If BD is an altitude, it splits triangle ABC into 2 triangles. It is also a median, so it splits the angle ABC into 2 congruent angles. Angle ABD and CBD are congruent. That means that angles A and C are congruent. This is true because the 2 angles at D are both right angles. Because of this, side AB and side CB are congruent. That means that this is an isosceles triangle.
