Gonna be way to technical, but I dont care.......
Not quite right Alkapton, the idea of Parallel doesn't really make sense in non euclidian space (or needs to be definited slightly more carefully). We have the notion of the parallel postulate
"given a line and a point not on that line, there exists one and only one straight line which passes through that point and never intersects the first line"
If this is true then we have Euclian space, if its not true then we have non-euclidian.
Since we live on a sphere, the surface we live on is not eucidian, but it is locally euclidian, so standard euclidian geometry is a good estimate, a so called Manifold. So for caves, the space inside them can be estimated using standard euclidian distance, as they are generally small scale, but globally this is not true.
For example if you dug a shaft at the north pole say 100m deap, then dug south, always keeping 100m below the surface (assuming the surface is smooth) to the south pole, then turned exactly 90 degrees and dug north again back to the same shaft at the north pole, then this space could not be descrbed by euclidian space, as you have two "straight" lines (well geodesics) starting and ending at the same point, which are not the same. The survey for this cave is gonna look a bit odd!
When we survey caves, we do assume they are eucidian, that is that they can be described by a coordinate system {x,y,z} where the distance between two points is given by Pythagorus's theorem, this gives a very good estimation, so good you wont notice the difference, or its well lost in the accuracy of the survey, so it doesn't matter.
In conclusion, the space inside caves is not really euclidian, but its a good enough estimation.
Hope this makes sence!