We present a new approach for the automated segmentation of synapses in image stacks acquired by Electron Microscopy (EM) that relies on image features specifically designed to take spatial context into account. These features are used to train a classifier that can effectively learn cues such as the presence of a nearby post-synaptic region. As a result, our algorithm successfully distinguishes synapses from the numerous other organelles that appear within an EM volume, including those whose local textural properties are relatively similar. Furthermore, as a by-product of the segmentation, our method flawlessly determines synaptic orientation, a crucial element in the interpretation of brain circuits. We evaluate our approach on three different datasets, compare it against the state-of-the-art in synapse segmentation and demonstrate our ability to reliably collect shape, density, and orientation statistics over hundreds of synapses.