Question

in the cube shown below, which lines are parallel? select all that apply. \\(\overleftrightarrow{sv}\\) and \\(\overleftrightarrow{tu}\\) \\(\overleftrightarrow{qr}\\) and \\(\overleftrightarrow{op}\\) \\(\overleftrightarrow{pq}\\) and \\(\overleftrightarrow{sv}\\) \\(\overleftrightarrow{os}\\) and \\(\overleftrightarrow{op}\\)

Explanation:

To determine which lines are parallel in a cube, we use the property that in a cube, opposite edges (or edges on parallel faces) are parallel. Let's analyze each option:

Step 1: Analyze $\overleftrightarrow{SV}$ and $\overleftrightarrow{TU}$

In a cube, $SV$ and $TU$ are edges on parallel faces (the front and back faces, for example) and run in the same direction. So, $\overleftrightarrow{SV} \parallel \overleftrightarrow{TU}$.

Step 2: Analyze $\overleftrightarrow{QR}$ and $\overleftrightarrow{OP}$

Looking at the cube, $QR$ and $OP$ are edges that are on parallel faces (the top and bottom faces, or other parallel faces) and have the same direction. So, $\overleftrightarrow{QR} \parallel \overleftrightarrow{OP}$.

Step 3: Analyze $\overleftrightarrow{PQ}$ and $\overleftrightarrow{SV}$

$PQ$ and $SV$ are not in the same direction or on parallel faces. $PQ$ is a horizontal edge on one face, while $SV$ is a vertical or slant edge (depending on the cube's orientation) on another face. So, they are not parallel.

Step 4: Analyze $\overleftrightarrow{OS}$ and $\overleftrightarrow{OP}$

$OS$ and $OP$ meet at point $O$, so they are intersecting, not parallel.

Answer:

$\overleftrightarrow{SV}$ and $\overleftrightarrow{TU}$, $\overleftrightarrow{QR}$ and $\overleftrightarrow{OP}$