If two straight lines are perpendicular to the same line, prove that they are parallel to each other.

Given:

Two straight lines are perpendicular to the same line.
To do:

We have to prove that they are parallel to each other.

Solution:

Let $m \perp l$ and $n \perp l$.

From the figure, we can observe that,

$m \perp l$ and $n \perp l$

This implies,

$\angle 1=90^o$ and $\angle 2= 90^o$

$\angle 1$ and $\angle 2$ are corresponding angles.

This implies,

$m \parallel n$.

Hence proved.

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Updated on: 10-Oct-2022

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