Question

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

Explanation:

Parallel lines are defined as coplanar lines that never intersect, and their perpendicular distance remains constant at all points along the lines. Option B and D are false because the distance between parallel lines does not change. Option C describes perpendicular lines, not parallel ones. Only option A matches the definition of parallel lines.

Answer:

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