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Properties of a Rhombus by hduong2020

Properties of a Rhombus by hduong2020
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2018-02-07 23:44
PolygonAngleCoordinate GeometryTransformationGeometric Construction
This interactive GeoGebra example dynamically demonstrates the fundamental properties of a rhombus, including equal side lengths, perpendicular bisecting diagonals, equal opposite angles, and supplementary adjacent angles. It integrates concepts from parallelograms, isosceles triangles, ratios, and even 3D vectors in a planar context. The construction uses commands such as Circle, Segment, Point, Mirror, Slope, Angle, Intersect, and Distance to build the rhombus and its diagonals, with measurements of side lengths, diagonal lengths, and angles displayed via text objects. Suitable for middle or high school geometry classes, this resource allows students to explore and verify rhombus properties through hands-on manipulation and measurement.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Segment(A, B) → f
  3. Point(c) → C
  4. Segment(A, C) → g
  5. Segment(C, B) → h
  6. Mirror(A, h) → A'
  7. Mirror(C, h) → C'
  8. Segment(A', C') → g'
  9. Mirror(A, h) → A'_1
  10. Mirror(B, h) → B'
  11. Segment(A'_1, B') → f'
  12. Slope(f) → m
  13. Angle(A, C, A') → α
  14. Angle(C, A', B) → β
  15. Angle(A', B, A) → γ
  16. Angle(B, A, C) → δ
  17. Slope(f') → m_3
  18. Segment(B, C) → i
  19. Segment(A, A') → j
  20. Intersect(i, j) → D
  21. Distance(B, D) → distanceBD
  22. Distance(D, C) → distanceDC
  23. Distance(A', D) → distanceA'D
  24. Distance(D, A) → distanceDA
  25. Angle(A', D, C) → ε
  26. Angle(A, D, B) → ζ
  27. Angle(B, D, A') → η
  28. Angle(C, D, A) → θ