### Theory:

The construction of a line parallel to the given line can be done using a ruler and a compass only.

Step 1: Draw a line $$x$$ and take a point $$P$$ outside the line.

Step 2: Take any point $$Q$$ on line $$x$$ and draw a line joining $$P$$ and $$Q$$.

Step 3: With $$Q$$ as the centre, and take any radius, draw an arc cutting the line $$x$$ at $$R$$ and $$PQ$$  at $$S$$.

Step 4: With $$P$$ as the centre and with the same radius, draw an arc $$TU$$ cutting $$PQ$$ at $$V$$.

Step 5: Measure the radius of $$RS$$ by placing the pointed tip of the compass at $$R$$ and the pencil at $$S$$. With the same measure of radius and with $$V$$ as the centre, draw an arc cutting the arc $$TU$$ at $$W$$.

Step 6: Join $$PW$$ and draw a line $$y$$.

From the diagram, we can see that $$\angle PQR$$ and $$\angle WPQ$$ are alternate interior angles.

Therefore, the lines $$x$$ and $$y$$ are parallel.