Final answer:
True, both Euclidean and non-Euclidean geometry have been accepted as valid types of geometry. Euclidean geometry assumes a flat space, while non-Euclidean geometry explores spaces with different properties.
Step-by-step explanation:
True. Both Euclidean and non-Euclidean geometry have been accepted as valid types of geometry.
Euclidean geometry, developed by Euclid, assumes a "flat" space where a straight line is the shortest distance between two points, the sum of angles in a triangle is 180 degrees, and parallel lines never intersect.
Non-Euclidean geometry, on the other hand, challenges these assumptions. It explores spaces with different properties, such as curved surfaces or non-parallel lines that can intersect. Examples of non-Euclidean geometries include hyperbolic geometry and elliptic geometry.