  We present a proof of the almost sure existence, uniqueness and coalescence
of directed semi-infinite geodesics in planar growth models that is based on
properties of an increment-stationary version of the growth process. The
argument is developed in the context of the exponential corner growth model. It
uses coupling, planar monotonicity, and properties of the stationary growth
process to derive the existence of Busemann functions, which in turn control
geodesics. This soft approach is in some situations an alternative to the
much-applied 20-year-old arguments of C. Newman and co-authors. Along the way
we derive some related results such as the distributional equality of the
directed geodesic tree and its dual, originally due to L. Pimentel.
