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Home >> Define Line, Line Segment and Rays >> Construction of Parallel Line >>

## Construction of Parallel Line

 Intersecting Lines Parallel Lines Transversal Line Congruent Line Segments Construction of Parallel Line

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.