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ASA Triangle Congruence Theorem: Dynamic Illustration

ASA Triangle Congruence Theorem: Dynamic Illustration
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2017-04-30 12:40
TriangleAngleGeometric ConstructionSlider Animation
This example dynamically illustrates the ASA (Angle-Side-Angle) Triangle Congruence Theorem. It involves core mathematical concepts such as triangle congruence criteria, angle measurement, and geometric transformations. The construction utilizes GeoGebra commands like Rotate, Angle, Ray, Point, Intersect, Polygon, Segment, Min, Circle, CircleSector, Dilate, Vector, Translate, and Line. It is suitable for high school mathematics education to visually understand geometric theorems and transformation applications.

GeoGebra Commands & Parameters

  1. Rotate(B, α, A) → B'
  2. Angle(B, A, B') → β
  3. Ray(A, B') → f
  4. Point(f) → C
  5. Rotate(A, (-γ), B) → A'
  6. Angle(A', B, A) → δ
  7. Ray(B, A') → g
  8. Intersect(f, g) → D
  9. Polygon(A, B, D) → poly1, d, a_1, b
  10. Segment(A, B) → h
  11. Segment(D, B) → i
  12. Segment(D, A) → j
  13. Min({h, i, j}) → c
  14. Circle(A, (0.2 * c)) → e
  15. Circle(B, (0.2 * c)) → k
  16. Intersect(e, h) → E,
  17. Intersect(e, j) → F, I
  18. Intersect(k, h) → G,
  19. Intersect(k, i) → H, J
  20. CircleSector(A, E, F) → p
  21. CircleSector(B, H, G) → q
  22. Rotate(K, β, L) → K'
  23. Angle(K, L, K') → ε
  24. Circle(L, h) → r
  25. Ray(L, K) → m
  26. Intersect(r, m, 1) → M
  27. Ray(L, K') → n
  28. Rotate(L, (-γ), M) → L'
  29. Angle(L', M, L) → ζ
  30. Ray(M, L') → s
  31. Intersect(n, s) → N
  32. Dilate(A, If[0 < l ≤ 1, 1 - l, 0], L) → A'_1
  33. Vector(A, A'_1) → u
  34. Translate(p, u) → p'
  35. Line(L, h) → t
  36. Translate(F, u) → F'
  37. Point(t) → O
  38. Angle(M, L, O) → η
  39. Rotate(p', If[1 < l ≤ 2, ((-(l - 1)) * η), (-η)], L) → p''
  40. Point(t) → P
  41. Angle(P, L, M) → θ
  42. Dilate(B, If[2 < l ≤ 3, 3 - l, 0], L) → B'_1
  43. Vector(B, B'_1) → v
  44. Translate(A, v) → A'_2
  45. Translate(B, v) → B'_2
  46. Segment(A'_2, B'_2) → h'
  47. Rotate(A'_2, If[3 < l ≤ 4, ((l - 3) * θ), θ], L) → Q
  48. Rotate(B'_2, If[3 < l ≤ 4, ((l - 3) * θ), θ], L) → R
  49. Segment(Q, R) → h''
  50. Dilate(B, If[4 < l ≤ 5, 5 - l, 0], M) → B'_3
  51. Vector(B, B'_3) → w
  52. Translate(q, w) → q'
  53. Line(M, g) → f_1
  54. Point(f_1) → S
  55. Angle(N, M, S) → τ
  56. Rotate(q', If[5 < l ≤ 6, ((l - 5) * ((2 * π) - τ)), (2 * π) - τ], M) → q''
  57. Dilate(B, If[6 < l ≤ 7, 7 - l, 0], M) → B'_4
  58. Vector(B, B'_4) → u_1
  59. Translate(A, u_1) → A'_3
  60. Translate(B, u_1) → B'_5
  61. Translate(D, u_1) → D'
  62. Polygon(A'_3, B'_5, D') → poly1', d', a'_3, b'_5
  63. Rotate(A'_3, If[7 < l ≤ 8, ((-(l - 7)) * τ), (-τ)], M) → T
  64. Rotate(B'_5, If[7 < l ≤ 8, ((-(l - 7)) * τ), (-τ)], M) → U
  65. Rotate(D', If[7 < l ≤ 8, ((-(l - 7)) * τ), (-τ)], M) → D''
  66. Polygon(T, U, D'') → poly1'', d'', t_1, u_2