Chapter 3.3, Problem 4CE

To determine

To state: the segments in the given figure which are parallel also state the postulate or theorem which justifies the answer.

Answer to Problem 4CE

  $\overline{GA}\parallel \overline{EM}$

Theorem 3-5

Explanation of Solution

Given:

The diagram:

Concept Used:

Theorem 3-5: If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.

Consider the given figure:

In this figure, it can be observed that for the lines $\overline{GA}$ and $\overline{EM}$ and the transversal $\overline{GM}$ :

  $\angle AGM\cong \angle GME=48°$

That is, the alternate interior angles $\angle AGM$ and $\angle GME$ are congruent.

Thus, by the theorem 3-5, it can be said that the lines $\overline{GA}$ and $\overline{EM}$ are parallel.