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Partial photodetachment and photoionization cross sections corresponding to highly excited residual atoms or ions are shown analytically to mirror one another in the neighborhood of a resonance. More precisely, any two groupings of partial cross sections are shown here to have components whose variations with energy near a resonance are equal in magnitude and opposite in direction. This work extends an analysis of Starace [Phys. Rev. A 16, 231 (1977)] for the behavior of partial cross sections near a resonance to the case when the ρ2 parameter of Fano and Cooper [Phys. Rev. 137, A1364 (1965)] tends to zero.