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Dynamic Illustration of Congruent Figures

Dynamic Illustration of Congruent Figures
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2017-04-19 21:09
TriangleVectorTransformationGeometric Construction
In collections Congruence (CO) Cluster CCSS High School: Geometry (Congruence) Volume 1
This example dynamically illustrates the definition of what it means for any two figures (triangles in this case) to be congruent. It involves core concepts like congruence, translation, rotation, and reflection. Constructed using commands such as Segment, Circle, Point, Angle, Rotate, Ray, Intersect, Line, Dilate, Vector, Polygon, Translate, If, Mirror in GeoGebra. Suitable for high school mathematics teaching or geometric concept learning.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(B, C) → b
  3. Segment(C, A) → c
  4. Circle(D, (k * a)) → d
  5. Point(d) → E
  6. Segment(D, E) → e
  7. Circle(E, (k * b)) → f
  8. Angle(A, B, C) → α
  9. Rotate(D, α, E) → D'
  10. Angle(D, E, D') → β
  11. Ray(E, D') → g
  12. Intersect(f, g, 1) → F
  13. Angle(C, A, B) → γ
  14. Rotate(E, (-γ), D) → E'
  15. Angle(E', D, E) → δ
  16. Ray(D, E') → h
  17. Segment(D, E') → i
  18. Segment(E', E) → j
  19. Line(E, D') → l
  20. Line(E, D') → n
  21. Circle(D, (k * c)) → p
  22. Ray(D, E') → m
  23. Intersect(p, m, 1) → G
  24. Segment(E, G) → q
  25. Segment(D, G) → r
  26. Dilate(D, If[0 < s ≤ 1, 1 - s], A) → D'_1
  27. Vector(D, D'_1) → u
  28. Polygon(A, C, B) → poly1, b_1, a_1, c_1
  29. Polygon(D, E, G) → poly2, g_1, d_1, e_1
  30. Translate(D, u) → D'_2
  31. Translate(E, u) → E'_1
  32. Translate(G, u) → G'
  33. Polygon(D'_2, E'_1, G') → poly2', g', d'_2, e'_1
  34. Vector(D, A) → v
  35. Translate(D, v) → D'_3
  36. Translate(E, v) → E'_2
  37. Translate(G, v) → G'_1
  38. Polygon(D'_3, E'_2, G'_1) → poly2'_1, g'_1, d'_3, e'_2
  39. Segment(D'_1, G') → t
  40. Segment(E'_1, D'_1) → h_1
  41. Segment(A, G'_1) → i_1
  42. Segment(G'_1, E'_2) → j_1
  43. Segment(E'_2, A) → k_1
  44. Angle(C, A, E'_2) → ε
  45. If(ε > γ, ε - γ, γ - ε) → ζ
  46. Rotate(D'_3, If[1 < s ≤ 2, ((-(s - 1)) * ζ), (-ζ)], A) → H
  47. Rotate(E'_2, If[1 < s ≤ 2, ((-(s - 1)) * ζ), (-ζ)], A) → I
  48. Rotate(G'_1, If[1 < s ≤ 2, ((-(s - 1)) * ζ), (-ζ)], A) → J
  49. Polygon(H, I, J) → poly3, j_2, h_2, i_2
  50. Segment(A, J) → l_1
  51. Segment(A, I) → m_1
  52. Segment(I, J) → n_1
  53. Dilate(J, If[2 < s ≤ 3, 3 - s, 0], C) → J'
  54. Dilate(I, If[2 < s ≤ 3, 3 - s, 0], B) → I'
  55. Segment(I', J') → p_1
  56. Angle(A, I, J) → θ
  57. Angle(D'_2, E'_1, G') → ι
  58. Angle(J, A, I) → λ
  59. Angle(G', D'_1, E'_1) → μ
  60. Polygon(A, J', I') → poly4, i', a_2, j'
  61. Segment(G'_1, E'_2) → q_1
  62. Segment(G', E'_1) → f_1
  63. Rotate(D'_3, ((s - 1) * ζ), A) → K
  64. Rotate(D'_3, If[1 < s ≤ 2, ((s - 1) * ζ), ζ], A) → L
  65. Rotate(E'_2, If[1 < s ≤ 2, ((s - 1) * ζ), ζ], A) → M
  66. Rotate(G'_1, If[1 < s ≤ 2, ((s - 1) * ζ), ζ], A) → N
  67. Polygon(L, M, N) → poly5, n_2, l_2, m_2
  68. Dilate(M, If[2 < s ≤ 3, 3 - s, 0], B) → M'
  69. Dilate(N, If[2 < s ≤ 3, 3 - s, 0], C) → N'
  70. Segment(M', N') → r_1
  71. Polygon(A, M', N') → poly6, n', a_3, m'
  72. Angle(A, M', N') → ο
  73. Angle(A, M, N) → ρ
  74. Segment(A, M) → t_1
  75. Segment(M, N) → b_2
  76. Segment(A, N) → c_2
  77. Angle(B, A, C) → σ
  78. Angle(G, E, D) → τ
  79. Angle(N, M, A) → υ
  80. Angle(N', M', A) → ϕ
  81. Line(E, G) → s_1
  82. Mirror(D, q) → D'_4
  83. Mirror(E, q) → E'_3
  84. Mirror(G, q) → G'_2
  85. Polygon(D'_4, E'_3, G'_2) → poly2'_2, g'_2, d'_4, e'_3
  86. Segment(E, D'_4) → f_2
  87. Segment(D'_4, G) → g_2