By looking at the history of geometry and the concept of congruence in geometry we can get a new perspective on how to think about the closeness in meaning of two sentences. As in the analysis of congruence in geometry, a definite and concrete set of proposals about congruence of meaning depends essentially on the kind of theoretical framework assumed. For this analysis a fixed, context-free grammar is assumed. Four definitions of congruence are established. This is followed by a discussion of the properties of congruence: first, a discussion of the natural analogues of classical geometric theorems about congruence of figures; second, an examination of the relation between congruence and groups of transformations; finally, a consideration of some conjectures about the expressiveness of language when the congruence relation is that of paraphrase. The geometrical analogy further suggests a relation between congruence of meaning and transformational grammars that has not yet been explored in linguistic or philosophical literature. This semantic theory, or the tools of logic, may eventually play the role in the study of natural languages that classical mathematical analysis has played in physics. (HOD)