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From Parallelogram to Arbitrary Quadrilateral

From Parallelogram to Arbitrary Quadrilateral
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2017-08-21 16:31
PolygonTransformationGeometric Construction
This example demonstrates the transformation from a parallelogram to an arbitrary quadrilateral. Key mathematical concepts include geometric transformations and properties of quadrilaterals. Using GeoGebra commands such as Line, Point, and Polygon, the shape of the quadrilateral can be dynamically adjusted. Suitable for students at the junior high school level and above to learn about geometric transformations and quadrilateral properties.

GeoGebra Commands & Parameters

  1. Line(D, A) → f
  2. Line(A, B) → g
  3. Line(B, C) → h
  4. Line(C, D) → i
  5. Point(g) → E
  6. Point(h) → F
  7. Point(i) → G
  8. Point(i) → H
  9. AngularBisector(A, B, F) → j
  10. AngularBisector(B, C, G) → k
  11. AngularBisector(A, D, H) → l
  12. AngularBisector(E, A, D) → m
  13. Intersect(j, m) → M
  14. Intersect(j, k) → N
  15. Intersect(k, l) → P
  16. Intersect(l, m) → Q
  17. Polygon(A, B, C, D) → poly1, a, b, c_1, d
  18. Angle(Q, M, N) → α
  19. Angle(M, N, P) → β
  20. Angle(N, P, Q) → γ
  21. Angle(P, Q, M) → δ
  22. Segment(M, N) → n
  23. Segment(N, P) → p
  24. Segment(P, Q) → q
  25. Segment(Q, M) → r
  26. Angle(Q, D, H) → ε
  27. Angle(Q, D, A) → ζ
  28. Point(f) → I
  29. Angle(B, A, M) → η
  30. Angle(M, A, I) → θ
  31. Segment(M, P) → s
  32. Segment(Q, N) → t
  33. Intersect(s, t) → J
  34. Angle(N, J, M) → ι
  35. Angle(D, A, B) → κ
  36. Angle(A, B, C) → λ
  37. Angle(B, C, D) → c
  38. Angle(C, D, A) → ν