Q. 104.3( 6 Votes )

Two lines l and m are perpendicular to the same line n. Are l and m perpendicular to each other? Give reason for your answer.

Answer :

The following figure can be drawn from the given details.


Here, we have


l and m are two lines perpendicular to the same line n.


lan = mbn = 90° - - - - (i)


Now, we can see that n is a transversal intersecting two lines l and m at points a and b, such that,


the corresponding angles, lan = mbn and are 90° each.


Since, the corresponding angles between two lines are equal when a transversal intersects these two lines at two different points, the two lines are parallel to each other.


Thus, the lines l and m are parallel to each other, not perpendicular.


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