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Rhombus Measurement and Properties

Rhombus Measurement and Properties
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2015-10-12 22:37
PolygonAngleTrigonometryGeometric ConstructionSlider Animation
This example demonstrates the intrinsic relationships between the sides, angles, and diagonals of a rhombus through dynamic measurement and geometric construction. Key math concepts include congruence, trigonometric functions, and coordinate geometry. GeoGebra commands like Point, Segment, Circle, Intersect, Distance, Angle, Polygon, and Slider are used to explore properties. Suitable for middle school and above, enhancing geometric reasoning and computational skills.

GeoGebra Commands & Parameters

  1. Point(Circle[B, abs(side)]) → C
  2. Segment(B, C) → a
  3. Point(Circle[C, abs(side)]) → D
  4. Segment(C, D) → b
  5. Circle(B, side) → c
  6. Circle(D, side) → d
  7. Intersect(c, d, 2) → A
  8. Segment(B, A) → e
  9. Segment(A, D) → f
  10. Segment(A, C) → g
  11. Segment(B, D) → h
  12. Intersect(h, g) → E
  13. Distance(A, B) → distanceAB
  14. Distance(B, C) → distanceBC
  15. Distance(C, D) → distanceCD
  16. Distance(D, A) → distanceDA
  17. Distance(A, C) → distanceAC
  18. Distance(B, D) → distanceBD
  19. Distance(A, E) → distanceAE
  20. Distance(C, E) → distanceCE
  21. Distance(B, E) → distanceBE
  22. Distance(D, E) → distanceDE
  23. Angle(D, A, B) → α
  24. Angle(A, B, C) → β
  25. Angle(B, C, D) → γ
  26. Angle(C, D, A) → δ
  27. Angle(B, E, A) → ε
  28. Angle(C, E, B) → ζ
  29. Angle(D, E, C) → η
  30. Angle(A, E, D) → θ
  31. Angle(E, A, B) → ι
  32. Angle(A, B, E) → κ
  33. Angle(E, B, C) → λ
  34. Angle(B, C, E) → μ
  35. Angle(E, C, D) → ν
  36. Angle(C, D, E) → ξ
  37. Angle(E, D, A) → ο
  38. Angle(D, A, E) → ρ
  39. Polygon(A, B, C, D) → poly1, a_1, b_1, c_1, d_1