Answer:
Always
Step-by-step explanation:
Given statement: Through a point not on a line, one and only one line can be drawn parallel to the given line.
Draw a line l.
Let point P not on the line l.
Slope of two parallel lines are same.
We need to draw a line which is passes through the point P and parallel to the line l.
Infinite number of lines having different slopes can pass through a single point.
That is two lines don't have same slope.
Hence only one line is possible, which is parallel to l and passes through the point P.
Therefore the given statement is always true.
