Question: we will call a noneuclidean geometry a geometry in which...
Question details
We will call a “nonEuclidean geometry” a geometry in which Eu clid’s five postulates do not all hold.

(a) Give an example of a nonEuclidean geometry, and explain how you know it is nonEuclidean.

(b) In most (but not all) nonEuclidean geometries, it’s Euclid’s Fifth pos tulate that fails to hold. Give another statement that is equivalent to Euclid’s fifth postulate. (You may choose any you like  from the text or by looking this up.) Is this statement true in the geometry you discussed in part (a)? Explain why or why not, drawing some pictures to illustrate.

(c) NonEuclidean geometries can be strange places. Explain why the Pythagorean Theorem (as we usually state it) does not hold in spherical geometry.