Video Transcript
True or False: Two coplanar lines perpendicular to the same line will always intersect each other.
We begin by recalling that two lines are coplanar if they lie on the same plane and two lines are perpendicular if they intersect at right angles or 90 degrees. Let’s consider a line that passes through the points 𝐴 and 𝐵 as shown. If we then draw two coplanar lines perpendicular to line 𝐴𝐵 that pass through points 𝐴 and 𝐵, respectively, our two lines will be parallel. And we know that two parallel lines do not intersect. This means that the statement in the question is false. Two coplanar lines perpendicular to the same line will not always intersect each other.
And we can actually go one stage further and say that the two coplanar lines perpendicular to the same line will never intersect each other unless the two lines are coincident. That is, they are the same line.