Chapter 3.3, Problem 15ST1

To determine

To state: the segments in the figure which are parallel given that $m\angle 7+m\angle AED=180$ .

Answer to Problem 15ST1

  $\overline{AE}\parallel \overline{BD}$

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 $\angle 7$ and $\angle AED$ are the same-side interior angles which are formed when the lines $\overline{AE}$ and $\overline{BD}$ are cut by the transversal $\overline{ED}$ .

Since it is given that

  $m\angle 7+m\angle AED=180$

It implies that, the same-side interior angles $\angle 7$ and $\angle AED$ are supplementary.

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