Question

in the rectangular prism shown below, which lines are intersecting? select all that apply.
(image of a rectangular prism with vertices labeled f, g, h, i, j, k, l, m)
options:

• $overleftrightarrow{hi}$ and $overleftrightarrow{fi}$
• $overleftrightarrow{jk}$ and $overleftrightarrow{lm}$
• $overleftrightarrow{fj}$ and $overleftrightarrow{kl}$
• $overleftrightarrow{hl}$ and $overleftrightarrow{fi}$

Explanation:

Step1: Define intersecting lines

Intersecting lines share a common point.

Step2: Check each pair

• $\overline{HI}$ and $\overline{FI}$: Meet at point I → intersecting.
• $\overline{JK}$ and $\overline{LM}$: Parallel (no common point) → not intersecting.
• $\overline{FJ}$ and $\overline{KL}$: No common point (skew) → not intersecting.
• $\overline{HL}$ and $\overline{FI}$: No common point (skew) → not intersecting.

Answer:

$\overline{HI}$ and $\overline{FI}$