Question

which statement is true regarding the parallel and perpendicular lines in the diagram?
× ( k parallel n ) and ( w perp m )
( \bigcirc ) ( k parallel n ) and ( n perp m )
( \bigcirc ) ( w parallel n ) and ( n perp m )
( \bigcirc ) ( w parallel n ) and ( w perp m )

Explanation:

To determine the correct statement, we analyze the relationships between the lines. Parallel lines (denoted by \( \parallel \)) never intersect, and perpendicular lines (denoted by \( \perp \)) intersect at a right angle (\( 90^\circ \)).

• For the parallel relationship: We check which lines are parallel. From the options, we evaluate the pairs.
• For the perpendicular relationship: We check which line is perpendicular to \( m \).

Looking at the options, the correct relationship is \( w \parallel n \) (they are parallel) and \( w \perp m \) (they intersect at a right angle).

Answer:

D. \( w \parallel n \) and \( w \perp m \) (assuming the last option is labeled D; if the options are labeled as per the order, the last option with \( w \parallel n \) and \( w \perp m \))