Question

Construct the parallel lines with steps.

Answer 1

Step 1: Start with a line $PQ$ and a point $R$ off the line.
Step 2: Draw a transverse line through $R$ and across the line $PQ$ at an angle, forming the point J where it intersects the line $PQ$. The exact angle is not important.
Step 3: With the compasses' width set to about half the distance between $R$ and $J,$ place the point on $J,$ and draw an arc across both lines.
Step 4: Without adjusting the compasses' width, move the compasses to $R$ and draw a similar arc to the one in step 2
Step 5: Set compasses' width to the distance where the lower arc crosses the two lines.
Step 6: Move the compasses to where the upper arc crosses the transverse line and draw an arc across the upper arc, forming point $S$.
Step 7: Draw a straight line through points $R$ and $S$.
Step 8: Finished. The line $RS$ is parallel to the line $PQ$.