Question 165242
Given:Triangle ABC 
Segment BD is perpendicular to segment AC
Segment BD is a median of Triangle ABC
What kind of triangle is Triange ABC? 

BD is perpendicular to AC.  This means that angle D is 90 degrees.
Two triangles are formed: Triangle ABD and Triangle CBD.  

BD is also a median.  This means that it divides AC into two equal parts.

From the given data, I gather that AB = BC but also that AB and BC do not equal AC.

I think this is an isosceles triangle.