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Explore Triangle Congruence Theorems

Explore Triangle Congruence Theorems
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2016-05-23 19:25
TriangleAngleGeometric Construction
This applet allows you to explore different triangle congruence theorems, including SSS, SAS, ASA, and AAS. By dragging points, you can change the shape of the triangle and observe the application of these theorems. The applet involves core concepts such as triangles and angles, and uses commands like Polygon, Circle, Point, Segment, and Angle in GeoGebra. Suitable for middle school and above students or teachers to help understand the conditions for triangle congruence.

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. Circle(F, a) → h
  7. Intersect(h, f) → E_1, G, ,
  8. Polygon(D, F, G) → poly2, g_1, d_1, f_1
  9. Segment(A, C) → i
  10. Segment(D, F) → j
  11. Segment(A, B) → k
  12. Segment(D, G) → l
  13. Segment(C, B) → m
  14. Segment(F, G) → n
  15. Segment(H, I) → p
  16. Segment(H, J) → q
  17. Angle(I, H, J) → α
  18. Segment(J, I) → r
  19. Point(Circle[K, abs(q)]) → L
  20. Segment(K, L) → s
  21. Rotate(K, (-α), L) → K'
  22. Angle(K', L, K) → β
  23. Ray(L, K') → t
  24. Circle(L, p) → c_1
  25. Intersect(c_1, t) → M,
  26. Segment(M, K) → a_1
  27. Segment(L, M) → b_1
  28. Segment(N, O) → e_1
  29. Segment(P, N) → h_1
  30. Segment(P, O) → i_1
  31. Angle(O, N, P) → γ
  32. Angle(P, O, N) → δ
  33. Point(Circle[Q, abs(e_1)]) → R
  34. Segment(Q, R) → j_1
  35. Rotate(R, γ, Q) → R'
  36. Angle(R, Q, R') → ε
  37. Rotate(Q, (-δ), R) → Q'
  38. Angle(Q', R, Q) → ζ
  39. Ray(Q, R') → k_1
  40. Ray(R, Q') → l_1
  41. Intersect(k_1, l_1) → S
  42. Segment(S, Q) → m_1
  43. Segment(S, R) → n_1
  44. Segment(T, U) → p_1
  45. Segment(U, V) → q_1
  46. Segment(V, T) → r_1
  47. Point(Circle[W, abs(p_1)]) → Z
  48. Segment(W, Z) → t_1
  49. Angle(T, U, V) → η
  50. Angle(U, V, T) → θ
  51. Rotate(W, η, Z) → W'
  52. Angle(W, Z, W') → ι
  53. Angle(V, T, U) → κ
  54. Rotate(Z, (-κ), W) → Z'
  55. Angle(Z', W, Z) → λ
  56. Ray(Z, W') → a_2
  57. Ray(W, Z') → b_2
  58. Intersect(b_2, a_2) → E
  59. Segment(W, E) → c_2
  60. Segment(E, Z) → d_2
  61. Angle(Z, E, W) → μ
  62. Segment(A, B) → e_2
  63. Segment(A, C) → f_2
  64. Segment(C, B) → h_2
  65. Segment(G, D) → i_2
  66. Segment(D, F) → j_2
  67. Segment(G, F) → k_2
  68. Segment(K, L) → l_2
  69. Segment(L, M) → m_2
  70. Segment(J, H) → n_2
  71. Segment(H, I) → p_2
  72. Angle(M, L, K) → ν
  73. Angle(I, H, J) → ξ
  74. Segment(N, O) → q_2
  75. Segment(Q, R) → r_2
  76. Angle(O, N, P) → ο
  77. Angle(R, Q, S) → ρ
  78. Angle(P, O, N) → σ
  79. Angle(S, R, Q) → τ
  80. Segment(U, T) → s_2
  81. Segment(Z, W) → t_2
  82. Angle(T, U, V) → υ
  83. Angle(W, Z, E) → ϕ
  84. Angle(U, V, T) → χ
  85. Angle(Z, E, W) → ψ

AI Drawing Prompt Reference

Draw triangle ABC, then draw three circles with A, B, and C as centers. Find specific points F, G, D, etc., on these circles and connect them to form triangle DEF. Mark the corresponding sides and angles of triangles ABC and DEF.
The prompt above was compiled from the original drawing commands and is for reference only.