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SSS Similarity Theorem Dynamic Demo

SSS Similarity Theorem Dynamic Demo
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2016-03-29 08:59
TriangleCircleTransformationGeometric ConstructionSlider Animation
In collections Similarity & Right Triangle Trigonometry Similarity, Right Triangles, and Trigonometry (SRT) Cluster Similarity Theorems! U9 Dilations and Similar Triangles
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. Construction highlights include commands/objects such as Circle, Intersect, Segment, Polygon, Point, CircleSector, Dilate, Vector, Line, Angle, Translate, Rotate, and CircleArc. Ideal for high school students learning and exploring geometric theorems.

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

AI Drawing Prompt Reference

Draw triangle ABC, then perform similarity transformations around points D and E to generate new triangle D'E'F', and show key steps including circles, segments, angles, and arcs.
The prompt above was compiled from the original drawing commands and is for reference only.