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

Parallel lines in a plane are defined as lines that do not intersect. A key property is that a transversal (a third - line) intersecting two parallel lines forms right - angles (perpendicular to both). Option 1 is incorrect as closeness is not a factor in parallelism. Option 2 is too general as non - touching lines could be skew in 3D (but we are in a plane here, and this still lacks the key perpendicular - transversal property). Option 3 is the correct definition based on the perpendicular transversal property for parallel lines in a plane.

Answer:

The third option: 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.