MathPlotAI Logo MathPlotAI

Geometric Properties and Constructions of Parallelograms and Rectangles

Geometric Properties and Constructions of Parallelograms and Rectangles
Loading the math board and drawing, please wait…
2012-09-26 19:11
CirclePolygonAngleGeometric Construction
This GeoGebra example dynamically demonstrates the geometric constructions, classifications, and core properties of parallelograms, rectangles, rhombuses, and squares. Key mathematical concepts include side and angle relationships, area and perimeter formulas, diagonal intersections (orthogonality and bisection), and circumcircles/incircles. To construct these shapes, the applet utilizes core GeoGebra commands including Point, Segment, Rotate, Angle, Line, Intersect, OrthogonalLine, Polygon, and Circle, driven by parameters a, b, alpha and vertices A, B, C, D to show the transition from general parallelograms to rectangles and squares. It is highly suitable for secondary school geometry lessons, university-level introductory courses, or self-paced mathematical exploration.

GeoGebra Commands & Parameters

  1. Point(Circle[A, a]) → B
  2. Segment(A, B) → AB
  3. Point(Circle[A, b]) → Dpomocna
  4. Segment(A, Dpomocna) → b'pomocni
  5. Rotate(Dpomocna, α, A) → D
  6. Angle(Dpomocna, A, D) → α_1
  7. Segment(A, D) → AD_1
  8. Line(D, AB) → la
  9. Line(B, AD_1) → lb
  10. Intersect(la, lb) → C
  11. Line(A, B) → lAB
  12. OrthogonalLine(D, lAB) → n_a
  13. Intersect(n_a, lAB) → E
  14. Segment(D, E) → h_a
  15. Polygon(A, B, C, D) → Paralelogram, a_0, b_0, c_0, d_0
  16. Polygon(A_2, B_2, C_2, D_2) → Pravougaonik, a_2, b_2, c_2, d_2
  17. Angle(B_2, A_2, D_2) → αP
  18. Polygon(A_3, B_3, C_3, D_3) → Kvadrat, a_3, b_3, c_3, d_3
  19. Polygon(A_4, B_4, C_4, D_4) → Romb, a_4, b_4, c_4, d_4
  20. Angle(B_3, A_3, D_3) → αK
  21. Angle(B_4, A_4, D_4) → αR
  22. Segment(D_4, Er_1) → h
  23. Segment(A, C) → AC
  24. Segment(B, D) → BD
  25. Intersect(AC, BD) → O
  26. Segment(B_2, D_2) → dp
  27. Segment(A_2, C_2) → dp_1
  28. Intersect(dp, dp_1) → O_1
  29. Segment(D_3, B_3) → dk
  30. Segment(A_3, C_3) → dk_1
  31. Segment(A_4, C_4) → dr1
  32. Segment(B_4, D_4) → dr2
  33. Intersect(dr2, dr1) → O_3
  34. Intersect(dk_1, dk) → O_2
  35. Circle(O_1, A_2) → k_p
  36. Circle(O_3, h / 2) → k_r
  37. Segment(O_1, B_2) → r_p
  38. Intersect(k_r, a_4) → Er_2,
  39. Segment(O_3, Er_2) → r_r
  40. Circle(O_2, dk / 2) → k_o
  41. Circle(O_2, a / 2) → k_u
  42. Segment(O_2, B_3) → r_o
  43. Intersect(k_u, a_3) → Ek,
  44. Segment(O_2, Ek) → r_u
  45. OrthogonalLine(D, lb) → n_b
  46. Intersect(lb, n_b) → F
  47. Segment(D, F) → h_b
  48. Point(lAB) → A_1
  49. Point(la) → D_1
  50. Polygon(A_1, B_1, C_1, D_1) → P, a_1, b_1, c_1, d_1
  51. Segment(D_1, E_0) → ha_0
  52. Angle(D, C, B) → γ
  53. Angle(C, B, A) → β
  54. Angle(A, D, C) → δ
  55. Angle(B_4, O_3, C_4) → αRd
  56. Segment(O_3, C_4) → dr1p
  57. Segment(B_4, O_3) → dr2p
  58. Angle(B_4, A_4, O_3) → αR_1
  59. Angle(O_3, A_4, D_4) → αR_2