MathPlotAI Logo MathPlotAI

Dynamic Parallelogram Problem

Dynamic Parallelogram Problem
Loading the math board and drawing, please wait…
2017-11-06 23:10
TriangleVectorGeometric Construction
This is a dynamic and modifiable illustration of a parallelogram problem posted by Antonio Gutierrez. The example demonstrates the properties of a parallelogram and its related triangles. Using GeoGebra commands such as rotation, angle, segment, and line, one can observe the symmetry of the parallelogram and the centroid of the triangle. Suitable for middle school and above students to learn geometric transformations and triangle properties.

GeoGebra Commands & Parameters

  1. Rotate(A, (a * π / 180), B) → A'
  2. Angle(A, B, A') → α
  3. Segment(A, B) → f
  4. Ray(B, A') → g
  5. Point(g) → C
  6. Line(C, f) → h
  7. Line(A, g) → i
  8. Intersect(i, h) → D
  9. Segment(B, C) → j
  10. Min(f, j) → b
  11. Circle(B, b) → c
  12. Intersect(g, j) → E
  13. Intersect(c, g) → F,
  14. Segment(F, B) → k
  15. Point(k) → G
  16. Dilate(A, If[0 < d ≤ 1, 1 - d, 0], B) → A'_1
  17. Segment(A, A'_1) → l
  18. Circle(B, (0.2 * Min[j, f])) → e
  19. Intersect(e, f) → H,
  20. Rotate(H, If[1 < d ≤ 2, ((d - 1) * α), α], B) → H'
  21. CircleSector(B, H, H') → p
  22. Polygon(B, A, D, C) → q1, b_1, a_1, d_1, c_1
  23. Circle(C, 2) → q
  24. Intersect(q, g) → I, J
  25. Circle(D, 2) → r
  26. Intersect(r, i) → K, L
  27. Dilate(B, If[2 < d ≤ 3, 3 - d, 0], C) → B'
  28. Segment(B, B') → m
  29. Vector(B, B') → u
  30. Translate(p, u) → p'
  31. Ray(C, J) → n
  32. Ray(D, L) → s
  33. Dilate(C, If[3 < d ≤ 4, 4 - d, 0], D) → C'
  34. Vector(C, C') → v
  35. Translate(p', v) → p''
  36. Segment(C, C') → t
  37. Dilate(A, If[3 < d ≤ 4, 4 - d, 0], D) → A'_2
  38. Segment(A, A'_2) → f_1
  39. Intersect(r, h) → M, N
  40. Ray(D, M) → g_1
  41. Segment(C, G) → h_1
  42. Circle(A, h_1) → e_1
  43. Intersect(e_1, f) → O,
  44. Line(C, O) → i_1
  45. Line(A, G) → j_1
  46. Intersect(i_1, j_1) → P
  47. Line(D, P) → k_1
  48. Circle(D, (0.2 * Min[j, f])) → p_1
  49. Intersect(p_1, t) → Q,
  50. Dilate(C, If[6 < d ≤ 7, 7 - d, 0], G) → C'_1
  51. Segment(C, C'_1) → l_1
  52. Rotate(C, If[7 < d ≤ 8, ((d - 7) * (π - α)), π - α], G) → C'_2
  53. Rotate(C'_1, If[7 < d ≤ 8, ((d - 7) * (π - α)), π - α], G) → R
  54. Segment(C'_2, R) → m_1
  55. Dilate(G, If[8 < d ≤ 9, 9 - d, 0], A) → G'
  56. Vector(G, G') → w
  57. Translate(C'_2, w) → S
  58. Translate(R, w) → R'
  59. Segment(S, R') → n_1
  60. Dilate(C, If[9 < d ≤ 10, 10 - d, 0], O) → C'_3
  61. Segment(C, C'_3) → q_1
  62. Dilate(A, If[10 < d ≤ 11, 11 - d, 0], P) → A'_3
  63. Segment(A, A'_3) → r_1
  64. Dilate(P, If[11 < d ≤ 12, 12 - d, 0], G) → P'
  65. Segment(P, P') → s_1
  66. Dilate(D, If[12 < d ≤ 13, 13 - d, 0], P) → D'
  67. Segment(D, D') → t_1
  68. Rotate(Q, If[13 < d ≤ 14, ((d - 13) * α / 2), α / 2], D) → Q'
  69. CircleSector(D, Q, Q') → c_2
  70. Rotate(c_2, If[15 < d ≤ 16, ((d - 15) * α / 2), α / 2], D) → d_2

AI Drawing Prompt Reference

Draw a dynamic parallelogram with points A, B, C, and D. Use rotation, angle, line segment, and ray to demonstrate the symmetry of the parallelogram and observe the centroid of the triangle. Start by creating points A and B, then rotate point A to get A', calculate angle α, draw line segment AB, and use rays and line segments to find point C. Continue by constructing other points and line segments through intersections and further adjustments with scaling and rotation to ensure all points and segments fit the parallelogram's properties.
The prompt above was compiled from the original drawing commands and is for reference only.