how to construct a line parallel to another line

A line parallel to another line should be constructed by using ruler and compass. The steps to construct are given below.

 

Suppose AB be a given line and C is a point outside it. Through C, a line parallel to AB can be drawn by following the steps given below:

 

1) Draw a line AB. Take a point P on it. Take a point C outside this line. Join C to P.

2) Taking P as centre and with a convenient radius, draw an arc intersecting line AB at point D and PC at point E.

3) Now taking C as centre and with the same radius as before, draw an arc FG intersecting PC at H.

4) 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.

5) Join the points C and I to draw a line ‘l’.

This is the required line which is parallel to the line AB.