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Rhombus and Square Construction Exploration

Rhombus and Square Construction Exploration
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2016-10-04 10:25
PolygonAngleCoordinate GeometryTransformationGeometric Construction
①This example demonstrates how to construct a rhombus and a square in GeoGebra, exploring relationships among side lengths, diagonals, and angles.②Core mathematical concepts include rhombus, square, parallelogram, perpendicular bisectors of diagonals, rotational symmetry, perimeter, and quadratic equations applied to geometric measurements.③Construction highlights: from the summary, commands such as Segment, Line, LineBisector, Intersect, Distance, Point, Angle, Rotate, and Midpoint are used, creating objects A, B, C, D, E, F, G, H, I, W, Y, and measuring distances AE, DB, FY, IY, YH, HW, with angles α and β labeled.④Suitable for middle and high school geometry classes to study properties of special quadrilaterals, step-by-step geometric construction, and dynamic measurement verification, also useful for exploring connections between quadratic equations and geometry.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Line(A, C) → g
  3. Line(B, g) → h
  4. LineBisector(f) → i
  5. Intersect(h, i) → D
  6. Intersect(g, i) → E
  7. Segment(E, B) → j
  8. Segment(A, D) → k
  9. Distance(g, k) → a
  10. Distance(A, E) → distanceAE
  11. Distance(h, j) → b
  12. Distance(D, B) → distanceDB
  13. Segment(W, Y) → l
  14. LineBisector(W, Y) → m
  15. Intersect(m, l) → F
  16. Distance(F, Y) → distanceFY
  17. Point(m) → G
  18. Point(m) → H
  19. Line(W, H) → n
  20. Line(Y, n) → p
  21. Intersect(m, p) → I
  22. Line(W, I) → q
  23. Line(H, Y) → r
  24. Angle(W, I, Y) → α
  25. Rotate(W, 90°, I) → W'
  26. Angle(W, I, W') → β
  27. Distance(I, Y) → distanceIY
  28. Midpoint(I, Y) →
  29. Distance(Y, H) → distanceYH
  30. Midpoint(Y, H) →
  31. Distance(H, W) → distanceHW
  32. Midpoint(H, W) →
  33. Distance(W, I) → distanceWI
  34. Midpoint(W, I) →