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Constructing a Square with the Same Area as a Given Rectangle

Constructing a Square with the Same Area as a Given Rectangle
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2015-12-16 23:00
PolygonCoordinate GeometryGeometric Construction
This example demonstrates how to construct a square with the same area as a given rectangle. Key mathematical concepts include geometric construction and area calculation. Commands used include Segment, OrthogonalLine, Circle, Intersect, Ray, Point, Rotate, Midpoint, Semicircle, Polygon, PointIn. Suitable for middle school and above students learning geometric construction and area calculation.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. Circle(A, C) → c
  4. Intersect(c, b) → D, E
  5. Ray(A, E) → d
  6. Point(d) → F
  7. OrthogonalLine(F, d) → e
  8. OrthogonalLine(B, a) → f
  9. Intersect(e, f) → G
  10. Segment(A, F) → g
  11. Segment(F, G) → h
  12. Segment(G, B) → i
  13. Rotate(G, (-(90°)), B) → G'
  14. Segment(B, G') → j
  15. Segment(A, G') → k
  16. Midpoint(k) → H
  17. Semicircle(A, G') → p
  18. OrthogonalLine(B, j) → l
  19. Intersect(p, l, 1) → I
  20. Segment(G, I) → m
  21. Polygon(I, B, 4) → poly1, n, q, r, s, J, K
  22. Polygon(A, F, G, B) → poly2, a_1, f_1, g_1, b_1
  23. PointIn(poly2) → Pointpoly2
  24. PointIn(poly1) → Pointpoly1