Question

In each exercise some information is given. Use this information to name the segments that must be parallel. If there are no such segments, write none.

Short answer

The obtained conclusion is that $\overline{\mathit{A}\mathit{B}}\mathbf{\Vert }\overline{\mathit{F}\mathit{C}}$and $\overline{\mathit{E}\mathit{F}}\mathbf{\Vert }\overline{\mathit{C}\mathit{B}}$.

Step-by-step solution

Step 1. Determine which theorem and postulate can be used

Postulate 10 states when a separate line travels through two lines which are having a parallel relation between them at that time the angles which are corresponding angles represents the congruent angles.

Theorem 3-2 states when a separate line travels through two lines which are having a parallel relation between them at that time the angles which are positioned on alternate interior side represents the congruent angles.

Step 2. Use the postulate and theorem

According to the figure the lines having parallel relation between them are AB and FC along with this the separate line is $\overline{AF}$and the angles that are corresponding in these lines are $\angle 1$and $\angle 8$which means that these angles are having the same measurement.

According to the figure the lines having parallel relation between them are EF and CB along with this the separate line is $\overline{FC}$and the angles that are positioned on alternate interior side in these lines are $\angle 4$and $\angle 8$which means that these angles are having the same measurement.

Step 3. Make the conclusion

As the obtained lines are related with the provided angles according to the theorem and postulate so the required segments are $\overline{AB}||\overline{FC}$and $\overline{EF}||\overline{CB}$.