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Properties of a Parallelogram by Philip Collett

Properties of a Parallelogram by Philip Collett
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2014-11-24 19:32
PolygonAngleVector
This example demonstrates the properties of a parallelogram, involving concepts such as vectors, angles, and line segments. Using GeoGebra commands like Polygon, PointIn, Line, etc., dynamic exploration of the sides, angles, and diagonals of a parallelogram is possible. Suitable for middle school and above students and teachers.

GeoGebra Commands & Parameters

  1. Polygon(J, K, L, M) → poly2, j_1, k_1, l_1, m_1
  2. PointIn(poly2) → N
  3. Line(A, D) → l
  4. PointIn(poly2) → B
  5. AngularBisector(B, A, D) → d
  6. Segment(D_1, E_1) → e
  7. Intersect(e, d) → F_1
  8. AngularBisector(D, A, B) → k
  9. Corner(1, 1) → Cnr1
  10. Corner(1, 2) → Cnr2
  11. Corner(1, 3) → Cnr3
  12. Corner(1, 4) → Cnr4
  13. Polygon(CN1, CN2, CN3, CN4) → Panel, cn1, cn2, cn3, cn4
  14. Angle(B, D, A) → γ
  15. Angle(A, B, D) → ε
  16. Line(B, l) → a
  17. OrthogonalLine(A, l) → b
  18. Intersect(a, b) → E
  19. OrthogonalLine(D, l) → c
  20. Intersect(a, c) → F
  21. Segment(A, B) → f
  22. Line(D, f) → g
  23. Intersect(a, g) → C
  24. Segment(E, F) → h
  25. Segment(B, C) → i
  26. Segment(D, F) → m
  27. Segment(A, E) → n
  28. Segment(A, D) → p
  29. Angle(F, D, A) → α
  30. Angle(A, E, F) → β
  31. Segment(D, C) → j
  32. Polygon(A, E, F, D) → poly1, a_1, g_1, h_1, c_1
  33. Polygon(A, B, C, D) → poly3, a_2, b_1, i_1, c_2
  34. Segment(A, C) → q
  35. Segment(B, D) → r
  36. Intersect(q, r) → O
  37. Segment(A, O) → s
  38. Segment(O, C) → t
  39. Segment(B, O) → d_1
  40. Segment(O, D) → e_1
  41. Angle(D, A, B) → δ
  42. Angle(B, C, D) → ζ
  43. Angle(A, B, C) → η
  44. Angle(C, D, A) → θ
  45. Point(f) → G
  46. Point(j) → H