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 carring the first triangle to the second one?