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Series of Similarity Transformations

Series of Similarity Transformations
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2015-08-09 13:03
SequenceTransformationGeometric Construction
This example demonstrates a series of similarity transformations. It involves core mathematical concepts such as reflection, rotation, and translation. Using GeoGebra commands like Polygon, Intersect, Rotate, Mirror, and Translate, a series of transformations can be constructed. Suitable for students at the junior high school level and above to learn about geometric transformations and similar figures.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D, E) → poly1, a, b, c, d, e
  2. Intersect(xAxis, yAxis) → F
  3. Rotate(A, 180*°, F) → A'
  4. Rotate(B, 180*°, F) → B'
  5. Rotate(C, 180*°, F) → C'
  6. Rotate(D, 180*°, F) → D'
  7. Rotate(E, 180*°, F) → E'
  8. Polygon(A', B', C', D', E') → poly1', a', b', c', d', e'
  9. Mirror(A', xAxis) → A''
  10. Mirror(B', xAxis) → B''
  11. Mirror(C', xAxis) → C''
  12. Mirror(D', xAxis) → D''
  13. Mirror(E', xAxis) → E''
  14. Polygon(A'', B'', C'', D'', E'') → poly1'', a'', b'', c'', d'', e''
  15. Vector(G, H) → u
  16. Translate(A'', u) → A'''
  17. Translate(B'', u) → B'''
  18. Translate(C'', u) → C'''
  19. Translate(D'', u) → D'''
  20. Translate(E'', u) → E'''
  21. Polygon(A''', B''', C''', D''', E''') → poly1''', a''', b''', c''', d''', e'''
  22. Angle(poly1) → ε, α, β, γ, δ
  23. Angle(poly1''') → ζ, η, θ, ι, κ
  24. Angle(E', A', B') → λ
  25. Angle(A', B', C') → μ
  26. Angle(B', C', D') → ν
  27. Angle(C', D', E') → ξ
  28. Angle(D', E', A') → ο
  29. Angle(B, C, D) → ρ
  30. Angle(C, D, E) → σ
  31. Angle(D, E, A) → τ
  32. Angle(E, A, B) → υ
  33. Angle(A, B, C) → ϕ
  34. Vector(I, J) → v
  35. Translate(A', v) → A''_1
  36. Translate(B', v) → B''_1
  37. Translate(C', v) → C''_1
  38. Translate(D', v) → D''_1
  39. Translate(E', v) → E''_1
  40. Polygon(A''_1, B''_1, C''_1, D''_1, E''_1) → poly1''_1, a''_1, b''_1, c''_1, d''_1, e''_1
  41. Mirror(A''_1, j) → A'''_1
  42. Mirror(B''_1, j) → B'''_1
  43. Mirror(C''_1, j) → C'''_1
  44. Mirror(D''_1, j) → D'''_1
  45. Mirror(E''_1, j) → E'''_1
  46. Polygon(A'''_1, B'''_1, C'''_1, D'''_1, E'''_1) → poly2, k_1, l_1, m_1, n_1, o_1
  47. Vector(G_1, H_1) → u_1
  48. Vector(I_1, J_1) → v_1
  49. Vector(K, L) → w
  50. Translate(A, w) → A'_1
  51. Translate(B, w) → B'_1
  52. Translate(C, w) → C'_1
  53. Translate(D, w) → D'_1
  54. Translate(E, w) → E'_1
  55. Polygon(A'_1, B'_1, C'_1, D'_1, E'_1) → poly1'_1, a'_1, b'_1, c'_1, d'_1, e'_1
  56. Mirror(A'_1, xAxis) → A''_4
  57. Mirror(B'_1, xAxis) → B''_4
  58. Mirror(C'_1, xAxis) → C''_4
  59. Mirror(D'_1, xAxis) → D''_5
  60. Mirror(E'_1, xAxis) → E''_5
  61. Polygon(A''_4, B''_4, C''_4, D''_5, E''_5) → poly3, m_2, n_2, o_2, p, q
  62. Rotate(A''_4, 180*°, F) → A'''_2
  63. Rotate(B''_4, 180*°, F) → B'''_2
  64. Rotate(C''_4, 180*°, F) → C'''_2
  65. Rotate(D''_5, 180*°, F) → D'''_2
  66. Rotate(E''_5, 180*°, F) → E'''_2
  67. Polygon(A'''_2, B'''_2, C'''_2, D'''_2, E'''_2) → poly3', m_3, n_3, o_3, p_1, q_1
  68. Rotate(A'_1, -90*°, F) → A''_5
  69. Rotate(B'_1, -90*°, F) → B''_5
  70. Rotate(C'_1, -90*°, F) → C''_5
  71. Rotate(D'_1, -90*°, F) → D''_4
  72. Rotate(E'_1, -90*°, F) → E''_4
  73. Polygon(A''_5, B''_5, C''_5, D''_4, E''_4) → poly4, m_4, n_4, o_4, p_2, q_2
  74. Mirror(A''_5, j) → A'''_3
  75. Mirror(B''_5, j) → B'''_3
  76. Mirror(C''_5, j) → C'''_3
  77. Mirror(D''_4, j) → D'''_3
  78. Mirror(E''_4, j) → E'''_3
  79. Polygon(A'''_3, B'''_3, C'''_3, D'''_3, E'''_3) → poly4', m_5, n_5, o_5, p_3, q_3
  80. Mirror(A, h_1) → A'_2
  81. Mirror(B, h_1) → B'_2
  82. Mirror(C, h_1) → C'_2
  83. Mirror(D, h_1) → D'_2
  84. Mirror(E, h_1) → E'_2
  85. Polygon(A'_2, B'_2, C'_2, D'_2, E'_2) → poly1'_2, a'_2, b'_2, c'_2, d'_2, e'_2
  86. Rotate(A'_2, -90*°, F) → A''_3
  87. Rotate(B'_2, -90*°, F) → B''_3
  88. Rotate(C'_2, -90*°, F) → C''_3
  89. Rotate(D'_2, -90*°, F) → D''_3
  90. Rotate(E'_2, -90*°, F) → E''_3
  91. Polygon(A''_3, B''_3, C''_3, D''_3, E''_3) → poly5, m_6, n_6, o_6, p_4, q_4
  92. Vector(M, O) → r
  93. Translate(A''_3, r) → A'''_4
  94. Translate(B''_3, r) → B'''_4
  95. Translate(C''_3, r) → C'''_4
  96. Translate(D''_3, r) → D'''_4
  97. Translate(E''_3, r) → E'''_4
  98. Polygon(A'''_4, B'''_4, C'''_4, D'''_4, E'''_4) → poly5', p_5, q_5, r_1, s, t
  99. Vector(N, P) → w_1
  100. Translate(A'_2, w_1) → A''_2
  101. Translate(B'_2, w_1) → B''_2
  102. Translate(C'_2, w_1) → C''_2
  103. Translate(D'_2, w_1) → D''_2
  104. Translate(E'_2, w_1) → E''_2
  105. Polygon(A''_2, B''_2, C''_2, D''_2, E''_2) → poly6, q_6, r_2, s_1, t_1, u_2
  106. Rotate(A''_2, 180*°, F) → A'''_5
  107. Rotate(B''_2, 180*°, F) → B'''_5
  108. Rotate(C''_2, 180*°, F) → C'''_5
  109. Rotate(D''_2, 180*°, F) → D'''_5
  110. Rotate(E''_2, 180*°, F) → E'''_5
  111. Polygon(A'''_5, B'''_5, C'''_5, D'''_5, E'''_5) → poly6', q_7, r_3, s_2, t_2, u_3
  112. Distance(B, A) → BA
  113. Distance(c'', b'') → a_1
  114. Distance(d, e) → b_1
  115. Distance(e', c) → c_1
  116. Distance(A, B) → distanceAB
  117. Distance(B, C) → distanceBC
  118. Distance(D, C) → distanceDC
  119. Distance(D, E) → distanceDE
  120. Distance(A, E) → distanceAE
  121. Distance(C, D) → distanceCD
  122. Distance(A'', B'') → distanceA''B''
  123. Distance(B'', C'') → distanceB''C''
  124. Distance(C'', D'') → distanceC''D''
  125. Distance(D'', E'') → distanceD''E''
  126. Distance(A'', E'') → distanceA''E''
  127. Perimeter(poly1') → perimeterpoly1'
  128. PointIn(poly1') → Pointpoly1'_1
  129. Perimeter(poly1') → d_1
  130. PointIn(poly1') → Pointpoly1'
  131. Angle(D''_1, E''_1, A''_1) → χ
  132. Angle(E''_1, A''_1, B''_1) → ψ
  133. Angle(A''_1, B''_1, C''_1) → ω
  134. Angle(B''_1, C''_1, D''_1) → α_1
  135. Angle(C''_1, D''_1, E''_1) → β_1
  136. Angle(poly2) → γ_1, δ_1, ε_1, ζ_1, η_1
  137. Angle(E', A', B') → θ_1
  138. Angle(D', E', A') → ι_1
  139. Angle(C', D', E') → κ_1
  140. Angle(B', C', D') → λ_1
  141. Angle(A', B', C') → μ_1