Answer
If the median is the altitude, then the triangle is an isosceles triangle.
Work Step by Step
We call the length of the base of this triangle 2a, and we call the triangle's height b. When the median is the altitude, this means that there are two right triangles formed: each has one leg of length a and another leg of length b. By the Pythagorean theorem, the two hypotenuses are equal. Thus, since the two sides of the larger triangle are equal, the triangle is an isosceles triangle.
