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Parallel四边形 and Related Geometric Transformations Animation

Parallel四边形 and Related Geometric Transformations Animation
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2017-02-10 05:56
PolygonTrigonometryTransformationGeometric Construction
In collections 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
This example demonstrates the construction and transformations of a parallelogram through animation. It involves core mathematical concepts such as properties of parallelograms, similar triangles, unit circle, ellipse, and transformations (rotation, translation, dilation). Construction highlights include commands like Rotate, Angle, Ray, Line, Point, Intersect, Segment, Min, Circle, Dilate, Vector, Polygon, Translate, Midpoint, and CircleSector. Suitable for high school mathematics education to understand geometric transformations and figure properties.

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(B, If[0 < o ≤ 1, 1 - o, 0], A) → A'
  29. Rotate(E, If[1 < o ≤ 2, ((o - 1) * α), α], A) → E'
  30. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], C) → A'_1
  31. Vector(A, A'_1) → u
  32. Segment(A, A'_1) → f_1
  33. Dilate(C, If[2 < o ≤ 3, 3 - o, 0], D) → C'
  34. Vector(C, C') → v
  35. Segment(C, C') → g_1
  36. Dilate(D, If[3 < o ≤ 4, 4 - o, 0], B) → D'
  37. Segment(D, D') → h_1
  38. Polygon(A, B, D, C) → poly1, a_1, b_1, d_2, c_2
  39. Dilate(A, If[5.5 < o ≤ 6.5, 6.5 - o, 0], C) → A'_2
  40. Vector(A, A'_2) → w
  41. Translate(A, w) → A'_3
  42. Translate(A', w) → A''
  43. Dilate(A, If[6.5 < o ≤ 7.5, 7.5 - o, 0], B) → A'_4
  44. Vector(A, A'_4) → u_1
  45. Translate(A, u_1) → A'_5
  46. Translate(A'_1, u_1) → L
  47. Intersect(d, i) → M, N
  48. Intersect(d, g) → O, P
  49. Angle(A, C, N) → β
  50. Rotate(N, If[6.5 < o ≤ 7.5, ((-(o - 6.5)) * β), (-β)], C) → N'
  51. Dilate(C, If[7.5 < o ≤ 8.5, 8.5 - o, 0], B) → C'_1
  52. Vector(C, C'_1) → v_1
  53. Midpoint(A, D) → Q
  54. Dilate(A, If[4.5 < o ≤ 5.5, 5.5 - o, 0], Q) → A'_6
  55. Segment(A, A'_6) → i_1
  56. Dilate(Q, If[5.5 < o ≤ 6.5, 6.5 - o, 0], D) → Q'
  57. Segment(Q, Q') → j_1
  58. Dilate(B, If[6.5 < o ≤ 7.5, 7.5 - o, 0], Q) → B'_1
  59. Segment(B, B'_1) → k_1
  60. Dilate(Q, If[7.5 < o ≤ 8.5, 8.5 - o, 0], C) → Q'_1
  61. Segment(Q, Q'_1) → l_1
  62. Rotate(A, If[8.5 < o ≤ 9.5, ((-(o - 8.5)) * π), (-π)], Q) → A'_7
  63. Rotate(A'_6, If[9.5 < o ≤ 10.5, ((-(o - 9.5)) * π), (-π)], Q) → R
  64. Segment(A'_7, R) → m_1
  65. Rotate(B, If[9.5 < o ≤ 10.5, ((-(o - 9.5)) * π), (-π)], Q) → B'_2
  66. Rotate(B'_1, If[10.5 < o ≤ 11.5, ((-(o - 10.5)) * π), (-π)], Q) → S
  67. Segment(B'_2, S) → n_1
  68. Line(A, B) → p_1
  69. Intersect(e, p_1) → T, U
  70. Ray(A, T) → q_1
  71. Intersect(e, f_1) → V,
  72. Intersect(d, i, 1) → W
  73. Ray(C, W) → r_1
  74. Segment(B, A') → t
  75. Rotate(V, If[11 < o ≤ 12, ((o - 11) * (π - α)), π - α], A) → V'
  76. CircleSector(A, V, V') → c_1
  77. Dilate(A, If[12 < o ≤ 13, 13 - o, 0], C) → A'_8
  78. Vector(A, A'_8) → w_1
  79. Translate(c_1, w_1) → d_1
  80. Dilate(C, If[13 < o ≤ 14, 14 - o, 0], D) → C'_2
  81. Vector(C, C'_2) → e_1
  82. Translate(d_1, e_1) → s_1