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, say so.

$m\angle 5=m\angle 4$

Short answer

The required segments are$\overline{\mathbf{P}\mathbf{L}}$and$\overline{\mathbf{A}\mathbf{R}}$.

Step-by-step solution

Step 1. Determine which theorem or postulate can be used

The theorem 3-5 can be used which states that the relation between two lines is parallel only when a separate line travels through these two lines and the angles which are positioned on the alternate interior side represents the congruent angles.

Step 2. Make an observation from the provided figure

The provided figure consists of two lines $\overline{PL}$and $\overline{AR}$and the separate line that travels through these lines is $\overline{PR}$. Use the relation between provided angles and make an equation that represents another relation.

$\angle 5\cong \angle 4$

Step 3. Make the conclusion

Using the theorem 3-5 determine the lines that are having a parallel relation between them.

$\overline{PL}||\overline{AR}$