Question

in the square pyramid shown below, which lines are parallel? select all that apply.
options:
$overleftrightarrow{uv}$ and $overleftrightarrow{wx}$
$overleftrightarrow{xy}$ and $overleftrightarrow{vw}$
$overleftrightarrow{uw}$ and $overleftrightarrow{wy}$
$overleftrightarrow{wy}$ and $overleftrightarrow{wx}$

Explanation:

Step1: Identify square base sides

The base of the square pyramid is a square, so opposite sides of the base are parallel.

Step2: Check option pairs

• $\overline{WX}$ and $\overline{YZ}$: Opposite sides of the square base, parallel.
• $\overline{XY}$ and $\overline{WZ}$: Opposite sides of the square base, parallel.
• $\overline{UW}$ and $\overline{YZ}$: $\overline{UW}$ is an edge from apex to base vertex, $\overline{YZ}$ is a base side—they are not parallel.
• $\overline{XY}$ and $\overline{WX}$: Adjacent sides of the base, intersect at $X$, not parallel.

Answer:

$\overline{WX}$ and $\overline{YZ}$, $\overline{XY}$ and $\overline{WZ}$