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Constructing a Shifted Rectangular Prism

Constructing a Shifted Rectangular Prism
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2020-10-07 11:15
VectorSolid GeometryTransformationGeometric Construction
This GeoGebra example demonstrates how to construct a shifted rectangular prism (rectangular solid). The construction uses Vector command to define translation direction and distance, Polygon to draw the base, Translate to move the base to create the top face, and Prism command to complete the 3D solid. It also calculates the prism's Volume and shows intersections (IntersectPath) between planes and the solid path. Suitable for middle and high school geometry teaching, this example helps students understand spatial translation transformations, prism properties, and volume calculation methods.

GeoGebra Commands & Parameters

  1. Vector(T, U) → v
  2. Polygon(A, B, 4) → poly1, f_2, g, h_1, i, C, D
  3. Vector(E, F) → u
  4. Translate(B, v) → B'
  5. Translate(D, v) → D'
  6. Translate(C, v) → C'
  7. Translate(A, v) → A'
  8. Polygon(A', B', C', D') → poly2, a', b', c', d'
  9. Polygon(G, H, I, J) → poly3, g_1, h_2, i_1, j
  10. Prism(poly1, N) → c, O, edgeBO, edgeCP, edgeDQ, edgeNO, edgeOP, edgePQ, edgeNQ, P, Q, faceABON, faceBCPO, faceCDQP, faceADQN, faceNOPQ, edgeAN
  11. Point(yAxis) → R
  12. Plane(S, xOyPlane) → d
  13. Volume(c) → volumec
  14. Point(c) → Pointc
  15. Translate(G, u) → G'
  16. Translate(J, u) → J'
  17. Translate(H, u) → H'
  18. Prism(poly2, G') → e, V, edgeB'V, edgeC'W, edgeD'Z, edgeG'V, edgeVW, edgeWZ, edgeG'Z, W, Z, faceA'B'VG', faceB'C'WV, faceC'D'ZW, faceA'D'ZG', faceG'VWZ, edgeA'G'
  19. IntersectPath(d, c) → poly4, K, L, M, A_1, k, l, n, p
  20. IntersectPath(d, e) → poly5, B_1, C_1, D_1, E_1, q, r, s, t

AI Drawing Prompt Reference

Draw a shifted rectangular prism. First, draw the base of a rectangular prism. Then, translate the base by a vector to form the top face. Next, use the prism command to complete the 3D solid. Calculate the volume of the prism and show the intersection lines between the base and the top face.
The prompt above was compiled from the original drawing commands and is for reference only.