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Congruence Theorems: Dynamic Geometric Construction

Congruence Theorems: Dynamic Geometric Construction
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2018-04-29 15:44
TrianglePolygonAngleTransformationGeometric Construction
This GeoGebra example provides an interactive demonstration of triangle congruence theorems (such as SSS, SAS, ASA) through dynamic geometric construction. It visually shows how corresponding sides and angles of congruent triangles are equal, while also touching on related concepts like polygon perimeter and median values. The construction uses commands including Polygon, Circle, Point, Segment, Intersect, Angle, Rotate, and Ray to build auxiliary circles, intersection points, and rotated copies, creating multiple objects (A, B, C, poly1, D, F, G, E_1, etc.) that illustrate different congruence scenarios. A text object (text1) labels the final conclusion. This resource is ideal for middle or high school geometry classes, helping students grasp the conditions for triangle congruence and serving as a template for teachers to create their own dynamic demonstrations.

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