Question

Identify the two-dimensional shape of the cross section if a cube is sliced horizontally. Then identify the two-dimensional shape of the cross section if
a cube is sliced vertically.
Explain why the shape are the same or different

Answer 1

[see the pictures attached for a better understanding !]

Horizontal cross section : we get a square in the horizontal plane, its side is the same as the cube's.

Vertical cross section : we get a square in the vertical plane, its side is the same as the cube's.

Hence, the two shapes are the same (two squares with same sides are the same)

Answer 2

-- First of all, you haven't specified how the cube itself is situated. 
That would make a difference.
Is it sitting flat on one of its faces ? 
Standing on one vertex ?
Standing on one edge ?

-- If I assume that the cube is sitting on a level, horizontal table, flat
on one of its faces parallel to the table and in contact with it, then ANY
slice that is parallel to any face, whether horizontal or vertical, reveals
a square cross section, congruent to any face of the cube.