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Step 5: Rotate and Apply Design to the Last Side

Step 5: Rotate and Apply Design to the Last Side
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2014-04-06 15:20
PolygonTransformationGeometric Construction
In collections Not Real, Practice Triangle Rotation Tessellation Math 206
This example demonstrates how to construct the last side of a polygon by rotating and applying a design. Key mathematical concepts include geometric transformations and polygon construction. It uses Segment, Rotate, Midpoint, and Point commands in GeoGebra. Suitable for middle school and above students learning geometric transformations and polygon construction.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(B, C) → b
  3. Segment(C, A) → c
  4. Segment(A, D) → d
  5. Segment(D, E) → e
  6. Segment(E, C) → f
  7. Rotate(A, 60*°, C) → A'
  8. Rotate(D, 60*°, C) → D'
  9. Segment(A', D') → d'
  10. Rotate(D, 60*°, C) → D'_1
  11. Rotate(E, 60*°, C) → E'
  12. Segment(D'_1, E') → e'
  13. Rotate(E, 60*°, C) → E'_1
  14. Rotate(C, 60*°, C) → C'
  15. Segment(E'_1, C') → f'
  16. Midpoint(a) → F
  17. Segment(F, G) → g
  18. Point(a) → H
  19. Segment(H, I) → h
  20. Segment(A, I) → i
  21. Segment(H, G) → j

AI Drawing Prompt Reference

Draw a polygon by first creating a triangle with three line segments, then extend three longer line segments from each vertex of the triangle to form a hexagon. Rotate the first vertex of the hexagon around the center of the triangle by 60 degrees, and connect the rotated vertex to the other end of the corresponding longer line segment. Repeat the rotation and connection steps until the entire shape is constructed. Finally, draw a line segment from the midpoint of the first line segment, and connect the endpoints of this segment to the sides of the polygon to create a decorative pattern.
The prompt above was compiled from the original drawing commands and is for reference only.