Question

State which segments (if any) are parallel. State the postulate or theorem that justifies your answer.

Short answer

The required segments are $\overline{\mathbf{G}\mathbf{A}}$and $\overline{\mathbf{E}\mathbf{M}}$along with this the theorem is Theorem 3-5.

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 $\overline{GA}$and $\overline{EM}$the separate line that travels through these lines is $\overline{GM}$. Using the figure determine the angles that are congruent.

$\angle AGM\cong \angle GME$

$=48°$

Step 3. Make the conclusion

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

$\overline{GA}||\overline{EM}$