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).

 

We see that the two black lines to the left are parallel. The measurements of the alternate interior angles are equal.

 

 

Now let's look at our triangle.

 

 

Thus we can see that yes, the lines are parallel.

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