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Rhombus Property Exploration

Rhombus Property Exploration
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2019-08-20 02:34
PolygonAngleGeometric Construction
This GeoGebra applet serves as a resource for students to informally discover the properties of a rhombus. It demonstrates key characteristics such as opposite sides parallel, equal side lengths, and diagonals that are perpendicular bisectors of each other. The construction uses GeoGebra commands including Circle, Point, Intersect, Segment, Midpoint, Angle, Polygon, and Mirror to dynamically generate the rhombus shape. It is suitable for middle and high school mathematics learners, particularly those exploring parallelogram families and geometric properties through interactive visualization.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → D
  3. Circle(B, A) → d
  4. Circle(D, A) → e
  5. Intersect(d, e, 2) → C
  6. Segment(A, B) → a
  7. Segment(B, C) → b
  8. Segment(C, D) → f
  9. Segment(D, A) → g
  10. Midpoint(A, C) → E
  11. Segment(D, E) → h
  12. Segment(E, B) → i
  13. Segment(C, E) → j
  14. Segment(E, A) → k
  15. Angle(D, C, E) → α
  16. Angle(E, C, B) → β
  17. Angle(B, A, E) → γ
  18. Angle(E, A, D) → δ
  19. Angle(C, B, E) → ε
  20. Angle(E, B, A) → ζ
  21. Angle(E, D, C) → η
  22. Angle(A, D, E) → θ
  23. Angle(C, E, D) → ι
  24. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  25. Mirror(A, k) → A'
  26. Mirror(B, k) → B'
  27. Mirror(C, k) → C'
  28. Polygon(A', B', C') → poly1', c', a', b'
  29. Polygon(D, A, B) → poly2, b_2, d_1, a_2
  30. Mirror(D, h) → D'
  31. Mirror(A, h) → A'_1
  32. Mirror(B, h) → B'_1
  33. Polygon(D', A'_1, B'_1) → poly2', b'_1, d', a'_1
  34. Polygon(A, B, C, D) → poly3, a_3, b_3, c_2, d_2
  35. Segment(D, B) → s
  36. Segment(A, C) → t