Question

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

Answer 1

Answer:

  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.