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Exploring Angle-Side-Angle Theorem

Exploring Angle-Side-Angle Theorem
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2017-11-30 03:02
TriangleAngleTransformationGeometric Construction
This example dynamically illustrates the ASA Triangle Congruence Theorem. By adjusting angles and sides, observe how the triangle changes. Key mathematical concepts include triangle congruence, angle and side relationships. GeoGebra commands used include Rotate, Angle, Ray, Point, Intersect, Polygon, Segment, etc. Suitable for middle school and above students to learn geometric construction of triangle congruence.

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