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AAA Congruence Demonstration

AAA Congruence Demonstration
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2016-10-03 09:24
TriangleAngleTrigonometryGeometric Construction
This example dynamically demonstrates triangles with three equal angles to verify that AAA (Angle-Angle-Angle) does not guarantee triangle congruence. It involves core concepts like congruence criteria, triangle similarity, angle measurement, and geometric transformations. Construction uses commands such as Vector, Angle, Rotate, Segment, Circle, Intersect, and Line to build and rotate triangles for verification. Suitable for high school mathematics education to understand the difference between similarity and congruence, and to develop spatial reasoning skills.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u
  2. Vector(A, C) → v
  3. Vector(D, E) → w
  4. Vector(D, F) → a
  5. Angle(C, A, B) → α
  6. Angle(F, D, E) → β
  7. Rotate(J, 180° - α - β, K) → J'
  8. Angle(J, K, J') → γ
  9. Vector(K, J') → d
  10. Vector(K, J) → e
  11. Segment(G, H) → f
  12. Circle(G, Segment[A, C]) → c
  13. Circle(G, Segment[A, B]) → g
  14. Intersect(c, f, 1) → I
  15. Circle(I, Segment[C, B]) → h
  16. Intersect(g, h, 1) → L
  17. Line(G, L) → i
  18. Circle(H, Segment[D, F]) → k
  19. Circle(H, Segment[D, E]) → p
  20. Intersect(k, f, 1) → M
  21. Circle(M, Segment[E, F]) → q
  22. Intersect(p, q, 2) → N
  23. Line(H, N) → j
  24. Intersect(i, j) → O
  25. Segment(H, O) → l
  26. Segment(O, G) → m
  27. Segment(P, Q) → n
  28. Circle(P, Segment[A, C]) → r
  29. Circle(P, Segment[A, B]) → s
  30. Intersect(r, n, 1) → R
  31. Circle(R, Segment[C, B]) → t
  32. Intersect(s, t, 1) → S
  33. Line(P, S) → b
  34. Circle(Q, Segment[F, D]) → c_1
  35. Circle(Q, Segment[D, E]) → d_1
  36. Intersect(c_1, n, 1) → T
  37. Circle(T, Segment[F, E]) → e_1
  38. Intersect(d_1, e_1, 2) → U
  39. Line(Q, U) → f_1
  40. Intersect(b, f_1) → V
  41. Segment(Q, V) → g_1
  42. Segment(V, P) → h_1
  43. Angle(H, G, O) → δ
  44. Angle(G, O, H) → ε
  45. Angle(O, H, G) → ζ
  46. Angle(P, V, Q) → η
  47. Angle(V, Q, P) → θ
  48. Angle(Q, P, V) → ι