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Interactive Triangle Congruence Tests Demo

Interactive Triangle Congruence Tests Demo
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2018-10-08 02:50
TriangleAngleGeometric Construction
This GeoGebra example demonstrates the four criteria for triangle congruence: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), and AAS (Angle-Angle-Side). The core mathematical concept is the conditions for triangle congruence and congruence transformation. Construction highlights: Using Rotate command to show congruence transformations dynamically, Angle and Segment tools to precisely measure sides and angles, Circle and Line tools to draw auxiliary lines, Point and Intersect tools to locate key points, and Textfield to display congruence conditions in real-time. Suitable for middle school geometry teaching, ideal for intuitive demonstration and exploratory learning of triangle congruence theorems.

GeoGebra Commands & Parameters

  1. Rotate(G, 30°, H) → G'
  2. Angle(G, H, G') → α
  3. Segment(G, H) → g
  4. Segment(G, G') → h
  5. Segment(G', H) → i
  6. Angle(G', G, H) → β
  7. Angle(H, G', G) → γ
  8. Circle(J, 3) → k
  9. Point(k) → K
  10. Segment(J, K) → j
  11. Rotate(K, 75°, J) → K'
  12. Angle(K, J, K') → δ
  13. Rotate(J, (-(40°)), K) → J'
  14. Angle(J', K, J) → ε
  15. Line(J, K') → l
  16. Line(J', K) → m
  17. Intersect(l, m) → L
  18. Segment(J, L) → n
  19. Segment(K, L) → p
  20. Angle(J, L, K) → ζ
  21. Circle(M, 3) → q
  22. Point(q) → N
  23. Segment(M, N) → r
  24. Rotate(N, 45°, M) → N'
  25. Angle(N, M, N') → η
  26. Line(M, N') → s
  27. Point(s) → O
  28. Rotate(M, 70°, O) → M'
  29. Angle(M, O, M') → θ
  30. Line(O, M') → t
  31. Line(N, M) → f_1
  32. Intersect(t, f_1) → P
  33. Segment(M, N) → g_1
  34. Segment(O, M) → h_1
  35. Segment(O, N) → i_1
  36. Circle(Q, 4) → c_1
  37. Point(c_1) → R
  38. Segment(Q, R) → j_1
  39. Rotate(Q, (-(90°)), R) → Q'
  40. Angle(Q', R, Q) → ι
  41. Circle(R, 3) → d_1
  42. Line(R, Q') → k_1
  43. Intersect(d_1, k_1) → S, T
  44. Segment(T, Q) → l_1
  45. Segment(R, T) → m_1
  46. Angle(Q, T, R) → κ
  47. Angle(R, Q, T) → λ
  48. Circle(U, 3) → e_1
  49. Point(e_1) → V
  50. Segment(U, V) → n_1
  51. Rotate(U, (-(70°)), V) → U'
  52. Angle(U', V, U) → μ
  53. Line(U', V) → q_1
  54. Circle(V, 4) → p_1
  55. Intersect(p_1, q_1) → W, Z
  56. Segment(U, W) → r_1
  57. Segment(V, W) → s_1
  58. Angle(V, U, W) → ν
  59. Angle(U, W, V) → ο
  60. Line(A_1, B_1) → t_1
  61. Rotate(B_1, 30°, A_1) → C_1
  62. Angle(B_1, A_1, C_1) → ξ
  63. Line(A_1, C_1) → a_1
  64. Circle(A_1, 5) → c_2
  65. Intersect(c_2, a_1) → D_1, E_1
  66. Segment(A_1, E_1) → b_1
  67. Circle(E_1, 3) → d_2
  68. Point(d_2) → F_1
  69. Segment(E_1, F_1) → f_2
  70. Line(E_1, F_1) → g_2
  71. Circle(F_1, 0.03) → h_2
  72. Intersect(h_2, g_2) → G_1, H_1
  73. Segment(F_1, H_1) → i_2
  74. Intersect(t_1, i_2) → I_1
  75. Segment(A_1, I_1) → j_2
  76. Angle(A_1, E_1, F_1) → ρ
  77. Angle(E_1, F_1, A_1) → σ
  78. Textfield() → InputBox1
  79. Textfield() → InputBox2