Question

struct arguments determine whether each statement is always, sometimes, or never true. justify is perpendicular to $overleftrightarrow{bc}$ and $overleftrightarrow{bc}$ is perpendicular to $overleftrightarrow{cd}$, then $overleftrightarrow{ab}$ is parallel to $overleftrightarrow{cd}$. sometimes this is true only if $overleftrightarrow{ab}$ and $overleftrightarrow{cd}$ are select choice select choice noncollinear coplanar need help with this question? get a hint show answer

Explanation:

Step1: Recall perpendicular - parallel relationships

In a plane (coplanar situation), if two lines are perpendicular to the same line, they are parallel. But in 3 - D space, this is not always the case.

Step2: Analyze the condition

If $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$ are coplanar and $\overleftrightarrow{AB}\perp\overleftrightarrow{BC}$ and $\overleftrightarrow{BC}\perp\overleftrightarrow{CD}$, then $\overleftrightarrow{AB}\parallel\overleftrightarrow{CD}$. If they are not coplanar, they may not be parallel.

Answer:

sometimes; coplanar