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Dynamic Proof of SSS Congruence Theorem

Dynamic Proof of SSS Congruence Theorem
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2017-11-30 02:57
TriangleTransformationGeometric ConstructionSlider Animation
This example demonstrates the dynamic proof of the Side-Side-Side (SSS) Congruence Theorem for triangles. It involves core mathematical concepts such as triangle congruence criteria and geometric transformations (reflection, rotation, translation). The construction utilizes GeoGebra commands like Circle, Intersect, Segment, Polygon, Point, Line, Angle, Dilate, Vector, Translate, Rotate, Mirror, and Ray. It is suitable for high school mathematics students and teachers to understand and teach the SSS congruence theorem.

GeoGebra Commands & Parameters

  1. Circle(A, a) → d
  2. Intersect(d, e) → B, C
  3. Circle(C, b) → f
  4. Segment(A, C) → g
  5. Circle(A, c) → k
  6. Intersect(k, f) → F, G, ,
  7. Segment(C, F) → h
  8. Segment(F, A) → i
  9. Polygon(A, C, F) → poly1, f_1, a_1, c_1
  10. Circle(D, i) → p
  11. Point(p) → E
  12. Segment(D, E) → n
  13. Circle(D, g) → q
  14. Circle(E, h) → r
  15. Intersect(q, r, 2) → H
  16. Segment(D, H) → s
  17. Segment(H, E) → t
  18. Line(A, n) → g_1
  19. Point(g_1) → I
  20. Angle(I, A, F) → α
  21. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], D) → A'
  22. Vector(A, A') → u
  23. Translate(F, u) → F'
  24. Translate(A, u) → A'_1
  25. Segment(F', A'_1) → i'
  26. Rotate(F', If[1 < o ≤ 2, ((-(o - 1)) * α), (-α)], D) → F''
  27. Rotate(A'_1, If[1 < o ≤ 2, ((-(o - 1)) * α), (-α)], D) → J
  28. Segment(F'', J) → i''
  29. Dilate(A, If[2 < o ≤ 3, 3 - o, 0], D) → A'_2
  30. Vector(A, A'_2) → v
  31. Translate(A, v) → A'_3
  32. Translate(C, v) → C'
  33. Segment(A'_3, C') → g'
  34. Line(D, g) → h_1
  35. Point(h_1) → K
  36. Angle(H, D, K) → β
  37. Rotate(A'_3, If[3 < o ≤ 4, ((-(o - 3)) * β), (-β)], D) → L
  38. Rotate(C', If[3 < o ≤ 4, ((-(o - 3)) * β), (-β)], D) → C''
  39. Segment(L, C'') → g''
  40. Line(C, t) → i_1
  41. Point(i_1) → M
  42. Angle(M, C, F) → γ
  43. Dilate(C, If[4 < o ≤ 5, 5 - o, 0], C'') → C'_1
  44. Vector(C, C'_1) → w
  45. Translate(C, w) → C'_2
  46. Translate(F, w) → F'_1
  47. Segment(C'_2, F'_1) → h'
  48. Rotate(C'_2, If[5 < o ≤ 6, ((-(o - 5)) * γ), (-γ)], C'') → N
  49. Rotate(F'_1, If[5 < o ≤ 6, ((-(o - 5)) * γ), (-γ)], C'') → O
  50. Segment(N, O) → h''
  51. Polygon(D, C'', E) → poly2, e_1, d_1, c''
  52. Dilate(A, If[(6 * 0.5) < o ≤ 7.5, 7.5 - o, 0], D) → A'_4
  53. Vector(A, A'_4) → u_1
  54. Translate(A, u_1) → A'_5
  55. Translate(C, u_1) → C'_3
  56. Translate(F, u_1) → F'_2
  57. Polygon(A'_5, C'_3, F'_2) → poly1', f'_2, a'_5, c'_3
  58. Rotate(A'_5, If[7.5 < o ≤ 8.5, ((-(o - 7.5)) * γ), (-γ)], D) → P
  59. Rotate(C'_3, If[7.5 < o ≤ 8.5, ((-(o - 7.5)) * γ), (-γ)], D) → Q
  60. Rotate(F'_2, If[7.5 < o ≤ 8.5, ((-(o - 7.5)) * γ), (-γ)], D) → R
  61. Polygon(P, Q, R) → poly1'', r_1, p_1, q_1
  62. Line(F, C) → j_1
  63. Mirror(A, j_1) → A'_6
  64. Mirror(C, j_1) → C'_4
  65. Mirror(F, j_1) → F'_3
  66. Polygon(A'_6, C'_4, F'_3) → poly1'_1, f'_3, a'_6, c'_4
  67. Point(j_1) → S
  68. Point(j_1) → T
  69. Ray(C'_4, T) → k_1
  70. Ray(F'_3, S) → l_1
  71. Segment(A'_6, F'_3) → m_1
  72. Segment(A'_6, C'_4) → n_1