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Dynamic Inequalities in a Triangle Applet

Dynamic Inequalities in a Triangle Applet
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2017-12-04 12:13
TriangleInequalityGeometric Construction
This example dynamically demonstrates inequalities within a triangle, covering core concepts like inequalities, plane figures, translation, arithmetic mean, piecewise functions, and algebra. It is constructed using GeoGebra commands such as Ray, Rotate, Angle, Point, Segment, Midpoint, Min, Circle, Intersect, CircleSector, Polygon, Dilate, Vector, Translate, and CircleArc. Ideal for high school mathematics instruction or geometric exploration.

GeoGebra Commands & Parameters

  1. Ray(A, B_1) → f
  2. Rotate(B_1, (a_2 * π / 180), A) → B'
  3. Angle(B_1, A, B') → α
  4. Ray(A, B') → g
  5. Point(g) → C
  6. Point(f) → B
  7. Segment(C, B) → h
  8. Midpoint(h) → E
  9. Midpoint(C, A) → F
  10. Midpoint(B, A) → G
  11. Segment(A, B) → i
  12. Segment(A, C) → j
  13. Min({i, h, j}) → b_1
  14. Circle(A, (0.2 * b_1)) → c_2
  15. Circle(C, (0.2 * b_1)) → d
  16. Circle(B, (0.2 * b_1)) → e
  17. Intersect(d, j, 1) → H
  18. Intersect(d, h, 1) → I
  19. Intersect(c_2, j, 1) → J
  20. Intersect(c_2, i, 1) → K
  21. Intersect(e, i, 1) → L
  22. Intersect(e, h, 1) → M
  23. CircleSector(A, K, J) → k
  24. CircleSector(B, M, L) → p
  25. CircleSector(C, H, I) → q
  26. Polygon(A, B, C) → poly1, c_1, a_1, d_1
  27. Rotate(K, If[0 < l ≤ 1, (l * α), α], A) → K'
  28. CircleSector(A, K, K') → r
  29. Dilate(B, If[1 < l ≤ 2, 2 - l, 0], C) → D'
  30. Segment(B, D') → a
  31. Dilate(A, If[2.5 < l ≤ 3.5, 3.5 - l, 0], E) → A'
  32. Vector(A, A') → u
  33. Translate(r, u) → r'
  34. Angle(M, B, L) → β
  35. Rotate(M, If[3.5 < l ≤ 4.5, ((l - 3.5) * β), β], B) → M'
  36. CircleSector(B, M, M') → s
  37. Dilate(A, If[4.5 < l ≤ 5.5, 5.5 - l, 0], C) → A'_1
  38. Segment(A, A'_1) → b
  39. Dilate(B, If[6 < l ≤ 7, 7 - l, 0], F) → D'_1
  40. Vector(B, D'_1) → v
  41. Translate(s, v) → s'
  42. Rotate(H, If[7 < l ≤ 8, ((l - 7) * (π - α - β)), π - α - β], C) → H'
  43. CircleSector(C, H, H') → t
  44. Dilate(B, If[8 < l ≤ 9, 9 - l, 0], A) → D'_2
  45. Segment(B, D'_2) → c
  46. Dilate(C, If[9.5 < l ≤ 10.5, 10.5 - l, 0], G) → C'
  47. Vector(C, C') → w
  48. Translate(t, w) → t'
  49. CircleArc(A, K, J) → e_1
  50. CircleArc(B, M, L) → g_1
  51. CircleArc(C, H, I) → h_1