#### Answer

Because the slopes of the two lines are the same, we see that they are parallel.

#### Work Step by Step

To do this, we must prove that the slopes are the same.
Finding the slope of the third side of the triangle is simple:
$ m=\frac{2c-0}{2b-0}=c/b$
We use the midpoint formula to find the points in the middle of each other side of the triangle:
$ (\frac{2a+2b}{2}, \frac{2c+0}{2})$
$ (a+b,c)$
And for the other side:
$ (\frac{2a+0}{2}, \frac{0+0}{2})$
$({a,0})$
We now use the slope formula for these two midpoints:
$ \frac{c-0}{(a+b)-a}$
$m = c/b$
Because the slopes of the two lines are the same, we see that they are parallel.