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Rectangle with Given Perimeter and Diagonal

Rectangle with Given Perimeter and Diagonal
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2017-07-02 04:31
PolygonCoordinate GeometryGeometric Construction
This example demonstrates constructing a rectangle with a given perimeter and diagonal. Key mathematical concepts include the properties of rectangles, diagonal length calculation, and geometric construction. Using GeoGebra commands such as Segment, LineBisector, and Intersect, you can dynamically adjust the rectangle's dimensions. Suitable for middle school and above students learning geometric construction and related properties.

GeoGebra Commands & Parameters

  1. Segment(A, B) → d
  2. Segment(D, E) → h_1
  3. LineBisector(A, B) → g
  4. Intersect(g, d) → C
  5. Circle(C, A) → c
  6. Circle(A, h_1) → d_1
  7. Point(c) → F
  8. Line(A, F) → i
  9. Segment(F, B) → j
  10. Circle(F, B) → e
  11. Intersect(e, i, 2) → G
  12. Segment(B, G) → l
  13. Angle(F, G, B) → α
  14. Circle(A, h_1) → k
  15. Circle(A, h_1) → f
  16. Circle(A, 8.580748170750233) → h

AI Drawing Prompt Reference

Draw a rectangle with a given perimeter of 20 units and a diagonal of 10 units. Start by drawing points A and B, then draw the perpendicular bisector of AB and the line segment AB, find the intersection point C of the bisector and the segment. Draw a circle centered at C, and the intersection point F is another vertex of the rectangle. Draw the line AF, and it intersects with the segment BF at point G. Connect BG to form the rectangle ABFG.
The prompt above was compiled from the original drawing commands and is for reference only.