Rhombus Construction and Metric Analysis

Rhombus Construction and Metric Analysis
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2016-11-15 23:02
① This example demonstrates how to construct a rhombus in GeoGebra and measure its side lengths, perimeter, diagonals, and angles. ② Core mathematical concepts include the definition of a rhombus (all sides equal), perpendicular bisecting diagonals, interior angle relationships, perimeter calculation, and geometric measurement (distances and angles). ③ Construction highlights: from the summary, commands such as Segment, Circle, Point, LineBisector, Intersect, Polygon, Distance, Perimeter, PointIn, Angle, and Midpoint are used, creating objects A, B, C, D, poly2, and auxiliary points with metric texts (e.g., distanceFH, perimeterpoly2, α, β, etc.), illustrating a complete geometric construction and dynamic measurement workflow. ④ Suitable for middle school geometry lessons or introductory geometric construction, helping learners understand rhombus properties, construction steps, and GeoGebra's measurement tools.

GeoGebra Commands & Parameters

  1. Segment(A, B) → j
  2. Circle(A, B) → e
  3. Point(e) → C
  4. LineBisector(B, C) → k
  5. Circle(B, A) → p
  6. Intersect(p, k, 2) → D
  7. Polygon(B, D, C, A) → poly2, f_1, h_1, g_1, e_1
  8. Segment(A, D) → t
  9. Segment(B, C) → i_1
  10. Intersect(t, i_1) → O_1
  11. Distance(A, D) → distanceFH
  12. Distance(B, C) → distanceGI
  13. Perimeter(poly2) → perimeterpoly2
  14. PointIn(poly2) → Pointpoly2
  15. Angle(C, A, B) → α
  16. Angle(A, B, D) → β
  17. Angle(D, C, A) → γ
  18. Angle(B, D, C) → δ
  19. Angle(B, O_1, A) → ε
  20. Angle(A, O_1, C) → ζ
  21. Angle(D, O_1, B) → η
  22. Angle(C, O_1, D) → θ
  23. Distance(A, O_1) → distanceAO1
  24. Midpoint(A, O_1) →
  25. Distance(D, O_1) → distanceDO1
  26. Midpoint(D, O_1) →
  27. Distance(C, O_1) → distanceCO1
  28. Midpoint(C, O_1) →
  29. Distance(B, O_1) → distanceBO1
  30. Midpoint(B, O_1) →