Question

question 2 of 5
if \overleftrightarrow{ab} is parallel to \overleftrightarrow{cd}, which statement must be true?

a. \overleftrightarrow{ab} and \overleftrightarrow{cd} do not intersect.
b. \overleftrightarrow{ab} and \overleftrightarrow{cd} intersect at 90° angles.
c. the perpendicular distance between \overleftrightarrow{ab} and \overleftrightarrow{cd} decreases as the lines are traversed right to left.
d. the perpendicular distance between \overleftrightarrow{ab} and \overleftrightarrow{cd} increases as the lines are traversed left to right.

Explanation:

Step1: Recall the definition of parallel lines

Parallel lines are lines in a plane that do not intersect.

Step2: Analyze each option

• Option A: By the definition of parallel lines (\(\overleftrightarrow{AB}\parallel\overleftrightarrow{CD}\)), they do not intersect.
• Option B: Lines that intersect at \(90^{\circ}\) angles are perpendicular, not parallel.
• Option C: The perpendicular distance between two parallel lines is constant.
• Option D: The perpendicular distance between two parallel lines is constant.

Answer:

A. \(\overleftrightarrow{AB}\) and \(\overleftrightarrow{CD}\) do not intersect.