Question

Use the give information to name the segments (if any) that must be parallel.

$m\angle 7+m\angle AED=180$

Short answer

The required segments are $\overline{\mathit{A}\mathit{E}}$and $\overline{\mathit{A}\mathit{E}}$.

Step-by-step solution

Step 1. Determine the theorem or postulate that can be used

The theorem 3-6 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 same side are supplementary which means that their measurement will be equal to if they are added.

Step 2. Observe the provided figure

The blue lines $\overline{AE}$and $\overline{BD}$are having a separate line $\overline{ED}$that is travelling through them and this result in formation of angles $\angle 7$and $\angle AED$which are positioned on same side of interior.

Step 3. Make the conclusion

According to the theorem 3-5 determine the lines $\overline{AE}$and$\overline{BD}$ are having a parallel relation between them because the angles formed by these lines are supplementary and positioned on same interior side.