Question

in the cube shown below, which lines are parallel? select all that apply.
(image of a cube with vertices labeled k, j, i, f, e, d, g, h)
options:

• $overleftrightarrow{fj}$ and $overleftrightarrow{gk}$
• $overleftrightarrow{dg}$ and $overleftrightarrow{ef}$
• $overleftrightarrow{fj}$ and $overleftrightarrow{ei}$
• $overleftrightarrow{jk}$ and $overleftrightarrow{de}$

Explanation:

Step1: Analyze parallelism in cubes

In a cube, opposite edges are parallel. Check each pair:

• $\overline{FJ}$ & $\overline{GK}$: Both vertical edges on opposite faces → parallel.
• $\overline{DG}$ & $\overline{EF}$: Both front-back horizontal edges → parallel.
• $\overline{FJ}$ & $\overline{EI}$: $\overline{FJ}$ is vertical, $\overline{EI}$ is front vertical? No, $\overline{EI}$ is adjacent vertical, not parallel.
• $\overline{JK}$ & $\overline{DE}$: $\overline{JK}$ is top horizontal, $\overline{DE}$ is bottom horizontal → parallel.

Step2: Verify correct pairs

Only pairs with same direction (opposite edges) are parallel.

Answer:

$\overline{FJ}$ and $\overline{GK}$, $\overline{DG}$ and $\overline{EF}$, $\overline{JK}$ and $\overline{DE}$