Question

in the square pyramid shown below, which lines are skew? select all that apply. hk and jl hi and kl ij and il ij and hl

Explanation:

Step1: Recall skew - line definition

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

Step2: Analyze each pair

• For $\overrightarrow{HK}$ and $\overrightarrow{JL}$: They are non - parallel and do not intersect, so they are skew.
• For $\overrightarrow{HI}$ and $\overrightarrow{KL}$: $\overrightarrow{HI}$ and $\overrightarrow{KL}$ are in the same plane (the base of the pyramid), so they are not skew.
• For $\overrightarrow{IJ}$ and $\overrightarrow{IL}$: They share a common point $I$, so they are not skew.
• For $\overrightarrow{IJ}$ and $\overrightarrow{HL}$: They are non - parallel and do not intersect, so they are skew.

Answer:

$\overrightarrow{HK}$ and $\overrightarrow{JL}$, $\overrightarrow{IJ}$ and $\overrightarrow{HL}$