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Parallelogram Properties Discovery

Parallelogram Properties Discovery
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2018-03-20 21:14
PolygonAngleGeometric Construction
This example demonstrates the geometric properties of a parallelogram, including equal opposite sides and angles, and supplementary adjacent angles. It uses commands like Segment, Line, Intersect, Midpoint, Angle, Polygon, Mirror in GeoGebra for construction. Suitable for middle school and above students to visually understand and verify parallelogram properties and assist in geometric construction learning.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(A, D) → b
  3. Line(D, a) → c
  4. Line(B, b) → d
  5. Intersect(c, d) → C
  6. Segment(D, C) → e
  7. Segment(B, C) → f
  8. Midpoint(A, C) → E
  9. Segment(A, E) → g
  10. Segment(E, C) → h
  11. Segment(D, E) → i
  12. Segment(E, B) → j
  13. Angle(B, A, E) → α
  14. Angle(D, C, E) → β
  15. Angle(E, A, D) → γ
  16. Angle(C, B, E) → δ
  17. Angle(A, D, E) → ε
  18. Angle(E, B, A) → ζ
  19. Angle(E, D, C) → η
  20. Angle(E, C, B) → θ
  21. Angle(C, E, D) → ι
  22. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  23. Mirror(A, g) → A'
  24. Mirror(B, g) → B'
  25. Mirror(C, g) → C'
  26. Polygon(A', B', C') → poly1', c', a', b'
  27. Polygon(A, B, D) → poly2, d_1, a_2, b_2
  28. Mirror(A, j) → A'_1
  29. Mirror(B, j) → B'_1
  30. Mirror(D, j) → D'
  31. Polygon(A'_1, B'_1, D') → poly2', d', a'_1, b'_1
  32. Angle(B, A, D) → κ
  33. Angle(A, D, C) → λ
  34. Angle(D, C, B) → μ
  35. Angle(C, B, A) → ν
  36. Polygon(A, B, C, D) → poly3, a_3, b_3, c_2, d_2