Question

Complete each statement with the word always, sometimes, or never.

If $\overleftrightarrow{\mathbf{\text{AB}}}$intersects $\overleftrightarrow{\mathbf{\text{CD}}}$, then $\overleftrightarrow{\mathbf{\text{AB}}}$_______ intersects $\overleftrightarrow{\mathbf{\text{CD}}}$.

Short answer

The sentence is:

If $\overleftrightarrow{\mathbf{\text{AB}}}$ intersects $\overleftrightarrow{\mathbf{\text{CD}}}$, then $\overleftrightarrow{\mathbf{\text{AB}}}$ sometimes intersects $\overleftrightarrow{\mathbf{\text{CD}}}$.

Step-by-step solution

Step 1. Define a line and a line segment. 

A line is a straight path of points that has no beginning or end.

Whereas a line segment is a portion of a line that has two end points.

Step 2. State the explanation.

Consider the ray if $\overleftrightarrow{AB}$intersects $\overleftrightarrow{CD}$.

The segment $\overline{AB}$ is the subset of the ray $\overleftrightarrow{AB}$.

So, $\overline{AB}$ sometimes intersects the segment $\overline{CD}$.

Step 3. State the conclusion.

Therefore, the statement is:

If $\overleftrightarrow{AB}$ intersects $\overleftrightarrow{CD}$, then $\overleftrightarrow{AB}$ sometimes intersects $\overleftrightarrow{CD}$.