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Rotation and Symmetry Transformation

Rotation and Symmetry Transformation
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2016-11-06 12:51
AngleTransformationGeometric Construction
In collections 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
This example demonstrates geometric figures through rotation and orthogonal symmetry transformations. Key mathematical concepts include rotation, symmetry, and geometric construction. It uses commands such as Line, OrthogonalLine, Point, Ray, Midpoint, Segment, Circle, Intersect, CircleSector, Polygon, Rotate, Dilate, Angle in GeoGebra. Suitable for middle school and above students to learn geometric transformations.

GeoGebra Commands & Parameters

  1. Line(C, B_1) → a
  2. OrthogonalLine(C, a) → d
  3. OrthogonalLine(B_1, a) → e
  4. Point(d) → C_1
  5. Ray(C, C_1) → c
  6. Point(d) → E
  7. Ray(C, E) → b
  8. Ray(C, B_1) → g
  9. Point(g) → F
  10. Ray(C, F) → h
  11. Point(h) → B
  12. Ray(C, E) → i
  13. Point(i) → A
  14. Midpoint(A, B) → M
  15. Segment(C, A) → j
  16. Segment(C, B) → k
  17. Circle(C, Min[(0.15 * j), (0.15 * k)]) → p
  18. Intersect(p, a, 2) → I
  19. Intersect(p, i, 1) → J
  20. Intersect(p, a, 1) → K
  21. CircleSector(C, J, K) → q
  22. Polygon(C, B, A) → poly1, h_1, a_1, g_1
  23. Rotate(q, If[0 < f ≤ 1, ((-f) * π / 2), -1.5707963267948966], C) → q'
  24. Dilate(B, If[1 < f ≤ 2, 2 - f, 0], M) → G'
  25. Rotate(B, If[2 < f ≤ 3, ((f - 2) * π), 3.141592653589793], M) → G'_1
  26. Rotate(G', If[2 < f ≤ 3, ((f - 2) * π), 3.141592653589793], M) → G''
  27. Angle(A, M, C) → α
  28. Rotate(G'_1, If[3 < f ≤ 4, ((f - 3) * α), α], M) → L
  29. Rotate(G'', If[3 < f ≤ 4, ((f - 3) * α), α], M) → G'''
  30. Rotate(B, 45°, C) → G'_2
  31. Angle(B, C, G'_2) → β
  32. Ray(C, G'_2) → m
  33. Segment(B, A) → n
  34. Intersect(m, n) → D
  35. OrthogonalLine(C, n) → r
  36. Intersect(r, n) → P
  37. Segment(C, P) → s
  38. Segment(C, M) → t
  39. Segment(C, D) → f_1
  40. Circle(P, (0.06 * n)) → c_1
  41. Intersect(c_1, s, 1) → O
  42. Intersect(c_1, n, 2) → P_1
  43. CircleSector(P, P_1, O) → d_1
  44. Dilate(C, If[1 < f ≤ 2, 2 - f, 0], D) → A'
  45. Segment(C, A') → l
  46. Circle(C, Radius[p]) → e_1
  47. Intersect(e_1, f_1) → Q,
  48. Intersect(e_1, j) → R,
  49. CircleSector(C, Q, R) → k_1
  50. Rotate(k_1, If[3 < f ≤ 4, ((-(f - 3)) * π / 4), ((-π)) / 4], C) → p_1
  51. Dilate(C, If[4.5 < f ≤ 5.5, 5.5 - f, 0], P) → A'_1
  52. Segment(C, A'_1) → i_1
  53. Rotate(d_1, If[6.25 < f ≤ 7.25, ((f - 6.25) * π / 2), π / 2], P) → q_1
  54. Dilate(B, If[8 < f ≤ 9, 9 - f, 0], M) → G'_3
  55. Rotate(B, If[9 < f ≤ 10, ((-(f - 9)) * π), (-π)], M) → G'_4
  56. Rotate(G'_3, If[9 < f ≤ 10, ((-(f - 9)) * π), (-π)], M) → S
  57. Dilate(A, If[8 < f ≤ 9, 9 - f, 0], M) → H'
  58. Segment(A, H') → j_1
  59. Angle(A, M, C) → γ
  60. Rotate(A, If[9 < f ≤ 10, ((f - 9) * γ), γ], M) → H'_1
  61. Rotate(H', If[9 < f ≤ 10, ((f - 9) * γ), γ], M) → H''
  62. Segment(H'_1, H'') → l_1
  63. Rotate(H'_1, If[10 < f ≤ 11, ((f - 10) * (π - γ)), π - γ], M) → T
  64. Rotate(H'', If[10 < f ≤ 11, ((f - 10) * (π - γ)), π - γ], M) → H'''
  65. Segment(T, H''') → m_1
  66. Intersect(e_1, s, 1) → U
  67. Intersect(e_1, f_1, 1) → V
  68. CircleSector(C, V, U) → r_1
  69. Angle(V, C, U) → δ
  70. Rotate(r_1, If[11.75 < f ≤ 12.75, ((-(f - 11.75)) * δ), (-δ)], C) → s_1
  71. Segment(A, P) → n_1
  72. Intersect(e_1, l, 1) → W
  73. Intersect(e_1, l_1, 1) → Z
  74. CircleSector(C, W, Z) → t_1
  75. Rotate(t_1, If[11.75 < f ≤ 12.75, ((-(f - 11.75)) * ((2 * π) - δ)), (-((2 * π) - δ))], C) → c_2