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Cuboid - Surface Diagonal and Diagonal Plane

Cuboid - Surface Diagonal and Diagonal Plane
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2013-05-03 03:08
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the surface diagonal and diagonal plane of a cuboid. Key mathematical concepts include the diagonal and diagonal plane in solid geometry. Using GeoGebra commands such as Intersect, Point, Vector, and Polygon, the cuboid and its diagonals and diagonal plane can be constructed. Suitable for middle school and above students to learn solid geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Point(xAxis) → U
  3. Point(yAxis) → V
  4. Vector(O, U) → u
  5. Vector(O, V) → v
  6. Vector(O, J) → j
  7. Vector(O, K) → k
  8. Vector(O, I) → i
  9. Polygon(A, B, C, D) → baza_1, a, b, c, d
  10. Polygon(A', B', C', D') → baza_2, a', b', c', d'
  11. Segment(A, A') → e
  12. Segment(D, D') → f
  13. Segment(B, B') → g
  14. Segment(C, C') → h
  15. Segment(B, C') → plošnDij_1
  16. Segment(B, D) → plošnDij_2
  17. Segment(B, A') → plošnDij_3
  18. Segment(A, C') → prostDijag
  19. Segment(A, C) → plošnDijag
  20. Polygon(A, C, C') → prostTrok, c'_1, a_1, c_1
  21. Angle(A, C, C') → α
  22. Polygon(A', B, C, D') → dijagPresj_3, a'_1, b_1, c_2, d'_1
  23. Polygon(D, B, B', D') → dijagPresj_2, d_1, b_2, b'_1, d'_2
  24. Polygon(B, C', D', A) → dijagPresj_1, b_3, c'_2, d'_3, a_2

AI Drawing Prompt Reference

Draw a cuboid with its surface diagonal and diagonal plane. Start by taking points O, U, and V on the x-axis and y-axis, then construct vectors u and v. Next, construct vectors j, k, and i from point O. Use these vectors and points to construct the bottom faces baza_1 and baza_2, and the side segments e, f, g, and h. Then, construct the diagonal lines plošnDij_1, plošnDij_2, plošnDij_3, and prostDijag, as well as the diagonal plane polygons prostTrok, dijagPresj_1, dijagPresj_2, and dijagPresj_3.
The prompt above was compiled from the original drawing commands and is for reference only.