Chapter 3.3, Problem 5CE

To determine

To state: the segments in the figure which are parallel given that $m\angle 1=m\angle 8$ .

Answer to Problem 5CE

  $\overline{PL}\parallel \overline{AR}$

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:

From the above figure, it can be observed that the angles $\angle 1$ and $\angle 8$ are the alternate interior angles which are formed when the lines $\overline{PL}$ and $\overline{AR}$ are cut by the transversal $\overline{AL}$ .

Since it is given that

  $m\angle 1=m\angle 8$

It implies that, the alternate interior angles $\angle 1$ and $\angle 8$ are congruent.

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