The success of deep learning depends heavily on the availability of large datasets, but in robotic manipulation there are many learning problems for which such datasets do not exist. Collecting these datasets is time-consuming and expensive, and therefore learning from small datasets is an important open problem. Within computer vision, a common approach to a lack of data is data augmentation. Data augmentation is the process of creating additional training examples by modifying existing ones. However, because the types of tasks and data differ, the methods used in computer vision cannot be easily adapted to manipulation. Therefore, we propose a data augmentation method for robotic manipulation. We argue that augmentations should be valid, relevant, and diverse. We use these principles to formalize augmentation as an optimization problem, with the objective function derived from physics and knowledge of the manipulation domain. This method applies rigid body transformations to trajectories of geometric state and action data. We test our method in two scenarios: 1) learning the dynamics of planar pushing of rigid cylinders, and 2) learning a constraint checker for rope manipulation. These two scenarios have different data and label types, yet in both scenarios, training on our augmented data significantly improves performance on downstream tasks. We also show how our augmentation method can be used on real-robot data to enable more data-efficient online learning.