The base of a cube is parallel to the horizon. If the cube is cut by a plane to form a cross section, under what circumstance would it be possible for the cross section be a non-rectangular parallelogram?

A. when the plane passes through a pair of vertices that do not share a common face
B.
when the plane is perpendicular to the base and intersects two adjacent vertical faces
C.
not enough information to answer the question

  A.  when the plane passes through a pair of vertices that do not share a common face

Step-by-step explanation:

The cross section will be a parallelogram if two pairs of opposite faces are intersected. Having the plane contain the space diagonal, but no other vertices, is one way to ensure a (non-rectangular) parallelogram.

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The only vertices not sharing a common face are the ones at opposite ends of a space diagonal. If the plane intersects both of those, it will contain the space diagonal.

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step-by-step explanation:

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