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GeoGebra Math Problem: Parallelogram and Cosine Function Construction

GeoGebra Math Problem: Parallelogram and Cosine Function Construction
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2019-05-06 03:22
FunctionCoordinate GeometryGeometric Construction
This example demonstrates how to use GeoGebra to draw a parallelogram and analyze it with cosine functions. Key mathematical concepts include area calculation, cosine theorem, quadratic functions, and coordinate geometry. Construction involves using commands like Line, Intersect, Polygon, Angle, and objects such as Point, Mirror, Midpoint. Suitable for high school students or college students learning geometry and function relationships, helping to understand transformations and graph associations.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Line(C, f) → g
  3. Line(A, C) → h
  4. Line(B, h) → i
  5. Intersect(i, g) → D
  6. Polygon(A, C, D, B) → q1, a, c, d, b
  7. Point(q1) → E
  8. Polygon(C, D, E) → t1, e, c_1, d_1
  9. Polygon(E, A, B) → t2, b_1, e_1, a_1
  10. Point(b) → F
  11. Point(c) → G
  12. Polygon(A, C, F) → t3, f_1, a_2, c_2
  13. Polygon(F, G, B) → t4, b_2, f_2, g_1
  14. Mirror(C, b) → C'
  15. Mirror(G, b) → G'
  16. Midpoint(b) → H
  17. CircleArc(H, C', C) → k
  18. Angle(C', H, C) → α
  19. CircleArc(H, G, G') → p
  20. Angle(G, H, G') → β
  21. Rotate(C, ((-α) * t), H) → C'_1
  22. Polygon(F, C'_1, A) → t5, a_3, f_3, c'_1
  23. Rotate(G, (β * t), H) → G'_1
  24. Polygon(F, G'_1, B) → t6, b_3, f_4, g'_1
  25. Mirror(C, d) → C'_2
  26. Mirror(A, d) → A'
  27. Midpoint(d) → I
  28. CircleArc(I, A', A) → q
  29. CircleArc(I, C, C'_2) → r
  30. Angle(A', I, A) → γ
  31. Angle(C, I, C'_2) → δ
  32. Rotate(A, ((-γ) * t), I) → A'_1
  33. Polygon(E, A'_1, B) → t7, b_4, e_2, a'_1
  34. Rotate(C, (δ * t), I) → C'_3
  35. Polygon(E, C'_3, D) → t8, d_2, e_3, c'_3
  36. Intersect(d_1, b_2) → J
  37. Intersect(d_1, f_2) → K
  38. Intersect(b_1, f_2) → L
  39. Intersect(b_1, b_2) → M
  40. Intersect(b_1, a_2) → N
  41. Polygon(C, J, M, N) → q2, c_3, j_1, m, n
  42. Polygon(J, G, K) → t9, k_1, j_2, g_2
  43. Polygon(L, K, E) → t10, e_4, l, k_2
  44. Polygon(L, B, F, M) → q3, l_1, b_5, f_5, m_1
  45. Polygon(A, N, F) → t11, f_6, a_4, n_1
  46. Point(a) → O
  47. Point(d) → P
  48. Segment(O, P) → s
  49. Intersect(a, c) → Q
  50. Segment(P, Q) → h_1
  51. OrthogonalLine(C', b) → i_1
  52. Mirror(A, f) → A'_2
  53. Mirror(C, f) → C'_4
  54. Mirror(D, f) → D'
  55. Mirror(B, f) → B'
  56. Polygon(A'_2, C'_4, D', B') → q1', a'_2, c'_4, d', b'
  57. Mirror(A, d) → A'_3
  58. Mirror(C, d) → C'_5
  59. Mirror(D, d) → D'_1
  60. Mirror(B, d) → B'_1
  61. Polygon(A'_3, C'_5, D'_1, B'_1) → q1'_1, a'_3, c'_5, d'_1, b'_1