Chapter 3.3, Problem 3CE

To determine

To state: the segments in the given figure which are parallel also state the postulate or theorem which justifies the answer.

Answer to Problem 3CE

  $\overline{LA}\parallel \overline{TS}$

Theorem 3-6

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:

In this figure, it can be observed that:

  $\begin{array}{c}m\angle LAS+m\angle AST=\left(m\angle LAT+m\angle TAS\right)+m\angle AST\\ =\left(46+44\right)+90\\ =90+90\\ =180\end{array}$

That is, the same-side interior angles $\angle LAS$ and $\angle AST$ are supplementary.

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