Draw a line, say AB, take a point C outside it. Through C, draw a line parallel to AB using ruler and compasses only.
The steps of construction are as follows.
(i)Draw a line AB. Take a point P on it. Take a point C outside this line. Join C to P.
(ii)Taking P as centre and with a convenient radius, draw an arc intersecting line AB at point D and PC at point E.
(iii) Taking C as centre and with the same radius as before, draw an arc FG intersecting PC at H.
(iv) Adjust the compasses up to the length of DE. Without changing the opening of compasses and taking H as the centre, draw an arc to intersect the previously drawn arc FG at point I.
(v) Join the points C and I to draw a line ‘l’.
This is the required line which is parallel to line AB.