Most people, if asked whether they know any geometry, will answer no; but most, if not all, can recognise a straight line, a right angle, or a circle; of course they will not be able to define them as a mathematician does: a straight line is the shortest curve between two points etc. So, it appears that their answer reflects their understanding of geometry as it stands in immediate relationship to themselves, rather than an understanding of pure mathematics.
Now: Does this mean that humans have an innate sense of geometry, or is this acquired knowledge?
Does Kant suggest this? Is geometric knowledge a priori?
We know now that these concepts are contingent. That is, there are geometries that are non-euclidean. Of course locally, i.e. in our immediate environment, they are euclidean. In fact these geometries are called manifolds in mathematics, and it is the property of local euclideaness that defines them.
This means that although there are such geometries, because as human beings we have only our immediate environment to purvey, that is, our spatial knowledge is local, what is a straight line or circle in the standard sense remains effective. It does not have to be acquired, but can be innate.
But when Kant suggests we know geometry a priori does he mean this in a deeper sense - i.e. we are spatially aware? That we have an intuition of what space is, which stands between our immediate sensory input and our conscious knowledge of space?