Construction of segments equal to the difference of given pairs of segments:

To construct segments equal to the difference of given pairs of segments, we will use the concept of ruler and compass construction. Here are the steps to follow:

Step 1: Understand the problem
- Read the problem carefully and identify the given pairs of segments.
- Find the difference between the measurements of the given pairs of segments.

Step 2: Gather the necessary tools
- You will need a ruler and a compass for this construction.

Step 3: Draw the given segments
- Use a ruler to draw the given segments on a piece of paper.

Step 4: Measure the difference
- Use a ruler to measure the difference between the lengths of the given segments.
- Note down this measurement.

Step 5: Construct a line segment of the measured difference
- Take a compass and set it to the measured difference obtained in the previous step.
- Place the compass at one end of one of the given segments and draw an arc.
- Without changing the compass opening, place the compass at the other end of the same given segment and draw another arc intersecting the previous arc.
- Join the points of intersection of the two arcs to obtain a line segment equal to the measured difference.

Step 6: Verify the construction
- Measure the length of the constructed segment using a ruler.
- Verify that the length of the constructed segment is indeed equal to the measured difference.

Step 7: Repeat the construction for other pairs of segments
- Follow the same steps for each given pair of segments to construct segments equal to their differences.

By following these steps, you can construct segments equal to the differences of the given pairs of segments using ruler and compass construction. Remember to measure accurately and be precise in your constructions to obtain accurate results.