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Classify eight pairs of lines in a cuboid

The diagram depicts a cuboid with vertices A,B,C,D,E,F,G,H. Write down whether each pair of lines is parallel, intersecting or skew: AC and CD; AE and DH; AE and CD; AF and BE; DG and BE; AD and GF; AH and CF; AH and BE.

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The source cuboid has front face A upper-left, B upper-right, C lower-left, D lower-right; corresponding back vertices are E,F,G,H. Hidden edges EG, CG, GH are dashed. Lines mentioned in the question include face and space diagonals.
The source cuboid has front face A upper-left, B upper-right, C lower-left, D lower-right; corresponding back vertices are E,F,G,H. Hidden edges EG, CG, GH are dashed. Lines mentioned in the question include face and space diagonals.
The source cuboid has front face A upper-left, B upper-right, C lower-left, D lower-right; corresponding back vertices are E,F,G,H. Hidden edges EG, CG, GH are dashed. Lines mentioned in the question include face and space diagonals.

CJC · Lecture · Cuboid question (unnumbered)

Choose a point on the line and a nonzero direction; keep one parameter consistent across all components.

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