**Construction of a Line Parallel to a Given Line through a Point not on the Line**

To construct a line parallel to a given line through a point not on the line, follow the steps below:

**Step 1:**
Draw the given line and label it as line AB. This will serve as a reference line for the construction.

**Step 2:**
Choose a point P outside the given line AB. This point will be used to construct the parallel line.

**Step 3:**
Take a compass and place the needle on point P. Adjust the compass width to a convenient size, but keep it fixed for the rest of the construction.

**Step 4:**
With the compass needle still on point P, draw two arcs intersecting the given line AB. Ensure that the arcs intersect the line at two different points.

**Step 5:**
Label the points of intersection as X and Y.

**Step 6:**
Keep the compass width unchanged and place the needle on point X.

**Step 7:**
Draw an arc starting from point X that intersects the previously drawn arc.

**Step 8:**
Keep the compass width unchanged and place the needle on point Y.

**Step 9:**
Draw an arc starting from point Y that intersects the previously drawn arc. Let the intersecting point be Z.

**Step 10:**
Draw a line through point P and point Z. This line will be parallel to the given line AB.

**Step 11:**
Label the parallel line as CD.

**Step 12:**
The line CD is the required line parallel to the given line AB through the point P.

By following these steps, you can construct a line parallel to a given line through a point not on the line. Remember to use a compass for accurate construction and ensure that the arcs intersect the given line at two different points. This construction technique is useful in various mathematical problems and can help you understand the concept of parallel lines better.