Question

in the rectangular prism shown below, which lines are intersecting? select all that apply.

Explanation:

Step1: Recall the definition of intersecting lines

Intersecting lines are lines that meet at a point.

Step2: Analyze each pair

• For \(\overleftrightarrow{QR}\) and \(\overleftrightarrow{QU}\): They meet at point \(Q\), so they are intersecting.
• For \(\overleftrightarrow{PQ}\) and \(\overleftrightarrow{PT}\): They meet at point \(P\), so they are intersecting.
• For \(\overleftrightarrow{PS}\) and \(\overleftrightarrow{QR}\): \(\overleftrightarrow{PS}\parallel\overleftrightarrow{QR}\) (in a rectangular prism, opposite sides of the base are parallel), so they are not intersecting.
• For \(\overleftrightarrow{TU}\) and \(\overleftrightarrow{UV}\): They meet at point \(U\), so they are intersecting.

Answer:

\(\overleftrightarrow{QR}\) and \(\overleftrightarrow{QU}\), \(\overleftrightarrow{PQ}\) and \(\overleftrightarrow{PT}\), \(\overleftrightarrow{TU}\) and \(\overleftrightarrow{UV}\)