Chapter 3.3, Problem 15WE

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

  $m\angle 7=m\angle 3=m\angle 10$

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

and corresponding angles are equal.

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

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

Consider, $\overline{FB}$ is transversal and $\overline{AF}\text{ and }\overline{BC}$ are the parallel lines. The alternate interior

angles $m\angle 3\text{ and }m\angle 10$ are equal.

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