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Triangle Congruency Postulates Demo

Triangle Congruency Postulates Demo
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2014-05-13 02:26
TriangleCoordinate GeometryGeometric Construction
This applet visually demonstrates all triangle congruency postulates except those involving right triangles. It covers core concepts like SSS, SAS, ASA, AAS congruence criteria, geometric transformations, and coordinate geometry. Constructed using commands like Segment, Angle, Circle, Point, Rotate, Line, Polygon, DynamicCoordinates, If, Intersect. Ideal for high school mathematics education to enhance understanding of congruence conditions through interactive visualization.

GeoGebra Commands & Parameters

  1. Segment(C, A) → b
  2. Angle(A, C, B) → γ_c
  3. Segment(B, C) → a_c
  4. Segment(A, B) → c_c
  5. Angle(B, A, C) → α_c
  6. Angle(C, B, A) → β_c
  7. Circle(H, c_c) → k_{cSSA}
  8. Circle(H, a_c) → p_{aSSA}
  9. Point(p_{aSSA}) → I
  10. Point(k_{cSSA}) → J
  11. Circle(I, b) → q_{bSSA}
  12. Segment(H, I) → l
  13. Segment(H, J) → m
  14. Rotate(H, (-γ_c), I) → H'
  15. Angle(H', I, H) → δ
  16. Line(H', I) → d
  17. Point(d) → D
  18. Polygon(C, A, B) → poly1, b_{O}, c_{O}, a_{O}
  19. Polygon(H, J, D, I) → poly2_1, h, j, b_{SSAc}, i
  20. DynamicCoordinates(D, If[Distance[D, J] < 0.13, x(J), x(D)], If[Distance[D, J] < 0.13, y(J), y(D)]) → E
  21. Segment(E, I) → b_{SSA}
  22. Polygon(H, I, E) → poly3, e_1, h_1, i_1
  23. If(poly1 - 1.5 ≤ poly2_1 ≤ poly1 + 1.5 ∧ E ≟ J, true, false) → g
  24. Circle(H_1, c_c) → k_{cSSS}
  25. Circle(H_1, a_c) → p_{aSSS}
  26. Point(p_{aSSS}) → I_1
  27. Point(k_{cSSS}) → J_1
  28. Circle(I_1, b) → q_{bSSS}
  29. Segment(H_1, I_1) → l_1
  30. Segment(H_1, J_1) → m_1
  31. Point(q_{bSSS}) → K_1
  32. Segment(I_1, K_1) → n_1
  33. Segment(B, A) → c
  34. Segment(A, C) → b_c
  35. Segment(B, C) → a
  36. DynamicCoordinates(K_1, If[Distance[J_1, K_1] < 0.13, x(J_1), x(K_1)], If[Distance[K_1, J_1] < 0.13, y(J_1), y(K_1)]) → F
  37. Polygon(J_1, H_1, I_1) → poly4, i_2, j_2, h_2
  38. Point(p_{aSSS}) → G
  39. Segment(H_1, G) → e
  40. Rotate(G, β_c, H_1) → G'
  41. Angle(G, H_1, G') → α
  42. Line(H_1, G') → f
  43. Intersect(k_{cSSA}, f, 2) → K
  44. Segment(G, L) → k
  45. Segment(H_1, K) → n
  46. DynamicCoordinates(L, If[Distance[K, L] < 0.13, x(K), x(L)], If[Distance[L, K] < 0.13, y(K), y(L)]) → M
  47. Polygon(H_1, G, M) → poly2, m_2, h_3, g_1
  48. Point(p_{aSSS}) → N
  49. Rotate(N, β_c, H_1) → N'
  50. Angle(N, H_1, N') → β
  51. Rotate(H_1, α_c, N') → O
  52. Line(H_1, N) → p
  53. Segment(H_1, N) → s
  54. Line(H_1, N') → q
  55. Point(q) → P
  56. Rotate(H_1, α_c, P) → Q
  57. Angle(H_1, P, Q) → γ
  58. Line(P, Q) → r
  59. Segment(H_1, P) → t
  60. Point(r) → R
  61. Segment(P, R) → a_1
  62. DynamicCoordinates(R, If[Distance[N, R] < 0.13, x(N), x(R)], If[Distance[R, N] < 0.13, y(N), y(R)]) → S
  63. Polygon(S, H_1, P) → poly5, p_1, s_1, h_4
  64. Point(p_{aSSA}) → T
  65. Rotate(T, β_c, H_1) → T'
  66. Angle(T, H_1, T') → ε
  67. Rotate(H_1, (-γ_c), T) → U
  68. Angle(U, T, H_1) → ζ
  69. Line(H_1, T') → b_1
  70. Line(U, T) → c_1
  71. Segment(H_1, T) → d_1
  72. Point(c_1) → V
  73. Point(b_1) → W
  74. DynamicCoordinates(W, If[Distance[V, W] < 0.13, x(V), x(W)], If[Distance[V, W] < 0.13, y(V), y(W)]) → Z
  75. Segment(Z, H_1) → f_1
  76. Segment(V, T) → k_1
  77. Polygon(H_1, V, T) → poly6, t_1, h_5, v
  78. Rotate(A_1, β_c, H_1) → B_1
  79. Angle(A_1, H_1, B_1) → η
  80. Line(H_1, B_1) → r_1
  81. Rotate(H_1, (-γ_c), A_1) → C_1
  82. Angle(C_1, A_1, H_1) → θ
  83. Line(C_1, A_1) → a_2
  84. Intersect(r_1, a_2) → D_1
  85. Angle(H_1, D_1, A_1) → ι
  86. Segment(H_1, A_1) → q_1
  87. Segment(D_1, A_1) → b_2
  88. Segment(D_1, H_1) → c_2
  89. Polygon(A_1, H_1, D_1) → poly7, d_2, a_3, h_6
  90. If(a - 0.1 ≤ q_1 ≤ a + 0.1, true, false) → g_2
  91. Polygon(H_1, D_1, A_1) → poly8, a_4, h_7, d_3