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 lines ( l ) and ( m ) are parallel if and only if they are close together but dont intersect.
b lines ( l ) and ( m ) are parallel if they are drawn such that they dont touch each other.
c 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.

Explanation:

• Option A is incorrect because the distance between lines (being close together) is not a factor in defining parallel lines. Parallelism is about non - intersection in the same plane, not proximity.
• Option B is too vague. Just saying "drawn such that they don't touch" doesn't capture the geometric essence. Parallel lines are non - intersecting lines in the same plane, but this option lacks the precision of a geometric property.
• Option C is correct. If a transversal line \(p\) intersects two lines \(l\) and \(m\) at right angles, then by the converse of the perpendicular transversal theorem, lines \(l\) and \(m\) are parallel. This is a precise geometric condition for parallelism.

Answer:

C. 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.