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SSS Similarity Theorem Dynamic Demonstration

SSS Similarity Theorem Dynamic Demonstration
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2019-02-19 21:05
TriangleCirclePolygonGeometric ConstructionSlider Animation
This example dynamically demonstrates the SSS Similarity Theorem for triangles, allowing students to visually explore and discover the theorem. It involves core math concepts like triangle similarity, geometric proof, and dynamic geometry. The construction utilizes GeoGebra commands/objects such as Circle, Intersect, Segment, Polygon, Point, CircleSector, Dilate, Vector, Line, Angle, Translate, Rotate, and CircleArc. It is suitable for high school mathematics students and teachers exploring triangle similarity.

GeoGebra Commands & Parameters

  1. Circle(A, a) → d
  2. Intersect(d, e) → B_1, B
  3. Circle(B, b) → f
  4. Segment(A, B) → g
  5. Circle(A, c) → k_1
  6. Intersect(k_1, f) → C, G, ,
  7. Segment(B, C) → h
  8. Segment(C, A) → i
  9. Polygon(A, B, C) → poly1, f_1, a_1, c_1
  10. Point(Circle[D, (k * i)]) → F
  11. Segment(D, F) → n
  12. Circle(D, (k * g)) → p
  13. Circle(F, (k * h)) → q
  14. Intersect(p, q, 2) → E
  15. Segment(D, E) → r
  16. Segment(F, E) → s
  17. Circle(A, 2) → t
  18. Circle(B, 2) → e_1
  19. Circle(D, 1.5) → d_1
  20. Circle(E, 1.5) → g_1
  21. Intersect(t, g, 1) → H
  22. Intersect(t, i, 1) → I
  23. Intersect(e_1, h, 1) → J
  24. Intersect(e_1, g, 1) → K
  25. Intersect(g_1, r, 1) → L
  26. Intersect(g_1, s, 1) → M
  27. Intersect(d_1, r, 1) → N
  28. Intersect(d_1, n, 1) → O
  29. CircleSector(D, N, O) → h_1
  30. CircleSector(E, M, L) → p_1
  31. Dilate(E, If[0 < o ≤ 1, 1 - o, 0], B) → D'
  32. Vector(E, D') → u
  33. Dilate(D, If[2 < o ≤ 3, 3 - o, 0], A) → D'_1
  34. Vector(D, D'_1) → v
  35. Line(E, h) → b_1
  36. Intersect(g_1, b_1) → P, Q
  37. Angle(M, E, Q) → α
  38. Translate(p_1, u) → q_1
  39. Rotate(q_1, If[1 < o ≤ 2, ((o - 1) * α), α], B) → r_1
  40. CircleArc(E, M, L) → s_1
  41. Translate(h_1, v) → t_1
  42. Line(D, i) → i_1
  43. Intersect(d_1, i_1) → R, S
  44. Angle(O, D, R) → γ
  45. Rotate(t_1, If[3 < o ≤ 4, ((o - 3) * γ), γ], A) → c_2
  46. CircleArc(D, N, O) → d_2