Radio constraints on the nature of BL Lacertae objects and their parent population

5 GHz VLA observations of 17 BL Lac objects with bright radio cores at both high and low resolution are reported. Extended emission is detected around most objects. None of the sources observed at low resolution show evidence of giant halos on the scale of tens of arcmin. In general, the sources with the most luminous extended emission exhibit FR II characteristics in both morphology and polarization, and less luminous sources exhibit FR I characteristics. Thus, the parent population of the BL Lac objects contains both FR I and FR II radio sources. No BL Lac objects are found that clearly exhibit quasarlike polarization at milliarcsec resolution. This argues against the view that the more luminous BL Lac objects are simply an extension of the quasar/OVV population, or that most BL Lac objects are gravitationally microlensed images of distant quasars. Other properties are generally consistent with the view the BL Lac objects are normal radio galaxies whose jets make a small angle to the line of sight.