Question

Through a point not on a line, one and only one line can be drawn parallel to the given line. always sometimes never

Answer 1

Always

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.

Answer 2

Always

Explanation:

The Parallel Postulate:

When a line is already given, let's say the line is a, and the point be called A. If there is a point outside the line, only one line can be drawn through the point which doesn't intersect the line i.e. which is parallel to the given line. Hence, this statement is always true ..