Question

in the cube shown below, which lines are skew? select all that apply. image of a cube with vertices labeled r, v, y, x, t, w, s, and line segments, and options: $overleftrightarrow{rv}$ and $overleftrightarrow{wx}$, $overleftrightarrow{tu}$ and $overleftrightarrow{sw}$, $overleftrightarrow{xy}$ and $overleftrightarrow{st}$, $overleftrightarrow{tu}$ and $overleftrightarrow{wv}$ (note: ocr correction for labels as per cube diagram context)

Explanation:

Step1: Define skew lines

Skew lines are non-parallel, non-intersecting lines in 3D space.

Step2: Analyze each pair

• $\overline{RV}$ & $\overline{WX}$: Parallel (same direction in cube), not skew.
• $\overline{TV}$ & $\overline{SW}$: Intersect at $W$ (assuming typo: $\overline{TW}$ & $\overline{SW}$ intersect), not skew.
• $\overline{XY}$ & $\overline{ST}$: Non-parallel, no common points → skew.
• $\overline{TV}$ & $\overline{WY}$: Non-parallel, no common points → skew.

Answer:

$\overline{XY}$ and $\overline{ST}$, $\overline{TV}$ and $\overline{WY}$