Chapter 3.3, Problem 16WE

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

  $m\angle 4=m\angle 8=m\angle 1$

When a transversal crosses the two parallel lines, the alternate interior angles are equal

and corresponding angles are equal.

Consider, $\overline{AF}$ is transversal and $\overline{AB}\text{ and }\overline{FC}$ are the parallel lines. The corresponding

angles $m\angle 1\text{ and }m\angle 8$ are equal.

Consider, $\overline{FC}$ is transversal and $\overline{EF}\text{ and }\overline{CB}$ are the parallel lines. The alternate interior

angles $m\angle 4\text{ and }m\angle 8$ are equal.

Hence, the parallel line segments are $\overline{AB}\parallel \overline{FC}$ and $\overline{EF}\parallel \overline{CB}$ .