Chapter 3.3, Problem 10CE

To determine

To state: the segments in the figure which are parallel given that $m\angle APL+m\angle PAR=180$ .

Answer to Problem 10CE

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

Explanation of Solution

Given:

The diagram:

Concept Used:

Theorem 3-6: If two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel.

Consider the given figure:

From the above figure, it can be observed that the angles $\angle APL$ and $\angle PAR$ are the same-side interior angles which are formed when the lines $\overline{PL}$ and $\overline{AR}$ are cut by the transversal $\overline{PA}$ .

Since it is given that

  $m\angle APL+m\angle PAR=180$

It implies that, the same-side interior angles $\angle APL$ and $\angle PAR$ are supplementary.

Thus, by the theorem 3-6, it can be said that the lines $\overline{PL}$ and $\overline{AR}$ are parallel.