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Polygon Transformation and Similarity Animation

Polygon Transformation and Similarity Animation
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2016-06-18 06:00
PolygonVectorCoordinate GeometryTransformationGeometric 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 CCSS High School: Geometry (Congruence) Volume 2
This example demonstrates polygon transformations and similarity through animation, involving core math concepts like polygon construction, similarity transformations, vector operations, and coordinate geometry. Key GeoGebra commands used include Polygon, Dilate, Segment, Rotate, Circle, Intersect, CircleSector, Vector, and Translate. Suitable for high school and above learners to understand dynamic geometric transformations and sequence generation.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  2. Dilate(A, If[0 < e ≤ 1, 1 - e, 0], B) → A'
  3. Segment(A, A') → f
  4. Rotate(A, If[1 < e ≤ 2, ((-(e - 1)) * π / 2), -1.5707963267948966], B) → A'_1
  5. Rotate(A', If[1 < e ≤ 2, ((-(e - 1)) * π / 2), -1.5707963267948966], B) → A''
  6. Segment(A'_1, A'') → f'
  7. Segment(A, B) → g
  8. Segment(B, C) → h
  9. Segment(C, D) → i
  10. Segment(D, A) → j
  11. Circle(C, (0.15 * j)) → k
  12. Circle(B, (0.15 * j)) → p
  13. Circle(A, (0.15 * j)) → q
  14. Circle(D, (0.15 * j)) → r
  15. Segment(A, C) → l
  16. Segment(D, B) → m
  17. Intersect(l, m) → E
  18. Intersect(r, j, 1) → F
  19. Intersect(r, m, 1) → G
  20. Intersect(r, i, 1) → H
  21. Intersect(k, i, 1) → I
  22. Intersect(k, l, 1) → J
  23. Intersect(k, h, 1) → K
  24. Intersect(p, h, 1) → L
  25. Intersect(p, m, 1) → M
  26. Intersect(p, g, 1) → N
  27. Intersect(q, g, 1) → O
  28. Intersect(q, l, 1) → P
  29. Intersect(q, j, 1) → Q
  30. Rotate(A'_1, If[2 < e ≤ 3, ((-(e - 2)) * π / 2), -1.5707963267948966], C) → R
  31. Rotate(A'', If[2 < e ≤ 3, ((-(e - 2)) * π / 2), -1.5707963267948966], C) → A'''
  32. Segment(R, A''') → f''
  33. CircleSector(B, L, N) → s
  34. Rotate(R, If[3 < e ≤ 4, ((-(e - 3)) * π / 2), -1.5707963267948966], D) → R'
  35. Rotate(A''', If[3 < e ≤ 4, ((-(e - 3)) * π / 2), -1.5707963267948966], D) → S
  36. Segment(R', S) → f'''
  37. Dilate(B, If[4 < e ≤ 5, 5 - e, 0], C) → B'
  38. Vector(B, B') → u
  39. Translate(s, u) → s'
  40. Rotate(s', If[5 < e ≤ 6, ((e - 5) * π / 2), 1.5707963267948966], C) → s''
  41. Dilate(C, If[6 < e ≤ 7, 7 - e, 0], D) → C'
  42. Vector(C, C') → v
  43. Translate(s'', v) → s'''
  44. Rotate(s''', If[7 < e ≤ 8, ((e - 7) * π / 2), 1.5707963267948966], D) → t
  45. Dilate(D, If[8 < e ≤ 9, 9 - e, 0], A) → D'
  46. Vector(D, D') → w
  47. Translate(t, w) → t'
  48. Rotate(t', If[9 < e ≤ 10, ((e - 9) * π / 2), 1.5707963267948966], A) → t''
  49. Dilate(A, If[10 < e ≤ 11, 11 - e, 0], E) → A'_2
  50. Segment(A, A'_2) → n
  51. Dilate(E, If[11 < e ≤ 12, 12 - e, 0], C) → E'
  52. Segment(E, E') → a_1
  53. Dilate(D, If[12 < e ≤ 13, 13 - e, 0], E) → D'_1
  54. Segment(D, D'_1) → b_1
  55. Dilate(E, If[13 < e ≤ 14, 14 - e, 0], B) → E'_1
  56. Segment(E, E'_1) → c_1
  57. Rotate(t, If[12 < e ≤ 13, (((e - 12) * 3) * π / 4), 2.356194490192345], D) → t'_1
  58. Dilate(D, If[17 < e ≤ 18, 18 - e, 0], E) → D'_2
  59. Vector(D, D'_2) → u_1
  60. Translate(t'_1, u_1) → d_1
  61. Rotate(E, If[15 < e ≤ 16, ((e - 15) * π / 2), 1.5707963267948966], E) → E'_2
  62. Rotate(E'_1, If[14 < e ≤ 15, ((e - 14) * π / 2), 1.5708], E) → T
  63. Segment(E'_2, T) → e_1
  64. Rotate(E'_2, If[16 < e ≤ 17, ((e - 16) * π / 2), 1.5707963267948966], E) → U
  65. Rotate(T, If[15 < e ≤ 16, ((e - 15) * π / 2), 1.5708], E) → T'
  66. Segment(U, T') → f_1
  67. Rotate(U, If[17 < e ≤ 18, ((e - 17) * π / 2), 1.5707963267948966], E) → U'
  68. Rotate(T', If[16 < e ≤ 17, ((e - 16) * π / 2), 1.5708], E) → T''
  69. Segment(U', T'') → g_1
  70. CircleSector(B, L, M) → h_1
  71. Dilate(B, If[18 < e ≤ 19, 19 - e, 0], C) → B'_1
  72. Dilate(B, If[18 < e ≤ 19, 19 - e, 0], A) → B'_2
  73. Dilate(B, If[18 < e ≤ 19, 19 - e, 0], D) → B'_3
  74. Vector(B, B'_1) → v_1
  75. Vector(B, B'_3) → w_1
  76. Vector(B, B'_2) → i_1
  77. Translate(h_1, v_1) → k_1
  78. Translate(h_1, i_1) → p_1
  79. Translate(h_1, w_1) → q_1
  80. Rotate(k_1, If[19 < e ≤ 20, ((e - 19) * π / 2), 1.5707963267948966], C) → r_1
  81. Rotate(p_1, If[19 < e ≤ 20, (((e - 19) * 3) * π / 2), 4.71238898038469], A) → t_1
  82. Rotate(h_1, If[20.5 < e ≤ 21.5, ((e - 20.5) * π / 4), 0.7853981633974483], B) → c_2
  83. Rotate(r_1, If[20.5 < e ≤ 21.5, ((e - 20.5) * π / 4), 0.7853981633974483], C) → d_2
  84. Rotate(q_1, If[19 < e ≤ 20, ((e - 19) * π), 3.141592653589793], D) → s_1
  85. Rotate(s_1, If[20.5 < e ≤ 21.5, ((e - 20.5) * π / 4), 0.7853981633974483], D) → e_2
  86. Rotate(t_1, If[20.5 < e ≤ 21.5, ((e - 20.5) * π / 4), 0.7853981633974483], A) → f_2