Is  the  hyperbolic  or  spherical  analogy of  the  following Euclidean fact, true?

>Two triangles  with equal corresponding medians are congruent.

More  precisely: Assume that $\Delta ABC$ and $  \Delta A'B'C'$ are two   triangles in the  hyperbolic  space $\mathbb{H}^2$ or elliptic  space $\mathbb{S}^2$ such that  $$AM_1=A'M_1',\; BM_2=B'M_2',\;CM_3=C'M_3'$$  where $M_i (M_i')$ in $XM_i(X'M_i')$ is the mid point of the edge opposite  to the vertex $X(X')$, respectively.

Under this condition, is there an isometry of the  corresponding space carrying the  first triangle  to the  second  one?