Describe the geodesics in the hyperbolic plane (in a model of your choice).

Let $l_{1}$ and $l_{2}$ be geodesics in the hyperbolic plane which do not meet either in the plane or at infinity. By considering the action on a suitable third geodesic, or otherwise, prove that the composite $R_{l_{1}} \circ R_{l_{2}}$ of the reflections in the two geodesics has infinite order.