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Rotation and Similar Triangles Animation

Rotation and Similar Triangles Animation
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2016-11-13 04:05
TriangleGeometric Construction
In collections Congruence (CO) Cluster Congruence (Vol 2) CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2
This example demonstrates the application of rotation transformations in similar triangles. Key mathematical concepts include the properties of similar triangles and rotation transformations. Using GeoGebra commands such as Rotate, Polygon, and Dilate, the animation dynamically shows the similarity relationship between the pre- and post-rotation triangles. Suitable for students at the junior high school level and above to learn about the properties and transformations of similar triangles.

GeoGebra Commands & Parameters

  1. Ray(E, L) → l
  2. Point(l) → M
  3. Rotate(M, α, E) → M'
  4. Ray(E, M') → m
  5. Point(y = 0) → A
  6. Segment(A, C) → j
  7. Rotate(C, α, A) → C'
  8. Ray(A, C') → g
  9. Point(g) → D
  10. Segment(A, D) → i
  11. Segment(D, C) → h
  12. Ray(A, C) → f
  13. Angle(C, A, C') → β
  14. Polygon(A, C, D) → poly1, d, a, c
  15. Angle(M, E, M') → γ
  16. Circle(E, i) → e
  17. Circle(E, j) → k
  18. Intersect(k, l, 1) → F
  19. Intersect(e, m, 1) → G
  20. Circle(G, 1) → p
  21. Circle(F, 1) → q
  22. Circle(G, h) → r
  23. Intersect(r, l) → H, U
  24. Dilate(G, b, E) → G'
  25. Dilate(H, b, E) → H'
  26. Segment(G', H') → n
  27. Polygon(E, H', G') → poly2, g', e_1, h'
  28. Angle(poly2) → δ, ε, ζ
  29. Angle(poly1) → η, θ, ι
  30. Segment(E, H') → s
  31. Segment(E, G') → t
  32. Min({j, i, h}) → o
  33. Circle(A, (0.2 * o)) → c_1
  34. Circle(D, (0.2 * o)) → d_1
  35. Circle(C, (0.2 * o)) → f_1
  36. Intersect(c_1, j, 1) → I
  37. Intersect(c_1, i, 1) → J
  38. Intersect(d_1, i, 1) → K
  39. Intersect(d_1, h, 1) → N
  40. Intersect(f_1, h, 1) → O
  41. Intersect(j, xAxis) → P
  42. Intersect(f_1, j, 1) → Q
  43. CircleSector(A, I, J) → g_1
  44. CircleSector(D, K, N) → h_1
  45. CircleSector(C, O, Q) → k_1
  46. Dilate(A, If[0 < u ≤ 1, 1 - u, 0], E) → A'
  47. Vector(A, A') → v
  48. Translate(g_1, v) → p_1
  49. Line(A, t) → i_1
  50. Point(i_1) → R
  51. Angle(D, A, R) → κ
  52. Rotate(p_1, If[1 < u ≤ 2, ((u - 1) * κ), κ], E) → q_1
  53. Dilate(D, If[2 < u ≤ 3, 3 - u, 0], G') → D'
  54. Vector(D, D') → w
  55. Translate(h_1, w) → r_1
  56. Line(D, n) → j_1
  57. Point(j_1) → S
  58. Angle(N, D, S) → λ
  59. Rotate(r_1, If[3 < u ≤ 4, ((u - 3) * λ), λ], G') → s_1
  60. Dilate(C, If[6 < u ≤ 7, 7 - u, 0], H') → C'_1
  61. Vector(C, C'_1) → u_1
  62. Translate(k_1, u_1) → t_1
  63. Line(C, s) → l_1
  64. Point(l_1) → T
  65. Angle(A, C, T) → μ
  66. Rotate(t_1, If[7 < u ≤ 8, ((u - 7) * μ), μ], H') → c_2
  67. CircleArc(A, I, J) → d_2
  68. CircleArc(D, K, N) → e_2
  69. CircleArc(C, O, Q) → f_2