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Rhombus, Rectangle, and Square Lab

Rhombus, Rectangle, and Square Lab
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2019-12-03 23:17
PolygonAngleCoordinate GeometryGeometric Construction
① This interactive GeoGebra lab demonstrates the properties and relationships among rhombus, rectangle, and square, three special types of parallelograms. ② Core mathematical concepts include classification of quadrilaterals, diagonal properties (perpendicularity, bisection, equality), angle relationships (right angles, equal opposite angles), side properties (equal sides, parallel opposite sides), and the criteria for identifying these special quadrilaterals. ③ Construction details: Based on the construction summary, the lab uses GeoGebra commands such as Segment, Circle, Point, Intersect, OrthogonalLine, Line, Distance, and Angle, creating objects A, B, C, D, E, F, G, H, I, J, K, L, O, and measuring distances CA, AB, DC with corresponding text labelscars. By dragging vertices, users can dynamically observe how the shape changes and which properties hold. ④ Suitable for middle school geometry lessons or self-study, helping students grasp the properties and identification of special parallelograms, and useful for teachers creating interactive instructional materials.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Circle(A, B) → c
  3. Point(c) → C
  4. Segment(A, C) → g
  5. Circle(C, A) → d
  6. Circle(B, A) → e
  7. Intersect(d, e, 2) → D
  8. Segment(C, D) → h
  9. Segment(D, B) → i
  10. Segment(E, F) → j
  11. OrthogonalLine(E, j) → k
  12. Point(k) → G
  13. Line(G, j) → l
  14. OrthogonalLine(F, j) → m
  15. Intersect(l, m) → H
  16. Segment(F, H) → n
  17. Segment(H, G) → p
  18. Segment(G, E) → q
  19. Segment(I, J) → r
  20. Circle(I, J) → s
  21. OrthogonalLine(I, r) → t
  22. Intersect(s, t, 1) → K
  23. Segment(I, K) → a
  24. OrthogonalLine(J, r) → b
  25. OrthogonalLine(K, a) → f_1
  26. Intersect(b, f_1) → L
  27. Segment(K, L) → g_1
  28. Segment(L, J) → h_1
  29. Distance(C, A) → distanceCA
  30. Distance(A, B) → distanceAB
  31. Distance(D, C) → distanceDC
  32. Distance(D, B) → distanceDB
  33. Distance(I, J) → distanceIJ
  34. Distance(L, K) → distanceLK
  35. Distance(K, I) → distanceKI
  36. Distance(L, J) → distanceLJ
  37. Distance(H, F) → distanceHF
  38. Distance(F, E) → distanceFE
  39. Distance(G, H) → distanceGH
  40. Distance(G, E) → distanceGE
  41. Angle(I, J, L) → α
  42. Angle(L, K, I) → β
  43. Angle(J, I, K) → γ
  44. Angle(K, L, J) → δ
  45. Angle(G, E, F) → ε
  46. Angle(F, H, G) → ζ
  47. Angle(E, G, H) → η
  48. Angle(H, F, E) → θ
  49. Angle(C, A, B) → ι
  50. Angle(C, D, B) → κ
  51. Angle(A, B, D) → λ
  52. Angle(A, C, D) → μ