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Parallel and Isosceles Triangle Animation

Parallel and Isosceles Triangle Animation
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2017-02-09 03:53
TriangleGeometric Construction
This example demonstrates the dynamic relationship and properties of parallelograms and isosceles triangles through animation. It involves core mathematical concepts such as parallelograms, isosceles triangles, logic, step functions, and inequalities. The construction utilizes commands like Rotate, Angle, Ray, Line, Point, Intersect, Segment, Min, Circle, Dilate, Vector, Polygon, Translate, and CircleSector. Suitable for high school mathematics education, helping students understand the integration of geometric transformations and algebraic logic.

GeoGebra Commands & Parameters

  1. Rotate(B, a°, A) → B'
  2. Angle(B, A, B') → α
  3. Ray(A, B) → f
  4. Ray(A, B') → g
  5. Line(B, g) → h
  6. Point(g) → C
  7. Line(C, f) → i
  8. Intersect(h, i) → D
  9. Segment(C, D) → j
  10. Segment(A, B) → k
  11. Segment(B, D) → l
  12. Segment(A, C) → m
  13. Min(m, k) → b
  14. Circle(C, (0.2 * b)) → d
  15. Circle(A, (0.2 * b)) → e
  16. Circle(B, (0.2 * b)) → p
  17. Circle(D, (0.2 * b)) → c
  18. Intersect(e, k, 1) → E
  19. Intersect(e, m, 1) → F
  20. Intersect(p, k, 1) → G
  21. Intersect(p, l, 1) → H
  22. Intersect(d, g, 2) → I
  23. Ray(C, I) → q
  24. Intersect(c, h, 2) → J
  25. Ray(D, J) → r
  26. Intersect(c, i, 2) → K
  27. Ray(D, K) → s
  28. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], B) → A'
  29. Segment(A, A') → t
  30. Rotate(E, If[1 < o ≤ 2, ((o - 1) * α), α], A) → E'
  31. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], C) → A'_1
  32. Vector(A, A'_1) → u
  33. Segment(A, A'_1) → f_1
  34. Dilate(C, If[2 < o ≤ 3, 3 - o, 0], D) → C'
  35. Vector(C, C') → v
  36. Segment(C, C') → g_1
  37. Dilate(D, If[3 < o ≤ 4, 4 - o, 0], B) → D'
  38. Segment(D, D') → h_1
  39. Polygon(A, B, D, C) → poly1, a_1, b_1, d_2, c_2
  40. Dilate(A, If[5.5 < o ≤ 6.5, 6.5 - o, 0], C) → A'_2
  41. Vector(A, A'_2) → w
  42. Translate(A, w) → A'_3
  43. Translate(A', w) → A''
  44. Dilate(A, If[5 < o ≤ 6, 6 - o, 0], B) → A'_4
  45. Vector(A, A'_4) → u_1
  46. Translate(A, u_1) → A'_5
  47. Translate(A'_1, u_1) → L
  48. Segment(A'_5, L) → i_1
  49. Dilate(A, If[4 < o ≤ 5, 5 - o, 0], C) → A'_6
  50. Vector(A, A'_6) → v_1
  51. Translate(A, v_1) → A'_7
  52. Translate(A', v_1) → A''_1
  53. Segment(A'_7, A''_1) → t'_1
  54. Rotate(E, If[6.5 < o ≤ 7.5, ((o - 6.5) * α), α], A) → E'_1
  55. CircleSector(A, E, E'_1) → c_1
  56. Dilate(A, If[7.5 < o ≤ 8.5, 8.5 - o, 0], C) → A'_8
  57. Vector(A, A'_8) → w_1
  58. Translate(c_1, w_1) → d_1
  59. Dilate(C, If[8.5 < o ≤ 9.5, 9.5 - o, 0], D) → C'_1
  60. Vector(C, C'_1) → e_1
  61. Translate(d_1, e_1) → k_1