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Sides and Angles of a Parallelogram

Sides and Angles of a Parallelogram
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2016-02-18 00:19
PolygonAngleGeometric Construction
In collections Investigating Parallelogram Sides and Angles
This example demonstrates the relationships between the sides and angles of a parallelogram. It involves core mathematical concepts such as properties of parallelograms, angle calculations, distance measurements, and slopes. The construction uses GeoGebra commands like Segment, Line, Point, Intersect, Slope, Distance, and Angle. It is suitable for middle school and above mathematics education to visually understand geometric properties of parallelograms.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Line(C, a) → b
  3. Point(b) → D
  4. Segment(B, D) → c
  5. Line(A, c) → d
  6. Intersect(b, d) → E
  7. Segment(A, E) → e
  8. Segment(E, D) → f
  9. Slope(f) → mED
  10. Slope(a) → mAB
  11. Slope(e) → mEA
  12. Slope(c) → mBD
  13. Distance(E, A) → distanceEA
  14. Distance(A, B) → distanceAB
  15. Distance(B, D) → distanceBD
  16. Distance(D, E) → distanceDE
  17. Angle(B, A, E) → α
  18. Angle(A, E, D) → β
  19. Angle(E, D, B) → γ
  20. Angle(D, B, A) → δ
  21. Segment(E, B) → j
  22. Segment(D, A) → k
  23. Intersect(j, k) → F
  24. Angle(E, F, A) → ε
  25. Angle(A, F, B) → ζ
  26. Angle(B, F, D) → η
  27. Angle(D, F, E) → θ
  28. Angle(E, D, F) → ι
  29. Angle(F, E, D) → κ
  30. Angle(D, B, F) → λ
  31. Angle(F, D, B) → μ
  32. Angle(F, B, A) → ν
  33. Angle(B, A, F) → ξ
  34. Angle(F, A, E) → ο
  35. Angle(A, E, F) → ρ
  36. Distance(E, F) → distanceEF
  37. Distance(F, B) → distanceFB
  38. Distance(D, F) → distanceDF
  39. Distance(F, A) → distanceFA