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Rectangle Dissection

Rectangle Dissection
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2017-04-10 21:17
PolygonTransformationGeometric Construction
This example demonstrates the transformation of a triangle into a rectangle through dissection. Key mathematical concepts include geometric transformations and polygons. Using GeoGebra commands such as PointIn, Polygon, and Rotate, a dynamic geometric figure is constructed. Suitable for middle school and above students to learn about geometric transformations and polygon properties.

GeoGebra Commands & Parameters

  1. PointIn(w) → B
  2. Polygon(A, C, B, D) → poly1, a_1, c, b, d
  3. Rotate(B, -90°, C) → B'
  4. Midpoint(A, B') → F
  5. Circle(F, A) → e
  6. Intersect(e, Line[B, C]) → G, H
  7. Circle(C, G) → g
  8. Intersect(g, b, 1) → I
  9. Segment(C, I) → h
  10. OrthogonalLine(A, h) → i
  11. Intersect(i, h) → J
  12. Point(Circle[K, Distance[A, J]]) → N
  13. Polygon(K, N, L) → poly2, l, k, n
  14. Point(Circle[M, Distance[C, B]]) → O
  15. Polygon(M, O, P) → poly3, p, m, o
  16. Point(Circle[Q, Distance[A, J]]) → R
  17. Intersect(Circle[S, Distance[I, D]], Circle[Q, Distance[A, D]]) → T, U, ,
  18. Polygon(Q, R, S, U) → poly4, q, r, s, u
  19. PolyLine(A, C, B, D, A) → j

AI Drawing Prompt Reference

Draw a triangle ABC and transform it into a rectangle through dissection and rotation. Start by taking a point D on BC and constructing rectangle ABCD. Then rotate B' 90 degrees counterclockwise around C to get B', and connect AF to make a circle F. Use the intersection of circle F and line BC to form part of a rectangle. Continue constructing other rectangles and polygons to form a dynamic geometric figure composed of multiple rectangles and triangles.
The prompt above was compiled from the original drawing commands and is for reference only.