Dear all, i'm trying to understand geometry by studying the subject myself. i came across idea that i'm very much confuse of. it say's that 'geometry is a studies of geometric properties that is invariant under transformation' such as distance for euclidean geometry. my question is: why do we studies invariant properties, why not study variant properties instead? why are we so interested in invariant properties? what role does it plays in the study of geometry? i do hope that someone will be able to enlighten this to me. some textbooks that i'm reading only stop at telling the geometry is a studies of invariants prop, w/o telling why. million of thanks.