Question

If two lines are perpendicular to the third line, then those two line are
A) Parallel to each other
B) Perpendicular to each other
C) Either parallel or perpendicular
D) Neither parallel nor perpendicular

Answer 1

Hint: Here, we will suppose the two lines which are perpendicular to the third line. Also, follow the properties of the two parallel and perpendicular lines.

Complete step by step answer:
 Let, $$l\text{, m, and n}$$ be the three lines, in such a way that line m and line n are perpendicular to the third line $l$.

From the above diagram it is clear that if line m and line n are perpendicular to the third line l, lines m and line n are parallel to each other as line m and line n makes the right angles with the third line.
Also, by the theorem perpendicular transversal theorem-
In the plane, if a transversal is perpendicular to one or the two parallel lines, then it is perpendicular to the other line.
If,
$$\begin{gathered} m\mathrm{\perp }l \\ n\mathrm{\perp }l \end{gathered}$$
Then, $m\parallel n$
If two lines are perpendicular to the third line then those two lines are parallel to each other as per the property of the parallel lines they would never meet. Since, they do not touch or intersect each other they are said to be parallel to each other.

Therefore, from the given multiple choices, option A is the correct answer.

Note: Parallel lines are the lines in the plane that are always the same and are equal distance apart. Parallel lines are the lines which never intersect and the perpendicular lines are the lines which intersect at the right angles i.e. ${90}^{\circ }$