We present high resolution VLA 21 cm line observations of five H II galaxies combined with previous lower resolution data from Taylor et al. [AJ, 105, 128 (1993)] and optical broadband R and Hα CCD images of the systems. Following Kennicutt [ApJ, 344, 685 (1989)] we have calculated the threshold H I surface density for star formation for the H II galaxies and compared the location and shape of this predicted threshold density contour with the optical shape of the galaxies. We find generally a good correlation between these two, although a constant density contour of 1021 cm-2 fits the images of the optical galaxies equally as well. The H I synthesis observations have revealed that the H II galaxies have sharply peaked H I radial profiles, in contrast to the relatively flattened profiles of low surface brightness (LSB) galaxies, suggesting that large central concentrations of gas are a necessary condition for the occurrence of bursts of massive star formation seen in H II galaxies. These observations are consistent with the hypothesis that LSB galaxies represent the quiescent phase of H II galaxies, if a suitable mechanism exists (such as galaxy interactions) to cause H I to concentrate at the center of LSB galaxies prior to the onset of the burst of star formation. However, it is noted that H II galaxies (and dwarf galaxies in general) span a relatively large range in mass. Since many properties correlate with mass (e.g., gas mass fraction), we point out that great care needs to be taken in choosing the proper comparison samples of LSB and H II galaxies.