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.
