Question

1. practice: making mental images

complete the diagram to show the rule.
parallel rule
given any line ab and any point p not
on \overleftrightarrow{ab}, there is exactly one line that is
both parallel to \overleftrightarrow{ab} and passes through
p.
show the rule
diagram with point p and line ab (a to b arrowed)

Explanation:

Step1: Identify given elements

Locate $\overleftrightarrow{AB}$ and point $P$ (not on $\overleftrightarrow{AB}$) in the diagram.

Step2: Draw the parallel line

Construct a straight line through $P$ such that it never intersects $\overleftrightarrow{AB}$ (this is the unique parallel line, per the rule). Label this new line, e.g., $\overleftrightarrow{PQ}$.

Answer:

A completed diagram with:

1. Line $\overleftrightarrow{AB}$ (already provided)
2. Point $P$ not on $\overleftrightarrow{AB}$ (already provided)
3. A single line passing through $P$ that is parallel to $\overleftrightarrow{AB}$ (labeled, e.g., $\overleftrightarrow{PQ}$)