1. **Problem Statement:** (a) Given line segments $\overline{AB} = 7.4$ cm and $\overline{CD} = 3.5$ cm, construct a line segment $\overline{PQ}$ such that $$\overline{PQ} = \overline{AB} - \overline{CD}.$$ Verify by measurement. 2. **Formula and Explanation:** To find the length of $\overline{PQ}$, use the subtraction of lengths: $$\overline{PQ} = \overline{AB} - \overline{CD}.$$ This means the length of $\overline{PQ}$ is the difference between the lengths of $\overline{AB}$ and $\overline{CD}$. 3. **Calculation:** $$\overline{PQ} = 7.4 - 3.5 = 3.9 \text{ cm}.$$ 4. **Construction Steps:** - Draw $\overline{AB}$ with length 7.4 cm using a ruler. - From one endpoint of $\overline{AB}$, mark a point $P$. - From $P$, measure 3.5 cm along $\overline{AB}$ and mark point $Q$. - The segment $\overline{PQ}$ between points $P$ and $Q$ will have length 3.9 cm. 5. **Verification:** Measure $\overline{PQ}$ with a ruler to confirm it is 3.9 cm. This completes the construction and verification of $\overline{PQ}$.