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Triangle Congruence Demo by Mr. Krebs

Triangle Congruence Demo by Mr. Krebs
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2014-02-06 10:45
TriangleAngleComplex NumberTransformationGeometric Construction
In collections Triangle Congruence - Collection Triangle congruence
This example demonstrates the criteria and properties of triangle congruence. It involves core mathematical concepts such as congruence, geometric transformations, reflection, angles, and ratios. The construction uses commands like Polygon, Circle, Point, Segment, Intersect, Angle, Rotate, and Ray in GeoGebra to illustrate congruence relationships through rotation and reflection. Suitable for high school mathematics education to understand congruence theorems and practical constructions.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Circle(A, B) → d
  3. Circle(C, B) → e
  4. Circle(D, c) → f
  5. Point(Circle[D, abs(b)]) → F
  6. Segment(D, F) → g
  7. Circle(F, a) → h
  8. Intersect(h, f) → E_1, G, ,
  9. Polygon(D, F, G) → poly2, g_1, d_1, f_1
  10. Segment(A, C) → i
  11. Segment(D, F) → j
  12. Segment(A, B) → k
  13. Segment(D, G) → l
  14. Segment(C, B) → m
  15. Segment(F, G) → n
  16. Segment(H, I) → p
  17. Segment(H, J) → q
  18. Angle(I, H, J) → α
  19. Segment(J, I) → r
  20. Point(Circle[K, abs(q)]) → L
  21. Segment(K, L) → s
  22. Rotate(K, (-α), L) → K'
  23. Angle(K', L, K) → β
  24. Ray(L, K') → t
  25. Circle(L, p) → c_1
  26. Intersect(c_1, t) → M,
  27. Segment(M, K) → a_1
  28. Segment(L, M) → b_1
  29. Segment(N, O) → e_1
  30. Segment(P, N) → h_1
  31. Segment(P, O) → i_1
  32. Angle(O, N, P) → γ
  33. Angle(P, O, N) → δ
  34. Point(Circle[Q, abs(e_1)]) → R
  35. Segment(Q, R) → j_1
  36. Rotate(R, γ, Q) → R'
  37. Angle(R, Q, R') → ε
  38. Rotate(Q, (-δ), R) → Q'
  39. Angle(Q', R, Q) → ζ
  40. Ray(Q, R') → k_1
  41. Ray(R, Q') → l_1
  42. Intersect(k_1, l_1) → S
  43. Segment(S, Q) → m_1
  44. Segment(S, R) → n_1
  45. Segment(T, U) → p_1
  46. Segment(U, V) → q_1
  47. Segment(V, T) → r_1
  48. Point(Circle[W, abs(p_1)]) → Z
  49. Segment(W, Z) → t_1
  50. Angle(T, U, V) → η
  51. Angle(U, V, T) → θ
  52. Rotate(W, η, Z) → W'
  53. Angle(W, Z, W') → ι
  54. Angle(V, T, U) → κ
  55. Rotate(Z, (-κ), W) → Z'
  56. Angle(Z', W, Z) → λ
  57. Ray(Z, W') → a_2
  58. Ray(W, Z') → b_2
  59. Intersect(b_2, a_2) → E
  60. Segment(W, E) → c_2
  61. Segment(E, Z) → d_2
  62. Angle(Z, E, W) → μ
  63. Segment(A, B) → e_2
  64. Segment(A, C) → f_2
  65. Segment(C, B) → h_2
  66. Segment(G, D) → i_2
  67. Segment(D, F) → j_2
  68. Segment(G, F) → k_2
  69. Segment(K, L) → l_2
  70. Segment(L, M) → m_2
  71. Segment(J, H) → n_2
  72. Segment(H, I) → p_2
  73. Angle(M, L, K) → ν
  74. Angle(I, H, J) → ξ
  75. Segment(N, O) → q_2
  76. Segment(Q, R) → r_2
  77. Angle(O, N, P) → ο
  78. Angle(R, Q, S) → ρ
  79. Angle(P, O, N) → σ
  80. Angle(S, R, Q) → τ
  81. Segment(U, T) → s_2
  82. Segment(Z, W) → t_2
  83. Angle(T, U, V) → υ
  84. Angle(W, Z, E) → ϕ
  85. Angle(U, V, T) → χ
  86. Angle(Z, E, W) → ψ