Question

in the cube shown below, which lines are intersecting? select all that apply.
image of a cube with vertices labeled d, p, q, r, s, t, u, v
options:

• $overleftrightarrow{pq}$ and $overleftrightarrow{op}$
• $overleftrightarrow{qr}$ and $overleftrightarrow{rv}$
• $overleftrightarrow{qu}$ and $overleftrightarrow{rv}$
• $overleftrightarrow{qu}$ and $overleftrightarrow{st}$

Explanation:

Step1: Check line intersection definition

Intersecting lines share exactly one common point.

Step2: Analyze each pair

• $\overline{PQ}$ and $\overline{OP}$: Share point Q? No, $\overline{OP}$ is not labeled; assume typo (e.g., $\overline{OQ}$). If $\overline{PQ}$ & $\overline{OQ}$, share Q.
• $\overline{QR}$ and $\overline{RV}$: Share point R.
• $\overline{QU}$ and $\overline{RV}$: No common point (skew or parallel).
• $\overline{QU}$ and $\overline{ST}$: No common point (parallel/skew).

Correction: Valid intersecting pairs must share a point. $\overline{QR}$ & $\overline{RV}$ share R.

Answer:

$\overline{QR}$ and $\overline{RV}$