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Sections of Rectangular Prisms (Cuboids)

Sections of Rectangular Prisms (Cuboids)
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2019-05-24 01:22
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates how to investigate different sections of a rectangular prism (cuboid) by intersecting it with various planes. Key math concepts include solid geometry, geometric sections, and spatial visualization. Construction highlights the use of commands like Polygon, PointIn, Translate, Rotate, Prism, Plane, IntersectPath, and OrthogonalLine. Suitable for high school students learning about 3D shapes and their cross-sections.

GeoGebra Commands & Parameters

  1. Polygon(B + (-2, -2), B + (2, -2), B + (2, 2), B + (-2, 2)) → poly3, e, f, g, i
  2. PointIn(poly3) → C
  3. Translate((0, 0, 0), Vector[B, C]) → A
  4. Polygon(A + (-4, -4), A + (4, -4), A + (4, 4), A + (-4, 4)) → poly1, a, b, c, d
  5. Rotate(Rotate[Translate[poly1, Vector[A, A + (0, 0, h)]], (90° * s), A + (0, 0, h), yAxis], (90° * t), A, zAxis) → poly2
  6. Rotate(D, 120°, (0, 0, 0)) → E
  7. Prism(Polygon[(-1.5, -1.25, 0), (1.5, -1.25, 0), (1.5, 1.25, 0), (-1.5, 1.25, 0)], (-1.5, -1.25, 4)) → m, M, edge2, edge3, edge4, edge5, edge6, edge7, edge8, N, Q, face1, face2, face3, face4, face5, edge1
  8. Polygon(D, E, 3, xOyPlane) → poly4, j, k, l, F
  9. PointIn(poly2) → G
  10. PointIn(poly2) → H
  11. PointIn(poly2) → I
  12. Plane(G, I, H) → n
  13. IntersectPath(n, m) → poly6, poly5, r, a_1, b_1, c_1, K, L_1, O, P, J, L, p, q
  14. Rotate(m, 0, zAxis) → m'
  15. Rotate(m, 0, zAxis) → m'_1
  16. OrthogonalLine(A, n) → d_1

AI Drawing Prompt Reference

Draw a rectangular prism and cut it with different planes to observe the changes in the cross-sections. First, draw a rectangular prism with a square base. Then, use a plane to cut it and generate a quadrilateral cross-section. Next, rotate the prism and use another plane to cut it again, generating another quadrilateral cross-section. Finally, use a third plane to cut it and generate a triangular cross-section.
The prompt above was compiled from the original drawing commands and is for reference only.