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Rhombus, Square, Trapezoid Geometric Relations

Rhombus, Square, Trapezoid Geometric Relations
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2016-03-09 21:55
PolygonAngleCoordinate GeometryGeometric Construction
This example demonstrates the geometric relationships and properties among rhombus, square, and trapezoid; Core math concepts include polygon properties, angle calculation, distance measurement, orthogonal lines, and linear functions; GeoGebra commands and objects used in construction are Circle, Intersect, Segment, Angle, Point, OrthogonalLine, Distance, Line, and Slope; Suitable for high school mathematics teaching, focusing on geometric construction and property exploration.

GeoGebra Commands & Parameters

  1. Circle(A, 5) → c
  2. Circle(B, 5) → d
  3. Intersect(c, d, 1) → C
  4. Intersect(c, d, 2) → D
  5. Segment(A, C) → a
  6. Segment(B, C) → b
  7. Segment(A, D) → e
  8. Segment(D, B) → f
  9. Angle(A, C, B) → α
  10. Angle(B, D, A) → β
  11. Angle(C, B, D) → γ
  12. Angle(D, A, C) → δ
  13. Circle(E, 5) → g
  14. Point(g) → F
  15. Segment(E, F) → h
  16. Circle(F, 5) → k
  17. OrthogonalLine(F, h) → i
  18. Intersect(k, i, 1) → G
  19. OrthogonalLine(G, i) → j
  20. OrthogonalLine(E, h) → l
  21. Distance(i, h) → m
  22. Distance(j, l) → n
  23. Intersect(g, j, 2) → H
  24. Distance(j, l) → o
  25. Distance(H, G) → distanceHG
  26. Distance(E, F) → distanceEF
  27. Distance(F, G) → distanceFG
  28. Distance(E, H) → distanceEH
  29. Circle(I, J) → p
  30. Segment(I, J) → q
  31. Point(p) → K
  32. Segment(I, K) → r
  33. Segment(K, J) → s
  34. Point(r) → L
  35. Line(L, s) → t
  36. Intersect(t, q) → M
  37. Slope(t) → m_1
  38. Slope(s) → m_2
  39. Slope(q) → m_3
  40. Slope(r) → m_4