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:

Parallel lines in the same - plane are defined as lines that do not intersect. Option A is incorrect because closeness is not a part of the definition of parallel lines. Option B is incorrect as non - touching does not accurately define parallelism. Option C is correct because if a third line intersects two lines at right angles, the two lines are parallel. This is based on the perpendicular - transversal theorem in geometry.

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.