Question

5
if ab is parallel to cd, which statement must be true?
o a. the perpendicular distance between ab and cd increases as the lines are traversed left to right.
o b. the perpendicular distance between ab and cd decreases as the lines are traversed right to left.
o c. ab and cd intersect at 90° angles.
o d. ab and cd do not intersect.

Explanation:

Step1: Recall the property of parallel lines

Parallel lines never intersect.

Step2: Analyze each option

• Option A: The perpendicular distance between parallel lines is constant. It does not increase or decrease as the lines are traversed. So, this option is wrong.
• Option B: The perpendicular distance between parallel lines is constant. It does not increase or decrease as the lines are traversed. So, this option is wrong.
• Option C: Parallel lines do not intersect. Lines that intersect at \(90^{\circ}\) are perpendicular, not parallel. So, this option is wrong.
• Option D: By the definition of parallel lines, parallel lines (\(\overleftrightarrow{AB}\) and \(\overleftrightarrow{CD}\)) do not intersect.

Answer:

D. \(AB\) and \(CD\) do not intersect.