Question

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

Answer 1

Hint:
It is given in the question that If two lines are perpendicular to the third line, then those two lines are
Firstly, we will draw the figure in which two lines are parallel to each other and the lines are perpendicular to the third line.
Then after, we will explain the answer with the help of a diagram. Also, follow the properties of the two parallel and perpendicular lines.

Complete step by step solution:
It is given in the question that If two lines are perpendicular to the third line, then those two lines are
Now, let P, Q and R be the three lines, in such a way that line P and line Q are perpendicular to the third line i.e. line R.

It is clear from the above diagram that line P and line Q are perpendicular to the line i.e. line R.
Since, line P and line Q are parallel to each other because line P and line Q make the right angle with line R.
As we know that by the theorem of perpendicular transversal theorem that in the plane, if a transverse is perpendicular to one or two parallel lines, then it is perpendicular to the third line.
If line P is parallel to line R and line Q is also parallel to line R then line P and line Q are perpendicular.
Since, if two lines are perpendicular to the third line then those two lines are parallel to each other.
As per the property of parallel lines they would never meet. Since, they do not touch or interact with each other they are said to be parallel to each other.

Therefore, if two lines are perpendicular to the third line, then those two lines are parallel to each other.

Note:
Parallel lines are lines in a plane which do not meet i.e. two straight lines in a plane that do not interact at any point are said to be parallel. Parallel lines are the lines which never interact and the perpendicular lines are the lines which intersect at the right angles i.e. $90^\circ $ .