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

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In 3-space, two lines that are perpendicular to the same plane must be parallel. However, two lines that are perpendicular to a third line do not have to be parallel. Explain why. I am having a very difficult time understanding this problem.

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

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