MathPlotAI Logo MathPlotAI

Dynamic Equilateral Triangle Construction

Dynamic Equilateral Triangle Construction
Loading the math board and drawing, please wait…
2019-10-16 21:00
TriangleVectorGeometric Construction
This example dynamically illustrates a geometric problem posed by Antonio Gutierrez, focusing on constructing equilateral triangles from any triangle's sides. It involves concepts like congruence, equilateral triangles, vectors, and transformations. Constructed using commands such as Segment, Rotate, Point, Polygon, and Vector. Suitable for high school geometry education and construction learning.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Rotate(B, (a * π / 180), A) → B'
  3. Angle(B, A, B') → α
  4. Ray(A, B') → g
  5. Point(g) → C
  6. Segment(B, C) → h
  7. Segment(A, C) → i
  8. Polygon(A, B, C) → poly1, c, a_1, b
  9. Polygon(C, B, 3) → poly2, j, k, l, D
  10. Polygon(A, C, 3) → poly3, m, n, p, E
  11. Rotate(A, If[0 < d ≤ 1, (d * π / 3), π / 3], A) → A'
  12. Rotate(C, If[0 < d ≤ 1, (d * π / 3), π / 3], A) → C'
  13. Segment(A', C') → i'
  14. Rotate(B, If[0 < d ≤ 1, (d * π / 3), π / 3], C) → B'_1
  15. Rotate(C, If[0 < d ≤ 1, (d * π / 3), π / 3], C) → C'_1
  16. Segment(B'_1, C'_1) → h'
  17. Rotate(B'_1, If[1 < d ≤ 2, ((d - 1) * π / 3), π / 3], D) → I
  18. Rotate(C'_1, If[1 < d ≤ 2, ((d - 1) * π / 3), π / 3], D) → J
  19. Segment(I, J) → h''
  20. Rotate(A', If[1 < d ≤ 2, ((d - 1) * π / 3), π / 3], E) → A''
  21. Rotate(C', If[1 < d ≤ 2, ((d - 1) * π / 3), π / 3], E) → C''
  22. Segment(A'', C'') → i''
  23. Midpoint(E, D) → L
  24. Dilate(D, If[4 < d ≤ 5, 5 - d, 0], L) → D'
  25. Dilate(L, If[5 < d ≤ 6, 6 - d, 0], E) → L'
  26. Rotate(D, If[6 < d ≤ 7, ((-(d - 6)) * π), (-π)], L) → D'_1
  27. Rotate(D', If[6 < d ≤ 7, ((-(d - 6)) * π), (-π)], L) → D''
  28. Dilate(A, If[3 < d ≤ 4, 4 - d, 0], D) → A'_1
  29. Segment(A, A'_1) → q
  30. Dilate(D, If[5 < d ≤ 6, 6 - d, 0], B) → D'_2
  31. Vector(D, D'_2) → u
  32. Translate(A, u) → A'_2
  33. Translate(A'_1, u) → F
  34. Segment(A'_2, F) → q'
  35. Line(B, q) → r
  36. Line(E, B) → s
  37. Point(r) → G
  38. Angle(E, B, G) → β
  39. Rotate(A'_2, If[5 < d ≤ 6, ((-(d - 5)) * β), (-β)], D'_2) → H
  40. Rotate(F, If[5 < d ≤ 6, ((-(d - 5)) * β), (-β)], D'_2) → F'
  41. Segment(H, F') → q''