(R, If[9 < o ≤ 10, 10 - o, 0], S) → R'
  79. Vector(R, R') → w_1
  80. Translate(A, w_1) → A'_7
  81. Translate(A'_6, w_1) → U
  82. Segment(A'_7, U) → f_2
  83. Dilate(D, If[10 < o ≤ 11, 11 - o, 0], C) → D'_2
  84. Vector(D, D'_2) → u_2
  85. Translate(D, u_2) → D'_3
  86. Translate(D'_1, u_2) → V
  87. Segment(D'_3, V) → g_2
  88. Segment(C, C'_2) → h_2
  89. Segment(A, A'_6) → i_2
  90. Dilate(S, If[9 < o ≤ 10, 10 - o, 0], R) → S'_1
  91. Vector(S, S'_1) → v_2
  92. Translate(C, v_2) → C'_3
  93. Translate(C'_2, v_2) → W
  94. Segment(C'_3, W) → j_2
  95. Dilate(T, If[10 < o ≤ 11, 11 - o, 0], A) → T'
  96. Vector(T, T') → w_2
  97. Translate(D, w_2) → D'_4
  98. Translate(D'_1, w_2) → Z
  99. Segment(D'_4, Z) → k_2
  100. Segment(C, C'_2) → l_2
  101. Segment(D, D'_1) → m_2
  102. Dilate(C, If[9 < o ≤ 10, 10 - o, 0], D) → C'_4
  103. Vector(C, C'_4) → a_2
  104. Translate(C, a_2) → C'_5
  105. Translate(C'_2, a_2) → A_1
  106. Segment(C'_5, A_1) → n_2
  107. Dilate(A, If[10 < o ≤ 11, 11 - o, 0], T) → A'_8
  108. Vector(A, A'_8) → b_2
  109. Translate(A, b_2) → A'_9
  110. Translate(A'_6, b_2) → B_1
  111. Segment(A'_9, B_1) → p_2

AI Drawing Prompt Reference

Draw a dynamic parallelogram to demonstrate the positional relationships and properties of special points like the intersection of diagonals and circumcenter. Rotate a point and draw rays to form the sides of the parallelogram. Calculate angles and use segments, circles, and vectors to mark special points. Show the sides, diagonals, and special points of the parallelogram. Use minimum values and circles to create a boxplot for probability and statistics. Demonstrate the dynamic variations of special points within the parallelogram.
The prompt above was compiled from the original drawing commands and is for reference only.