Chapter 3.3, Problem 12WE

To determine

To name: the segments that must be parallel with the given information.

Explanation of Solution

Given information:

The given figure is as follows

  $\angle 7$ and $\angle EFB$ are supplementary.

From given figure,

  $\angle EFB=\angle 8+\angle 9$

  $\angle 7$ and, $\angle EFB$ are supplementary.

  $\begin{array}{l}\angle 7+\angle 8+\angle 9=180\text{ given}\\ \angle 10+\angle 8+\angle 9=180\text{ from the given figure}\\ \Rightarrow \angle 7=\angle 10\end{array}$

When a transversal crosses the two parallel lines, the corresponding angles are equal.

Here, $\overline{AE}$ is transversal and $\overline{CE}\text{ and }\overline{BF}$ are the parallel lines. The corresponding

angles are $\angle 7\text{ and }\angle 10$ .

Hence, the parallel line segments are $\overline{CE}\text{ and }\overline{BF}$ .