  In the present paper we study $S^2 \times R$ and $H^2 \times R$ geometries,
which are homogeneous Thurston 3-geometries. We analyse the interior angle sums
of geodesic triangles in both geometries and prove, that in $S^2 \times R$
space it can be larger or equal than $\pi$ and in $H^2 \times R$ space the
angle sums can be less or equal than $\pi$. In our work we will use the
projective model of $S^2 \times R$ and $H^2 \times R$ geometries described by
E. Moln\'ar in \cite{M97}.
