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

In order to prove that two lines are parallel to each other, you need to show that they have the same slope.

Line 1 is perpendicular to a line that has slope m, thus it has a slope of - 1/m.

Line 2 is perpendicular to the same line with slope m, thus it has a slope of - 1/m.

Line 1 and Line 2 have the same slope so they are parallel.