The linearized invariant-imbedding T-matrix method (LIITM) and linearized physical-geometric optics method (LPGOM) were applied on regular hexagonal prisms from small to large sizes to obtain the scattering properties and their partial derivatives. T-matrices and their derivatives from the LIITM are presented and discussed in the expansion order, where the minor diagonal elements are dominant. The simulation results of single-scattering properties and their corresponding linearization from both methods are compared. The mutual agreements can be treated as further verification of both linearized methods. Using extinction efficiency as the criterion, the LPGOM are convergent at the LIITM for the particle size parameter larger than 130 with a relative difference of less than 1%, with errors of about 3% and 5% for particle sizes of 50 and 30, respectively. The capability and convergence of the LIITM and LPGOM are discussed in detail based on linearized properties.