Abstract Several studies have shown that the recently developed techniques of geometric morphometrics are extremely powerful descriptive tools. And yet, one potential use of the resulting descriptions, phylogenetic analysis, has generally been neglected. This neglect is understandable because prominent systematists as well as prominent morphometricians have objected to the use of morphometric data in phylogenetic systematics. We agree that some methods of morphometric analysis produce results that cannot be used in phylogenetic systematics, and that some methods of incorporating morphometric results into statements about character transformation are not appropriate. However, we do not agree that these objections to specific techniques support a blanket rejection of the use of morphometric data in systematic studies. In this paper, we review the principles of phylogenetic systematics and show that they are equally applicable to qualitative descriptions of triangles and to quantitative descriptions (shape coordinates of the apex) of those same shapes. Then we show how these principles would he applied to complex shapes like skulls of marmotine squirrels, and that the resulting analysis leads to legitimate hypotheses about marmotine phylogeny and the evolution of skull shape in these animals.