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Dynamic SSS Triangle Similarity Theorem Applet

Dynamic SSS Triangle Similarity Theorem Applet
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2019-02-08 00:15
TriangleGeometric Construction
This example dynamically demonstrates the SSS Triangle Similarity Theorem, allowing students to visually explore and confirm the principle. Key math concepts include triangle similarity criteria and dynamic geometric transformations. GeoGebra commands used in construction are Circle, Intersect, Segment, Polygon, Point, Dilate, etc. Ideal for high school mathematics instruction to enhance understanding and verification of the theorem.

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[1 < o ≤ 2, 2 - 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. CircleArc(E, M, L) → s_1
  40. Translate(h_1, v) → t_1
  41. Line(D, i) → i_1
  42. Intersect(d_1, i_1) → R, S
  43. Angle(O, D, R) → γ
  44. CircleArc(D, N, O) → d_2
  45. Rotate(q_1, If[0 < o ≤ 1, (o * α), α], D') → e_2
  46. Rotate(t_1, If[1 < o ≤ 2, ((o - 1) * γ), γ], D'_1) → r_1