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Parallelogram, Square, Rectangle, Rhombus

Parallelogram, Square, Rectangle, Rhombus
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2018-02-09 01:51
PolygonAngleGeometric Construction
This example demonstrates the construction of a parallelogram, square, rectangle, and rhombus. Key mathematical concepts include parallel lines, perpendicular lines, distance, and angles. Using GeoGebra commands such as Segment, Line, Intersect, and Polygon, the properties of these shapes are visually illustrated. Suitable for middle school and above students to learn geometric construction.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(A, C) → g
  3. Line(C, f) → h
  4. Line(B, g) → i
  5. Intersect(h, i) → D
  6. Polygon(C, A, B, D) → q1, c, a, b, d
  7. Distance(g, d) → e
  8. Angle(C, D, B) → α
  9. Angle(C, A, B) → β
  10. Angle(D, C, A) → γ
  11. Angle(D, B, A) → δ
  12. Segment(B, C) → j
  13. Segment(A, D) → k
  14. Intersect(j, k) → E
  15. Distance(B, E) → distanceBE
  16. Distance(A, E) → distanceAE
  17. Distance(D, E) → distanceDE
  18. Distance(C, E) → distanceCE
  19. Segment(F, G) → l
  20. Circle(F, G) → p
  21. Point(p) → H
  22. Segment(F, H) → m
  23. Line(H, l) → n
  24. Line(G, m) → q
  25. Intersect(n, q) → I
  26. Segment(H, I) → r
  27. Segment(G, I) → s
  28. Polygon(I, G, F, H) → q2, i_1, g_1, f_1, h_1
  29. Angle(G, F, H) → ε
  30. Angle(H, I, G) → ζ
  31. Angle(F, H, I) → η
  32. Angle(F, G, I) → θ
  33. Segment(J, K) → t
  34. OrthogonalLine(J, t) → j_1
  35. OrthogonalLine(K, t) → k_1
  36. Circle(J, K) → c_1
  37. Intersect(c_1, j_1, 2) → L
  38. OrthogonalLine(L, j_1) → l_1
  39. Intersect(k_1, l_1) → M
  40. Segment(J, L) → m_1
  41. Segment(L, M) → n_1
  42. Segment(K, M) → p_1
  43. Polygon(J, L, M, K) → q3, j_2, l_2, m_2, k_2
  44. Distance(H, I) → distanceHI
  45. Distance(G, I) → distanceGI
  46. Distance(F, G) → distanceFG
  47. Distance(H, F) → distanceHF
  48. Angle(J, L, M) → ι
  49. Angle(J, K, M) → κ
  50. Angle(L, J, K) → λ
  51. Angle(K, M, L) → μ
  52. Distance(m_1, p_1) → o
  53. Distance(J, K) → distanceJK
  54. Distance(K, M) → distanceKM
  55. Distance(M, L) → distanceML
  56. Distance(L, J) → distanceLJ
  57. Segment(N, O) → q_1
  58. OrthogonalLine(N, q_1) → r_1
  59. OrthogonalLine(O, q_1) → s_1
  60. Point(s_1) → P
  61. Line(P, q_1) → t_1
  62. Intersect(r_1, t_1) → Q
  63. Segment(N, Q) → a_1
  64. Segment(Q, P) → b_1
  65. Segment(P, O) → d_1
  66. Angle(N, Q, P) → ν
  67. Angle(Q, N, O) → ξ
  68. Angle(O, P, Q) → ο
  69. Angle(N, O, P) → ρ
  70. Distance(Q, N) → distanceQN
  71. Midpoint(Q, N) →
  72. Distance(O, P) → distanceOP
  73. Midpoint(O, P) →
  74. Distance(N, O) → distanceNO
  75. Midpoint(N, O) →
  76. Distance(Q, P) → distanceQP
  77. Midpoint(Q, P) →
  78. Polygon(N, Q, P, O) → q4, n_2, q_2, p_2, o_1

AI Drawing Prompt Reference

Draw a parallelogram first, then construct a square, rectangle, and rhombus. Start by drawing two parallel line segments AB and AC, then draw a line parallel to AC through point B, and another line parallel to AB through point D, intersecting at point D. Connect points A, B, C, and D to form the parallelogram. Measure the lengths and angles to ensure AB=CD, AD=BC, and angle ABC=angle CDA. Next, construct a square by ensuring AB=BC=CD=DA and all angles are right angles. Then, construct a rectangle by ensuring AB=CD, AD=BC, and angle ABC=angle CDA=angle ADC=angle DAB. Finally, construct a rhombus by ensuring AB=BC=CD=DA and angle ABC+angle BCD=180 degrees.
The prompt above was compiled from the original drawing commands and is for reference only.