Extended x-ray absorption fine structure at the manganese K edge has been used to study the first oxygen coordination shell at the manganese site as a function of temperature in mixed-valence perovskites. La1-xCaxMnO3 (x=0, 0.15, 0.33, 0.5, 0.66, and 1), La0.60Y0.07Ca1/3MnO3, La0.57Tb0.1Ca1/3MnO3, and Tb1-xCaxMnO3 (x=0, 0.33, 0.5, and 0.67) were studied. Our results show that the manganese atom is surrounded by a regular oxygen octahedra in the metric-ferromagnetic phase. The analysis of the spectra at temperatures above the magnetic transition can be described in terms of either a unique Mn-O interatomic distance with a large Debye-Waller factor or two Mn-O distances with a distortion lower than 0.1 Angstrom. Such distortion or disorder must be dynamic since it cannot be detected by diffraction measurements. This result supports the evidence of a large phonon-electronic interaction and the polaronic origin as a possible mechanism of electrical conduction in the paramagnetic phase.