Question

In a plane, if two lines are perpendicular to the same line, then they are _____ to each other.

Answer 1

In a plane, if two lines are perpendicular to the same line, then they are parallel to each other

Answer 2

Answer: The answer is parallel.

Step-by-step explanation: We are asked the relation between two lines which are perpendicular to the same line.

As shown in the attached figure, lines 'm' and 'n' are perpendicular to the line 'l'.

If k, p and g are the slopes of the lines 'l', 'm' and 'n' respectively, then we will have

`k* p=-1,\\\\k* g=-1.`

Comparing both the equations, we arrive at

`p=g.`

We know that if the slopes of two lines are equal, then they must be parallel. So, the complete statement is

"In a plane, if two lines are perpendicular to the same line, then they are parallel to each other."