Before revision:   First, we show when it is possible how to construct geodesic triangles which either have one, two, or three interior right angles .
After revision:  We consider non-self dual Bregman manifolds since Mahalanobis self-dual manifolds amount to Euclidean geometry. First, we show when it is possible how to construct geodesic triangles which either have one, two, or three interior right angles .