Question

select the most precise and correct statement about perpendicular lines from among those that are given.
choose 1 answer:
a (overleftrightarrow{ab}) is perpendicular to (overleftrightarrow{cd}) if the two lines intersect such that the measure of (angle aod) equals the measure of (angle boc).
b (overleftrightarrow{ab}) is perpendicular to (overleftrightarrow{cd}) if the two lines intersect such that (angle aod) is a right angle.
c (overleftrightarrow{ab}) is perpendicular to (overleftrightarrow{cd}) if the two lines never meet.

Explanation:

Step1: Analyze Option A

When two lines intersect, vertical angles (like \( \angle AOD \) and \( \angle BOC \)) are always equal, regardless of whether the lines are perpendicular. So this condition is not sufficient for perpendicularity.

Step2: Analyze Option B

By definition, two lines are perpendicular if they intersect at a right angle. If \( \angle AOD \) is a right angle (\( 90^\circ \)), then the lines \( \overleftrightarrow{AB} \) and \( \overleftrightarrow{CD} \) are perpendicular.

Step3: Analyze Option C

Lines that never meet are parallel, not perpendicular. Perpendicular lines must intersect (at a right angle).

Answer:

B. \( \overleftrightarrow{AB} \) is perpendicular to \( \overleftrightarrow{CD} \) if the two lines intersect such that \( \angle AOD \) is a right angle.