Question

what is the main characteristic of non - euclidean geometry?
a. it only uses right angles.
b. it allows for curved spaces.
c. it strictly follows euclids postulates.
d. it involves only flat surfaces.

Explanation:

Non - Euclidean geometry is a type of geometry that differs from Euclidean geometry. Euclidean geometry is based on flat spaces and Euclid's postulates. Non - Euclidean geometry, on the other hand, allows for curved spaces. For example, in spherical geometry (a type of non - Euclidean geometry), the sum of the angles of a triangle is greater than 180 degrees, which is due to the curved nature of the space. Option a is incorrect because non - Euclidean geometry does not only use right angles. Option c is incorrect because non - Euclidean geometry does not strictly follow Euclid's postulates (in fact, it modifies some of them). Option d is incorrect because it does not involve only flat surfaces.

Answer:

b. It allows for curved spaces.