Final answer:
Side CE is not a diagonal through the interior of the cube if C and E are vertices on the same face or edge; thus, it is the correct answer to the question regarding which line segment is not a diagonal of a cube. So, the correct answer is c) Side CE.
Step-by-step explanation:
The question is asking which line segment mentioned does not represent a diagonal through the interior of a cube.
A diagonal of a cube is a line segment that connects two vertices of the cube which are not on the same face.
Let's go through the options:
- Side BE: This is a diagonal if B and E are opposite vertices of the cube.
- Side CH: This is also a diagonal if C and H are opposite vertices of the cube.
- Side CE: If C and E are vertices on the same edge or face, CE is not a diagonal but rather an edge of the cube.
- Side DG: This can be considered a diagonal if D and G are opposite vertices of the cube.
Therefore, the correct answer is c) Side CE, as it does not represent a diagonal through the interior of the cube if C and E are on the same face or edge of the cube.
So, the correct answer is c) Side CE.