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Rhombus Measurement and Properties by matthew.hardie

Rhombus Measurement and Properties by matthew.hardie
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2015-03-19 10:07
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In collections Quadrilateral Investigation
This example demonstrates the relationships between the sides, angles, and diagonals of a rhombus. It involves core mathematical concepts such as geometric construction, distance measurement, angle calculation, polygon properties, and equation solving. Key GeoGebra commands used include Point, Segment, Circle, Intersect, Distance, Angle, and Polygon for point placement, line segment drawing, intersection calculation, distance and angle measurement, and polygon construction. Suitable for middle school and above students to understand the geometric properties of rhombuses and explore their inherent patterns.

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

AI Drawing Prompt Reference

Draw a rhombus by creating circles with centers B and D, finding their intersection points A and C, and connecting these points. Measure the lengths of the sides and diagonals, and calculate the angles.
The prompt above was compiled from the original drawing commands and is for reference only.