Transmission electron microscopy can be described in terms of the measurement, in an appropriate quantum basis, of the quantum state of an electron after scattering through a sample. Recently developed methods for measuring the orbital angular momentum (OAM) of an electron beam using an OAM sorter can be used to reveal the n-fold symmetry of a sample. Here, we introduce and demonstrate a new composite planar chirality operator, which is based on rotation and scaling operators. We show that an electron OAM sorter can be used to determine the planar chiralities of biomolecules, either in the form of a stand-alone analysis for the fast identification of protein structures or in combination with conventional cryo-electron microscopy to provide faster and more detailed 3D reconstructions by solving upside-down orientation ambiguities.