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AAS Congruence Theorem Demo

AAS Congruence Theorem Demo
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2016-10-03 09:20
TriangleAngleGeometric Construction
In collections Chapter 4 - Triangle Congruence - Geometry
This example dynamically demonstrates the AAS (Angle-Angle-Side) Congruence Theorem, illustrating triangle congruence criteria, angle-side relationships, and involving concepts like circles and loci. It uses commands such as Vector, Segment, Angle, Circle, Point, Intersect, Line, and Ray for construction, making it suitable for high school geometry education and understanding congruence conditions.

GeoGebra Commands & Parameters

  1. Vector(D, E) → w
  2. Vector(D, F) → a
  3. Segment(G, H) → f
  4. Angle(E, D, F) → γ
  5. Circle(I, Segment[G, H]) → c
  6. Point(c) → J
  7. Segment(I, J) → g
  8. Circle(J, Segment[E, D]) → d
  9. Circle(J, Segment[D, F]) → e
  10. Intersect(d, g, 1) → K
  11. Circle(K, Segment[F, E]) → h
  12. Intersect(e, h, 1) → L
  13. Line(J, L) → i
  14. Circle(J, Segment[D, F]) → k
  15. Circle(J, Segment[D, E]) → p
  16. Intersect(p, g, 1) → B
  17. Circle(B, Segment[F, E]) → q
  18. Intersect(k, q, 1) → M
  19. Line(M, J) → j
  20. Point(j) → N
  21. Segment(I, N) → l
  22. Segment(N, J) → m
  23. Angle(I, J, N) → α
  24. Circle(R, Segment[G, H]) → c_1
  25. Point(c_1) → S
  26. Segment(R, S) → b
  27. Point(a) → T
  28. Point(w) → U
  29. Point(a) → V
  30. Circle(R, Segment[T, U]) → d_1
  31. Circle(R, Segment[T, V]) → e_1
  32. Circle(S, Segment[U, V]) → f_1
  33. Circle(R, Segment[D, E]) → g_1
  34. Circle(R, Segment[D, F]) → h_1
  35. Intersect(g_1, b, 1) → W
  36. Circle(W, Segment[E, F]) → k_1
  37. Intersect(h_1, k_1, 1) → Z
  38. Line(R, Z) → i_1
  39. Circle(R, Segment[J, N]) → p_1
  40. Intersect(p_1, i_1, 2) → A_1
  41. Circle(A_1, Segment[N, I]) → q_1
  42. Circle(R, Segment[J, I]) → r_1
  43. Segment(S, A_1) → j_1
  44. Segment(R, A_1) → l_1
  45. Angle(S, R, A_1) → β
  46. Angle(R, A_1, S) → δ
  47. Angle(J, N, I) → ε
  48. Circle(A, Segment[J, N]) → r
  49. Point(r) → C
  50. Segment(A, C) → n
  51. Circle(A, Segment[N, I]) → s
  52. Circle(C, Segment[J, I]) → t
  53. Intersect(s, t, 1) → O
  54. Ray(A, O) → m_1
  55. Point(n) → P
  56. Vector(A, P) → u
  57. Point(m_1) → Q
  58. Vector(A, Q) → v
  59. Angle(P, A, Q) → ζ