We describe an analytical method for interpreting the geometry and structural history of asymmetric half grabens in rift basins with extensional fault-bend fold theory. Using seismic reflection profiles from the Central Sumatra basin and balanced forward models, we show how local variations in tectonic subsidence relative to deposition rates yield distinctive patterns of folded synrift strata and unconformities that record basin history. If the deposition rate exceeds the local subsidence rate, folded growth strata form upwardly narrowing kink bands that have been described previously as growth triangles. In contrast, if the deposition rate is less than or equals the local subsidence rate, growth strata are folded and truncated at the surface on half-graben margins. Subsequent increases in deposition rate relative to subsidence rate form angular unconformities near the half-graben margins. These unconformities develop without the necessity of erosion and are folded by continuing fault slip. Strata above and below the unconformities are concordant in the deeper parts of the half grabens. Thus, angular unconformities on half-graben margins are helpful for defining sequence boundaries that may reflect changes in deposition and tectonic subsidence rates. In addition, fault-bend fold interpretations yield fault geometry and measures of horizontal extension, both of which control three-dimensional half-graben geometry and accommodation space. We show how along-strike variations in fault geometry produce intrabasinal structures that may form prospective fairways or local depocenters.