Two lines are
parallel if they do not intersect. To test if two lines are parallel
we can draw a line that intersects both and see if their alternate
interior angles are congruent (shown in the diagram below).
![](Image%201.gif)
We see that the two
black lines to the left are parallel. The measurements of the
alternate interior angles are equal.
![](Image%202.gif)
Now let's look at our triangle.
![](Image%203.gif)
Thus we can see
that yes, the lines are parallel.