Photo below is mathematically not correct. But if you, with Euclidean heart, stand at a street in the Non-Euclidean World, you might see scenery like the photo. If the Hyperbolic NonEuclidean World is such strange, we should see it concretely. Yes, it had been proven. She did not give us any reason.
Some people say that it is a natural property.
Others say that it is a character of Euclidean geometry itself. The black circle is infinity in the Hyperbolic NonEuclidean World. We can not help but use such model because it is impossible to draw the NonEuclidean World as it is. In that disc straight line is a circlar arc which is perpendicular to the model disc edge. The angle of intersection of straight lines is the angle of that of circlar arcs.