The intrinsic E2 matrix elements 〈K=2|E2|K=0〉 for 25 deformed nuclei, covering from neodymium to uranium, have been deduced from measured interband E2 matrix elements between the ground band and \ensuremath{\gamma} band after correcting for the first-order angular momentum dependence of the coupling between the rotation and intrinsic motion. Fairly precise centroids for the triaxiality of the intrinsic E2 moments are obtained, and these correlate well with the triaxiality implied by the excitation energies. The strong correlation of the triaxiality derived from the E2 properties and level energies provides a quantitative measure of triaxial quadrupole deformation of the nuclear shape for these states. \textcopyright{} 1996 The American Physical Society.