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Rectangles of Same Area: Geometric Construction Method

Rectangles of Same Area: Geometric Construction Method
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2015-01-13 08:21
PolygonCoordinate GeometryGeometric Construction
This example demonstrates how to cut and rearrange one rectangle into another of the same area using geometric construction. Key mathematical concepts include area conservation, rectangle partitioning, and rearrangement. The construction involves GeoGebra commands such as Polygon, Circle, OrthogonalLine, and Intersect. Suitable for middle school students learning geometric transformations and area calculations, also useful for math competition geometry proofs.

GeoGebra Commands & Parameters

  1. Polygon(A, C, D, B) → poly1, a, c, d, b
  2. Circle(A, K) → p
  3. Point(p) → L
  4. Segment(A, L) → i
  5. OrthogonalLine(L, i) → j
  6. OrthogonalLine(A, i) → l
  7. Segment(K, E) → e
  8. Polygon(K, E, F, A) → poly2, k, e_1, f, a_1
  9. Circle(L, e) → g
  10. Intersect(g, j, 2) → G
  11. OrthogonalLine(G, j) → h
  12. Intersect(l, h) → H
  13. Polygon(L, G, H, A) → poly3, l_1, g_1, h_1, a_2
  14. Line(C, D) → m
  15. Line(A, B) → n
  16. Line(K, I) → q
  17. Line(L, G) → r
  18. Intersect(m, g_1) → J
  19. Intersect(m, r) → M
  20. Polygon(J, G, M) → poly4, m_1, j_1, g_2

AI Drawing Prompt Reference

Draw a geometric construction diagram showing the cutting and rearranging of one rectangle into another of the same area. The diagram includes rectangles, circles, line segments, and lines, connected by intersection points. The construction order is: first draw the initial rectangle and circle, then use line segments and lines to cut, and finally form a new rectangle through intersection points. Ensure the diagram reflects the concepts of area conservation and rectangle partitioning.
The prompt above was compiled from the original drawing commands and is for reference only.