When contraction a parallel line from a point say N, outside the line, the first thing is to draw a line from point N to the that line.
The point where this line from N intersect with line, name it say P. From this point you can use the properties of angles in a parallel lines to construct the parallel line.
The line NP can act like a transverse of the two parallel lines. The diagram 2 shows first step.
The steps for the construction of a parallel line on a point outside a line is as follows:
First draw a transverse that passes through the point and across the line.
Now place a compass at the point where the transverse meet the line mark an arc passing through the transverse and the line.
Now put the compass on the point that is taken outside the circle and draw the arc.
Now measure the angle between the transverse axis and the line and place the compass at the point taken outside the circle and intersect the arc that is created in the previous step.
Hence, draw a straight line that passes through the point where the two arc intersects; it will be a parallel line to the given line.
