Question

State which segments (if any) are parallel. State the postulate or theorem that justifies your answer.

Short answer

The required segments are $\overline{\mathbf{L}\mathbf{A}}$and $\overline{\mathbf{T}\mathbf{S}}$along with this the theorem is Theorem 3-6.

Step-by-step solution

Step 1. Determine which theorem or postulate 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. Make an observation from the provided figure

The provided figure consists of only two angles $\angle LAS$and $\angle AST$where $\angle LAS$consists of two angles which are $\angle LAT$and $\angle TAS$along with this $\angle LAS$and $\angle AST$are positioned on the same side and are supplementary because:

$m\angle LAS+m\angle AST=\left(m\angle LAT+m\angle TAS\right)+m\angle AST$

role="math" localid="1637822945923" $=\left(46+44\right)+90$

$=90+90$

role="math" localid="1637822952381" $=180$

Step 3. Make the conclusion

Using the theorem 3-6 determine the lines that are having a parallel relation between them.

$\overline{LA}||\overline{TS}$