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SSA Theorem Exploration

SSA Theorem Exploration
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2016-12-10 09:18
TriangleAngleTransformationGeometric ConstructionSlider Animation
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This interactive example demonstrates constructing triangles given two sides and a non-included angle, exploring the SSA condition. Users can adjust the side lengths and angles to visually understand the applicability and limitations of the SSA theorem. The construction uses commands like Circle, Ray, Segment, Mirror, and Polygon in GeoGebra. Suitable for high school geometry students and teachers.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Circle(A, b) → c
  4. Ray(A, B) → f
  5. CircleArc(A, C, D) → d
  6. Point(d) → E
  7. Circle(E, a) → e
  8. Intersect(g, f) → F
  9. Segment(E, F) → h
  10. Segment(E, A) → i
  11. Intersect(e, f) → G, H
  12. Segment(E, H) → j
  13. Mirror(E, h) → E'
  14. Mirror(H, h) → H'
  15. Segment(E', H') → j'
  16. Circle(I, i) → k
  17. Point(k) → J
  18. Circle(I, Distance[A, G]) → p
  19. Segment(I, J) → l
  20. Circle(J, j) → q
  21. Intersect(p, q, 2) → K
  22. Segment(J, K) → m
  23. Segment(K, I) → n
  24. Segment(A, G) → r
  25. Min(r, i) → o
  26. Circle(A, (0.4 * o)) → s
  27. Intersect(s, r, 1) → L
  28. Intersect(s, i, 1) → M
  29. CircleSector(A, L, M) → t
  30. Polygon(A, G, E) → poly1, e_1, a_1, g_1
  31. Dilate(A, If[1 < u ≤ 2, 2 - u, 0], E) → A'
  32. Segment(A, A') → f_1
  33. Angle(L, A, M) → α
  34. Rotate(L, If[0 < u ≤ 1, (u * α), α], A) → L'
  35. CircleSector(A, L, L') → c_1
  36. Dilate(E, If[2 < u ≤ 3, 3 - u, 0], G) → E'_1
  37. Segment(E, E'_1) → h_1
  38. Ray(I, K) → i_1
  39. Line(A, i_1) → j_1
  40. Point(j_1) → N
  41. Angle(G, A, N) → β
  42. Dilate(A, If[4 < u ≤ 5, 5 - u, 0], I) → A'_1
  43. Vector(A, A'_1) → v
  44. Translate(c_1, v) → d_1
  45. Rotate(d_1, If[5 < u ≤ 6, ((u - 5) * β), β], I) → k_1
  46. Dilate(A, If[6 < u ≤ 7, 7 - u, 0], I) → E'_2
  47. Vector(A, E'_2) → w
  48. Translate(A, w) → A'_2
  49. Translate(A', w) → A''
  50. Segment(A'_2, A'') → l_1
  51. Rotate(A'_2, If[7 < u ≤ 8, ((u - 7) * β), β], I) → O
  52. Rotate(A'', If[7 < u ≤ 8, ((u - 7) * β), β], I) → A'''
  53. Segment(O, A''') → m_1
  54. Dilate(E, If[8 < u ≤ 9, 9 - u, 0], J) → E'_3
  55. Line(J, h_1) → p_1
  56. Dilate(G, If[8 < u ≤ 9, 9 - u, 0], K) → G'
  57. Vector(G, G') → u_1
  58. Translate(E, u_1) → E'_4
  59. Translate(E'_1, u_1) → P
  60. Segment(E'_4, P) → n_1
  61. Line(K, J) → q_1
  62. Point(n_1) → Q
  63. Angle(Q, K, J) → γ
  64. Rotate(E'_4, If[9 < u ≤ 10, ((u - 9) * γ), γ], K) → R
  65. Rotate(P, If[9 < u ≤ 10, ((u - 9) * γ), γ], K) → P'
  66. Segment(R, P') → r_1
  67. Dilate(A, If[10 < u ≤ 11, 11 - u, 0], I) → A'_3
  68. Vector(A, A'_3) → v_1
  69. Translate(A, v_1) → A'_4
  70. Translate(G, v_1) → G'_1
  71. Translate(E, v_1) → E'_5
  72. Polygon(A'_4, G'_1, E'_5) → poly1', e'_5, a'_4, g'_1
  73. Rotate(A'_4, If[11 < u ≤ 12, ((u - 11) * β), β], I) → S
  74. Rotate(G'_1, If[11 < u ≤ 12, ((u - 11) * β), β], I) → T
  75. Rotate(E'_5, If[11 < u ≤ 12, ((u - 11) * β), β], I) → U
  76. Polygon(S, T, U) → poly1'', u_2, s_1, t_1
  77. Polygon(A, E, G) → poly2, g_2, a_2, e_2

AI Drawing Prompt Reference

Draw a triangle given two sides and a non-included angle. Start with points A and B, draw a circle with center A and radius b, and another circle with center B and radius a. Find the intersection points E and F of these circles, and use them to form triangle AEG. Draw line segments AE and AF, and then construct triangle AEG. Use point A and G to draw a circle, find its intersection with AE at point J, and draw line segment EJ. Reflect EJ to get E'H', and finally construct triangle AE'G.
The prompt above was compiled from the original drawing commands and is for reference only.