Construction of Parallel Line

Intersecting Lines	Parallel Lines	Transversal Line	Congruent Line Segments	Construction of Parallel Line
Distance of line from a point

Construction of a parallel line to a given line, through a point which does not lie on the given line (with the help of compass and ruler only) The steps of this construction are as follows: 1. With the help of a ruler draw a line X of any convenient length and mark a point P anywhere outside the given line X (as shown in the following diagram) 2. Take a point Q, anywhere on given line X (as shown in the following diagram) 3. With the help of ruler, join points P and Q (as shown below) 4. Now use compass and open it to any convenient radius. And with Q as center draw an arc which cuts Line X at B and PQ at A (as shown below) 5. Now again with compass and opened to radius same of step 4, draw an arc with center P. This arc cuts PQ at C (as shown below): 6. Again use compass and open is to the radius equals to AB (as shown below in dotted lines): 7. Now with the radius as explained in step 6, draw another arc from point C. This new arc cuts previous arc at point D (as shown below): 8. Now with the help of ruler join points P and D (as shown below): 9. Again with the help of ruler draw a line Y through points PD (as shown below): 10. Hence, in the resultant above diagram we get Line X // Line Y.