Question

Which is a diagonal through the interior of the cube?


A cube. The top face has points A, B, D, C. The bottom face has points E, F, H, G.
Side B E
Side C F
Side D G
Side G F

Answer 1

In a cube, a diagonal through the interior connects two opposite vertices that are not on the same face.

Given the points you have specified:

- Top face: A, B, C, D
- Bottom face: E, F, G, H

The vertices can be represented in a 3D space:

- A (0, 0, 1)
- B (1, 0, 1)
- C (1, 1, 1)
- D (0, 1, 1)
- E (0, 0, 0)
- F (1, 0, 0)
- G (1, 1, 0)
- H (0, 1, 0)

To find the diagonals through the interior of the cube, we can consider pairs of opposite vertices:

1. **A (top) and G (bottom)**
2. **B (top) and H (bottom)**
3. **C (top) and E (bottom)**
4. **D (top) and F (bottom)**

Any of these pairs represent a diagonal through the interior of the cube:

- For example, the diagonal from A to G is a direct line connecting these two points through the interior of the cube.

So, any line connecting these opposite corner vertices will be a diagonal through the interior of the cube.