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Animation Demonstrating Inequalities and Geometric Transformations

Animation Demonstrating Inequalities and Geometric Transformations
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2017-03-26 11:58
Coordinate GeometryInequalityGeometric Construction
In collections Congruence (CO) Cluster Geometry Review CCSS High School: Geometry (Congruence) Volume 1 Unit 5: Triangle Congruence
This example dynamically illustrates the application of inequalities and geometric transformations in plane figures. It involves core concepts like inequalities, straight lines, polygons, means, vectors, and transformations. Key GeoGebra commands used include Line, Segment, Circle, Intersect, Rotate, Angle, Polygon, Vector, and Translate to construct and manipulate shapes. Suitable for high school mathematics students and educators to understand the dynamic relationship between geometric transformations and inequalities.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Segment(A, B) → g
  3. OrthogonalLine(B, g) → h
  4. Circle(B, 1) → c
  5. Intersect(c, h, 2) → C
  6. Ray(B, C) → i
  7. Rotate(B, (a * π / 180), A) → B'
  8. Angle(B, A, B') → α
  9. Ray(A, B') → j
  10. Intersect(h, j) → D
  11. Segment(A, D) → k
  12. Segment(D, B) → l
  13. Angle(D, B, A) → β
  14. Circle(E, g) → d
  15. Point(d) → F
  16. Segment(E, F) → m
  17. OrthogonalLine(F, m) → n
  18. Circle(F, l) → e
  19. Intersect(e, n, 2) → G
  20. Segment(F, G) → p
  21. Segment(G, E) → q
  22. Polygon(A, B, D) → poly1, d_1, a_1, b
  23. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], D) → A'
  24. Segment(A, A') → r
  25. Dilate(D, If[1 < o ≤ 2, 2 - o, 0], B) → D'
  26. Segment(D, D') → s
  27. Line(A, q) → t
  28. Point(t) → H
  29. Angle(D, A, H) → γ
  30. Dilate(D, If[3 < o ≤ 4, 4 - o, 0], G) → D'_1
  31. Vector(D, D'_1) → u
  32. Translate(A, u) → A'_1
  33. Translate(A', u) → A''
  34. Segment(A'_1, A'') → r'
  35. Rotate(A'_1, If[3 < o ≤ 4, ((o - 3) * γ), γ], A'') → I
  36. Rotate(A'', If[3 < o ≤ 4, ((o - 3) * γ), γ], A'') → A'''
  37. Segment(I, A''') → r''
  38. Line(D, p) → f_1
  39. Point(f_1) → J
  40. Angle(B, D, J) → δ
  41. Dilate(D, If[4 < o ≤ 5, 5 - o, 0], G) → D'_2
  42. Vector(D, D'_2) → v
  43. Translate(D, v) → D'_3
  44. Translate(D', v) → D''
  45. Segment(D'_3, D'') → s'
  46. Rotate(D'_3, If[4 < o ≤ 5, ((o - 4) * δ), δ], D'_3) → K
  47. Rotate(D'', If[4 < o ≤ 5, ((o - 4) * δ), δ], D'_3) → D'''
  48. Segment(K, D''') → s''
  49. Segment(E, F) → g_1
  50. Angle(G, F, E) → ε
  51. Dilate(D, If[6 < o ≤ 7, 7 - o, 0], G) → D'_4
  52. Vector(D, D'_4) → w
  53. Translate(A, w) → A'_2
  54. Translate(B, w) → B'_1
  55. Translate(D, w) → D'_5
  56. Polygon(A'_2, B'_1, D'_5) → poly1', d'_5, a'_2, b'_1
  57. Rotate(A'_2, If[7 < o ≤ 8, ((o - 7) * γ), γ], G) → L
  58. Rotate(B'_1, If[7 < o ≤ 8, ((o - 7) * γ), γ], G) → M
  59. Rotate(D'_5, If[7 < o ≤ 8, ((o - 7) * γ), γ], G) → N
  60. Polygon(L, M, N) → poly1'', n_1, l_1, m_1
  61. Segment(A, B) → h_1