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Animation 31: Properties of a Rectangle

Animation 31: Properties of a Rectangle
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2016-06-16 11:19
PolygonAngleProbability & StatisticsTransformationGeometric Construction
This example demonstrates the properties of a rectangle, including angles, side lengths, and area. Using GeoGebra commands such as Segment, Angle, and Polygon, the transformation process of the rectangle can be dynamically shown. Suitable for middle and high school students to learn geometric transformations and probability statistics.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Slope(a) → c
  3. OrthogonalLine(A, a) → e
  4. Point(e) → C
  5. Ray(A, C) → d
  6. Point(d) → D
  7. Segment(A, D) → f
  8. Line(D, a) → g
  9. Line(B, f) → h
  10. Intersect(g, h) → E
  11. Segment(D, E) → i
  12. Segment(E, B) → j
  13. Midpoint(A, E) → F
  14. Circle(A, (0.2 * Min[f, i])) → k
  15. Intersect(k, f) → G,
  16. Intersect(k, a, 1) → H
  17. Dilate(A, If[0 < l ≤ 1, 1 - l, 0], B) → A'
  18. Vector(A, A') → u
  19. CircleSector(A, H, G) → p
  20. Translate(p, u) → p'
  21. Rotate(p', If[1 < l ≤ 2, ((l - 1) * π / 2), 1.5707963267948966], B) → p''
  22. Dilate(B, If[2 < l ≤ 3, 3 - l, 0], E) → B'
  23. Vector(B, B') → v
  24. Translate(p'', v) → p'''
  25. Rotate(p''', If[3 < l ≤ 4, ((l - 3) * π / 2), 1.5707963267948966], E) → q
  26. Dilate(E, If[4 < l ≤ 5, 5 - l, 0], D) → E'
  27. Vector(E, E') → w
  28. Translate(q, w) → q'
  29. Rotate(q', If[5 < l ≤ 6, ((l - 5) * π / 2), 1.5707963267948966], D) → q''
  30. Dilate(D, If[6 < l ≤ 7, 7 - l, 0], F) → D'
  31. Vector(D, D') → m
  32. Segment(D, D') → n
  33. Dilate(F, If[7 < l ≤ 8, 8 - l, 0], B) → F'
  34. Segment(F, F') → r
  35. Dilate(A, If[8 < l ≤ 9, 9 - l, 0], F) → A'_1
  36. Segment(A, A'_1) → s
  37. Dilate(F, If[9 < l ≤ 10, 10 - l, 0], E) → F'_1
  38. Segment(F, F'_1) → t
  39. Polygon(A, B, E, D) → poly1, a_1, b_1, e_1, d_1
  40. Angle(E, F, D) → α
  41. Angle(B, A, F) → γ
  42. Angle(F, A, D) → δ
  43. Rotate(F, If[10 < l ≤ 11, ((l - 10) * α), α], F) → F'_2
  44. Rotate(F'_1, If[10 < l ≤ 11, ((l - 10) * α), α], F) → I
  45. Segment(F'_2, I) → t'
  46. Rotate(F'_2, If[11 < l ≤ 12, ((l - 11) * (π - α)), π - α], F) → J
  47. Rotate(I, If[11 < l ≤ 12, ((l - 11) * (π - α)), π - α], F) → I'
  48. Segment(J, I') → t''
  49. Rotate(J, If[12 < l ≤ 13, ((l - 12) * α), α], F) → J'
  50. Rotate(I', If[12 < l ≤ 13, ((l - 12) * α), α], F) → I''
  51. Segment(J', I'') → t'''
  52. Segment(A, F) → c_1
  53. Intersect(k, c_1) → K,
  54. CircleSector(A, H, K) → f_1
  55. CircleSector(A, K, G) → g_1
  56. Dilate(A, If[16 < l ≤ 17, 17 - l, 0], E) → A'_2
  57. Dilate(A, If[16 < l ≤ 17, 17 - l, 0], B) → A'_3
  58. Dilate(A, If[16 < l ≤ 17, 17 - l, 0], D) → A'_4
  59. Vector(A, A'_3) → u_1
  60. Vector(A, A'_2) → v_1
  61. Vector(A, A'_4) → w_1
  62. Translate(f_1, u_1) → h_1
  63. Translate(f_1, v_1) → k_1
  64. Translate(f_1, w_1) → p_1
  65. Rotate(h_1, If[17 < l ≤ 18, ((l - 17) * (π / 2 + δ)), π / 2 + δ], B) → q_1
  66. Rotate(p_1, If[17 < l ≤ 18, ((l - 17) * ((3 * π / 2) + δ)), (3 * π / 2) + δ], D) → r_1
  67. Rotate(k_1, If[17 < l ≤ 18, ((l - 17) * π), 3.141592653589793], E) → s_1
  68. Dilate(A, If[18 < l ≤ 19, 19 - l, 0], E) → A'_5
  69. Dilate(A, If[18 < l ≤ 19, 19 - l, 0], D) → A'_6
  70. Dilate(A, If[18 < l ≤ 19, 19 - l, 0], B) → A'_7
  71. Vector(A, A'_7) → i_1
  72. Vector(A, A'_5) → j_1
  73. Vector(A, A'_6) → l_1
  74. Translate(g_1, l_1) → t_1
  75. Translate(g_1, j_1) → c_2
  76. Translate(g_1, i_1) → d_2
  77. Rotate(d_2, If[19 < l ≤ 20, ((l - 19) * δ), δ], B) → e_2
  78. Rotate(c_2, If[19 < l ≤ 20, ((-(l - 19)) * π), -3.141592653589793], E) → f_2
  79. Rotate(t_1, If[19 < l ≤ 20, ((l - 19) * (π + δ)), π + δ], D) → g_2

AI Drawing Prompt Reference

Draw a rectangle and show its transformation process. First, draw the four sides of the rectangle. Then, use scaling, rotation, and translation to dynamically show how the rectangle transforms. Finally, calculate and display the angles of the rectangle's interior angles.
The prompt above was compiled from the original drawing commands and is for reference only.