Answer
The median of the vertex is perpendicular to the base.
Work Step by Step
We call the top of the triangle the point x, y, and we put one corner of the triangle at the origin. Since it is isosceles, we find the slopes:
$m_1 = \frac{0-0}{a-0}=0$
$m_1 = \frac{b-0}{a-a}$=undefined
Since one slope is undefined and one slope is vertical, one line is vertical, and the other is horizontal. Thus, the two lines are perpendicular.
