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Space Diagonals

Space Diagonals
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2014-06-10 18:21
VectorSolid GeometryGeometric Construction
In collections Pythagoras' Theorem
This example demonstrates the properties and calculations of diagonals in spatial polygons. It involves core mathematical concepts like polygons, spatial geometry, vector operations, and distance calculations. Construction highlights include using Polygon, Dilate, Segment, and Distance commands in GeoGebra. Suitable for high school and above students studying solid geometry and vector geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → poly1, a_1, b, c, d
  2. Dilate(A, a, E) → A'
  3. Dilate(B, a, E) → B'
  4. Dilate(C, a, E) → C'
  5. Dilate(D, a, E) → D'
  6. Polygon(A', B', C', D') → poly1', a', b', c', d'
  7. Segment(A, A') → e
  8. Segment(D, D') → f
  9. Segment(C', C) → g
  10. Segment(B', B) → h
  11. Polygon(A', A, D, D') → poly2, a'_1, a_2, d_1, d'_1
  12. Polygon(A', A, B, B') → poly3, a'_2, a_3, b_1, b'_1
  13. Polygon(B, B', C', C) → poly4, b_2, b'_2, c'_1, c_1
  14. Polygon(D', D, C, C') → poly5, d'_2, d_2, c_2, c'_2
  15. Segment(D', B) → i
  16. Distance(g, c') → j
  17. Segment(D', C) → k

AI Drawing Prompt Reference

Draw a spatial quadrilateral ABCD, then scale points A, B, C, and D to A', B', C', and D' respectively with point E as the center. Draw the diagonals AA', DD', CC', and BB' of the spatial quadrilateral A'B'C'D'. Then, draw the diagonals A'D', AD, BC, and B'C' between the spatial quadrilateral A'B'C'D' and the original quadrilateral ABCD. Finally, draw the line segments DD' to B and CC' to C, and measure the distance between C and C'.
The prompt above was compiled from the original drawing commands and is for reference only.