Chapter 3.3, Problem 13WE

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

  $\angle 2$ and $\angle 3$ are complementary and $m\angle 1={90}^0$

From given data,

  $\begin{array}{l}\angle 2+\angle 3={90}^0\\ \angle 1={90}^0\end{array}$

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

Here, $\overline{AB}$ is transversal and $\overline{AF}\text{ and }\overline{BC}$ are the parallel lines. The interior

angles are $\angle 1\text{ and }\angle 2+\angle 3$ .

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