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Diagonals of a Rectangular Prism

Diagonals of a Rectangular Prism
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2016-11-04 00:02
VectorCoordinate GeometrySolid Geometry
This example demonstrates the spatial geometric properties of a rectangular prism, focusing on the calculation and visualization of its diagonals. Key math concepts include solid geometry, vector operations, and 3D coordinate geometry. Construction involves commands like Intersect, Point, Prism, and Segment to build the prism and its diagonals. Suitable for high school and above students studying solid geometry, spatial vectors, and 3D modeling.

GeoGebra Commands & Parameters

  1. Intersect(zAxis, xAxis) → A
  2. Point(zAxis) → B
  3. Point(xAxis) → C
  4. Point(yAxis) → H
  5. Prism(A, B, D, C, H) → a, E, edgeAB, edgeBD, edgeCD, edgeAC, edgeAH, edgeBE, edgeDF, edgeCG, edgeEH, edgeEF, F, edgeFG, edgeGH, G, faceABDC, faceABEH, faceBDFE, faceCDFG, faceACGH, faceEFGH
  6. Intersect(edgeDF, edgeFG) → I
  7. Segment(A, F) → f
  8. Point(xAxis) → J
  9. Point(xAxis) → K
  10. Prism(J, M, L, K, Q) → b, N, edgeJM, edgeLM, edgeKL, edgeJK, edgeJQ, edgeMN, edgeLO, edgeKP, edgeNQ, edgeNO, O, edgeOP, edgePQ, P, faceJKLM, faceJMNQ, faceLMNO, faceKLOP, faceJKPQ, faceNOPQ
  11. Segment(Q, L) → g
  12. Point(xAxis) → R
  13. Point(xAxis) → S
  14. Prism(R, T, U, S, A_1) → c, V, edgeRT, edgeTU, edgeSU, edgeRS, edge1, edgeTV, edgeUW, edgeSZ, edge2, edgeVW, W, edgeWZ, edge3, Z, faceRSUT, face2, faceTUWV, faceSUWZ, face1, face3
  15. Segment(A_1, R) → h
  16. Segment(U, A_1) → i