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Parallelogram Investigation

Parallelogram Investigation
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2018-02-27 03:48
VectorFunctionGeometric Construction
This example demonstrates the properties of parallelograms. Key mathematical concepts include vectors and linear functions. Using GeoGebra commands such as Segment, Circle, Point, etc., you can construct a parallelogram and explore its properties. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Circle(B, A) → c
  3. Point(c) → C
  4. Segment(B, C) → b
  5. Circle(C, B) → d
  6. Circle(A, B) → e
  7. Intersect(d, e, 2) → D
  8. Segment(A, D) → f
  9. Segment(D, C) → g
  10. Segment(A, C) → i
  11. Segment(D, B) → j
  12. Intersect(i, j) → E
  13. Segment(E, A) → k
  14. Segment(E, D) → l
  15. Segment(E, C) → m
  16. Segment(E, B) → n
  17. Angle(C, E, D) → α
  18. Angle(D, C, E) → β
  19. Angle(B, C, E) → γ
  20. Angle(E, A, B) → δ
  21. Angle(E, A, D) → ε
  22. Angle(E, B, C) → ζ
  23. Angle(A, B, E) → η
  24. Angle(A, D, E) → θ
  25. Angle(C, D, E) → ι
  26. Angle(A, D, C) → κ
  27. Angle(D, C, B) → λ
  28. Angle(C, B, A) → μ
  29. Angle(B, A, D) → ν
  30. Segment(F, G) → r
  31. OrthogonalLine(F, r) → s
  32. OrthogonalLine(G, r) → t
  33. Point(t) → H
  34. OrthogonalLine(H, t) → a_1
  35. Intersect(s, a_1) → I
  36. Segment(I, F) → b_1
  37. Segment(I, H) → c_1
  38. Segment(H, G) → d_1
  39. Segment(I, G) → e_1
  40. Segment(F, H) → f_1
  41. Intersect(e_1, f_1) → J
  42. Segment(J, I) → g_1
  43. Segment(J, H) → h_1
  44. Segment(J, G) → i_1
  45. Segment(J, F) → j_1
  46. Angle(H, I, F) → ξ
  47. Angle(H, I, J) → ο
  48. Angle(F, I, J) → ρ
  49. Angle(I, H, J) → σ
  50. Angle(J, H, G) → τ
  51. Angle(I, H, G) → υ
  52. Angle(H, G, J) → ϕ
  53. Angle(F, G, J) → χ
  54. Angle(H, G, F) → ψ
  55. Angle(H, J, G) → ω
  56. Angle(I, J, F) → α_1
  57. Angle(F, J, G) → β_1
  58. Angle(H, J, I) → γ_1
  59. Angle(J, F, I) → δ_1
  60. Angle(G, F, J) → ε_1
  61. Angle(G, F, I) → ζ_1
  62. Segment(K, L) → k_1
  63. Segment(K, M) → l_1
  64. Line(M, k_1) → m_1
  65. Line(L, l_1) → n_1
  66. Intersect(m_1, n_1) → N
  67. Segment(N, M) → p_1
  68. Segment(N, L) → q_1
  69. Segment(K, N) → r_1
  70. Segment(L, M) → s_1
  71. Intersect(r_1, s_1) → O
  72. Segment(O, N) → t_1
  73. Segment(O, M) → a_2
  74. Segment(O, K) → b_2
  75. Segment(O, L) → c_2
  76. Angle(O, L, K) → η_1
  77. Angle(N, L, O) → θ_1
  78. Angle(O, N, L) → ι_1
  79. Angle(M, N, O) → κ_1
  80. Angle(N, M, O) → λ_1
  81. Angle(K, M, O) → μ_1
  82. Angle(O, K, L) → ν_1
  83. Angle(M, K, O) → ξ_1
  84. Angle(L, O, K) → ο_1
  85. Angle(N, O, M) → ρ_1
  86. Angle(K, O, M) → σ_1
  87. Angle(N, O, L) → τ_1
  88. Angle(N, L, K) → υ_1
  89. Angle(L, K, M) → ϕ_1
  90. Angle(K, M, N) → χ_1
  91. Angle(L, N, M) → ψ_1
  92. Segment(P, Q) → d_2
  93. OrthogonalLine(Q, d_2) → e_2
  94. OrthogonalLine(P, d_2) → f_2
  95. Circle(P, Q) → g_2
  96. Circle(Q, P) → h_2
  97. Intersect(g_2, f_2, 2) → R
  98. Intersect(h_2, e_2, 2) → S
  99. Segment(R, S) → i_2
  100. Segment(S, Q) → j_2
  101. Segment(R, P) → k_2
  102. Angle(P, R, S) → ω_1
  103. Angle(R, S, Q) → α_2
  104. Angle(S, Q, P) → β_2
  105. Angle(Q, P, R) → γ_2
  106. Segment(R, Q) → m_2
  107. Segment(P, S) → n_2
  108. Intersect(m_2, n_2) → T
  109. Segment(R, T) → p_2
  110. Segment(T, S) → q_2
  111. Segment(T, Q) → r_2
  112. Segment(T, P) → s_2
  113. Angle(Q, R, S) → δ_2
  114. Angle(R, S, P) → ε_2
  115. Angle(P, S, Q) → ζ_2
  116. Angle(S, Q, R) → η_2
  117. Angle(R, Q, P) → θ_2
  118. Angle(Q, P, S) → ι_2
  119. Angle(S, P, R) → κ_2
  120. Angle(P, R, Q) → λ_2
  121. Angle(S, T, R) → μ_2