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Folding an Envelope

Folding an Envelope
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2022-06-19 16:00
AngleTransformationGeometric Construction
This example demonstrates how to fold an envelope to explore geometric transformations. Key mathematical concepts include reflection, rotation, and geometric construction. Using GeoGebra commands such as Midpoint, Segment, Point, and Line, the folding process of the envelope can be constructed. Suitable for students at the junior high school level and above to learn about geometric transformations and figure construction.

GeoGebra Commands & Parameters

  1. Midpoint(B, C) → E
  2. Midpoint(D, A) → F
  3. Segment(B, C) → f
  4. Segment(C, A) → g
  5. Segment(A, D) → h
  6. Segment(D, B) → i
  7. Point(g) → G
  8. Segment(F, G) → j
  9. Line(E, j) → k
  10. OrthogonalLine(G, xOyPlane) → l
  11. Segment(G, E) → m
  12. Line(F, m) → n
  13. Intersect(k, i) → H
  14. Segment(H, F) → p
  15. Segment(H, E) → q
  16. Rotate(D, a, p) → D'
  17. Polygon(F, D', H) → t1, h_1, f_1, d'
  18. Rotate(A, a, j) → A'
  19. Polygon(F, G, A') → t2, a', f_2, g_1
  20. Rotate(C, a, m) → C'
  21. Rotate(B, (-a), q) → B'
  22. Polygon(G, E, C') → t3, c', g_2, e
  23. Polygon(B', H, E) → t4, e_1, b', h_2
  24. Polygon(H, E, G, F) → q1, h_3, e_2, g_3, f_3

AI Drawing Prompt Reference

Draw a geometric figure of folding an envelope to demonstrate reflection, rotation, and geometric construction. Start by drawing four sides, finding midpoints, and connecting them. Construct key points using midpoints and perpendicular lines, then apply rotations and connections to form multiple polygons, resulting in a complex folded structure that illustrates geometric transformations.
The prompt above was compiled from the original drawing commands and is for reference only.