Question

1. what is the main characteristic of non - euclidean geometry?

a. it allows for curved spaces.
b. it involves only flat surfaces.
c. it strictly follows euclids postulates.
d. it only uses right angles.

Explanation:

Non - Euclidean geometry is a type of geometry that differs from Euclidean geometry. Euclidean geometry is based on flat spaces (like the plane in 2D) and follows Euclid's postulates. Non - Euclidean geometry, on the other hand, allows for curved spaces. For example, spherical geometry (a type of non - Euclidean geometry) deals with curved surfaces (like the surface of a sphere). Option b is incorrect because it is a characteristic of Euclidean geometry. Option c is incorrect as non - Euclidean geometry does not strictly follow Euclid's postulates (for example, the parallel postulate is modified in non - Euclidean geometry). Option d is incorrect as there is no such restriction in non - Euclidean geometry.

Answer:

A. It allows for curved spaces.