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Properties of a Parallelogram by kjmillikan

Properties of a Parallelogram by kjmillikan
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2014-12-05 05:33
PolygonVectorCoordinate GeometryGeometric Construction
This example demonstrates the geometric properties of a parallelogram, including parallel opposite sides, equal opposite angles, equal opposite sides, and bisecting diagonals. It involves core mathematical concepts such as properties of parallel lines, congruent triangles, similarity transformations, vector operations, and coordinate geometry. The construction uses GeoGebra commands and objects like Line, Segment, Intersect, Angle, Distance, and Slope to create vertices A, B, C, D, sides a, b, c, d, diagonals AC and BD, midpoints E, heights h, etc. It is suitable for high school students and teachers to explore dynamic properties of parallelograms.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Line(C, a) → b
  3. Segment(A, C) → c
  4. Line(B, c) → d
  5. Intersect(b, d) → D
  6. Segment(B, D) → e
  7. Segment(A, B) → f
  8. Segment(C, D) → g
  9. Angle(A, B, D) → α
  10. Angle(D, C, A) → β
  11. Angle(C, A, B) → γ
  12. Angle(B, D, C) → δ
  13. Distance(B, D) → distanceBD
  14. Distance(A, B) → distanceAB
  15. Distance(A, C) → distanceAC
  16. Distance(D, C) → distanceDC
  17. Slope(e) → m
  18. Slope(g) → m_1
  19. Slope(c) → m_2
  20. Slope(f) → m_3
  21. Segment(A, D) → k
  22. Segment(B, C) → l
  23. Intersect(l, k) → E
  24. Distance(B, E) → distanceBE
  25. Distance(C, E) → distanceCE
  26. Distance(A, E) → distanceAE
  27. Distance(D, E) → distanceDE
  28. Distance(B, C) → distanceBC
  29. Distance(A, D) → distanceAD
  30. Angle(C, A, D) → ε
  31. Angle(D, A, B) → ζ
  32. Angle(B, D, A) → η
  33. Angle(A, D, C) → θ
  34. Angle(B, C, A) → ι
  35. Angle(D, C, B) → κ
  36. Angle(C, B, D) → λ
  37. Angle(A, B, C) → μ
  38. Angle(A, E, C) → ν
  39. Angle(C, E, D) → ξ
  40. Angle(D, E, B) → ο
  41. Angle(B, E, A) → ρ