Question

can the altitude and median be the same for a triangle

Answer 1

 If median drawn from vertex A is also the angle bisector, the triangle is isosceles such that AB = AC and BC is the base. Hence this median is also the altitude. In an equilateral triangle, each altitude, median and angle bisector drawn from the same vertex, overlap. 

Answer 2

yes.. altitude and the median is same for the triangle for a given side