Isotopic signatures of nitrogen, argon, and xenon have been determined in separated millimeter-sized pockets of shock-melted glass in a recently identified lithology of the meteorite Zagami, a shergottite. The ratio of nitrogen-15 to nitrogen-14, which is at least 282 per mil larger than the terrestrial value, the ratio of xenon-129 to xenon-132 = 2.40, and the argon isotopic abundances match the signatures previously observed in the glassy lithology of the Antarctic shergottite EETA 79001. These results show that the signatures in EETA 79001 are not unique but characterize the trapped gas component in shock-melted glass of shergottites. The isotopic and elemental ratios of nitrogen, argon, and xenon closely resemble the Viking spacecraft data for the martian atmosphere and provide compelling evidence for a martian origin of the two shergottites and, by extension, of the meteorites in the shergottites-nakhlites-chassignites (SNC) group.