As G1 and G2 are connected, let us say one vertex is V,now there is a way from V to all other vertices in both G1 and G2,but as their intersection is disconnected,means there are some edges which are in G1 but not in G2 and vice versa.Or we can say there is atleast one from V to V' which is different in both G1 and G2 because if for all vertices it is same path from V to all other vertices then it will not give disconnected graph as intersection.
Now whn union will be done then their will be two paths from V to V' (one of G and other of G1) and then it will form a cycle.