Question

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

Answer 1

if there are perpends to the same line, they have the same gradient, meaning they are parallel.

Answer 2

if we draw a line parallel to the original one we form a rectangle
(all 4 angles equal to 90 degrees)
the internal angles at end of each vertical line are 90
therefore the two vertical lines are parallel