Question

select the most precise and correct statement about parallel lines from among those that are given.
lines ( l ) and ( m ) are distinct lines that lie in the same plane.
choose 1 answer:
a line ( l ) is parallel to line ( m ) if a third line ( p ) can be constructed such that it intersects ( l ) and ( m ) both at right angles.
b lines ( l ) and ( m ) are parallel if they are drawn such that they dont touch each other.
c lines ( l ) and ( m ) are parallel if and only if they are close together but dont intersect.

Explanation:

• Option A:
• According to the definition of parallel lines in a plane, if a transversal (line \(p\)) intersects two lines (\(l\) and \(m\)) at right angles, then the two lines \(l\) and \(m\) are parallel. This is a valid and precise geometric condition for parallelism.
• Option B:
• Just saying that two lines don't touch each other is not a precise enough definition. In three - dimensional space, non - intersecting lines may not be parallel (they can be skew). But in the context of a plane (as given in the problem statement: "lines \(l\) and \(m\) are distinct lines that lie in the same plane"), while non - intersecting is a property of parallel lines, it is not as precise as the condition in Option A. For example, we need to be more specific about the geometric relationships (not just the non - intersection in a plane).
• Option C:
• The distance between the lines (being "close together") is not a part of the definition of parallel lines. Parallel lines can be at any distance from each other in a plane as long as they do not intersect and have the same slope (in coordinate geometry) or satisfy the transversal - right - angle condition.

Answer:

A. Line \(l\) is parallel to line \(m\) if a third line \(p\) can be constructed such that it intersects \(l\) and \(m\) both at right angles.