In the spirit of \textit{J. E. Bonin} and \textit{W. P. Miller} [Eur. J. Comb. 20, No. 8, 713-724 (1999; Zbl 0946.05020)], the author provides several characterization theorems for finite projective and affine geometries, such as ``If any three of the following four matroid invariants of a rank-\(n\) combinatorial geometry -- the number of points, the number of lines, the coefficient of \(\lambda^{n-2}\) in the characteristic polynomial, and the number of 3-element dependent sets -- are the same as those of a rank-\(n\) projective geometry of order \(q\), then it is a projective geometry of the same order''.