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Perimeter of Quadrilateral

Perimeter of Quadrilateral
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2020-07-26 16:38
PolygonGeometric Construction
This example demonstrates how to calculate the perimeter of a quadrilateral using geometric construction methods. Key mathematical concepts include the properties of quadrilaterals and geometric construction. It utilizes commands such as Polygon, Line, Point, Angle, Rotate, Segment, OrthogonalLine, Intersect, Perimeter, and PointIn in GeoGebra. Suitable for middle school and above students to learn geometric construction and perimeter calculation.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → q1, a, b, c, d
  2. Line(A, D) → f
  3. Line(D, C) → g
  4. Point(f) → E
  5. Point(f) → F
  6. Point(g) → G
  7. Angle(B, A, E) → α
  8. Angle(F, D, C) → β
  9. Angle(G, C, B) → γ
  10. Rotate(B, If[0 ≤ k < 1, (-((k * γ))), (-γ)], C) → B'
  11. Rotate(C, If[0 ≤ k < 1, (-((k * γ))), (-γ)], C) → C'
  12. Segment(B', C') → b'
  13. Rotate(C, If[1 ≤ k ≤ 2, ((-(k - 1)) * β)], D) → C'_1
  14. Rotate(D, If[1 ≤ k ≤ 2, ((-(k - 1)) * β)], D) → D'
  15. Segment(C'_1, D') → c'
  16. Rotate(A, If[1 ≤ k ≤ 2, ((k - 1) * α)], A) → A'
  17. Rotate(B, If[1 ≤ k ≤ 2, ((k - 1) * α)], A) → B'_1
  18. Segment(A', B'_1) → a'
  19. Rotate(B', If[1 ≤ k ≤ 2, ((-(k - 1)) * β)], D) → B''
  20. Rotate(C', If[1 ≤ k ≤ 2, ((-(k - 1)) * β)], D) → C''
  21. Segment(B'', C'') → b''
  22. OrthogonalLine(B'_1, a') → h
  23. OrthogonalLine(B'', b'') → i
  24. Point(h) → H
  25. Line(H, d) → j
  26. Intersect(i, j) → I
  27. Segment(H, I) → l
  28. Perimeter(q1) → perimeterq1
  29. PointIn(q1) → Pointq1

AI Drawing Prompt Reference

Draw a quadrilateral and demonstrate how to calculate its perimeter using geometric construction. Start by sketching the quadrilateral, then draw perpendicular lines from two vertices to the opposite sides to find the feet of the perpendiculars. Use rotations and angle relationships to construct diagonals inside the quadrilateral, marking key angles. Finally, create new geometric shapes by rotating and connecting segments, and calculate the perimeter of the original quadrilateral to verify the construction.
The prompt above was compiled from the original drawing commands and is for reference only.