Answer
By changing the basic assumption in Exercise 4, we obtain non-Euclidean geometries. In one of these geometries, called elliptic geometry, there are no parallel lines.
Work Step by Step
According to Euclidean geometry,it is assumed that if a line is given and a point taken, which is not on the line, there can only be one line that passes through that point and is parallel to the given line.
This assumption is used to prove that the sum of the measures of all the angles in a triangle is .But, in the non-Euclidean geometries, this assumption is not taken into consideration. One of these geometries, called elliptic geometry, was proposed by German mathematician Bernhard Riemann.
Riemann began his geometry by assuming that there are no parallel lines. Elliptic geometry is on a sphere and the sum of the measures of the angles of a triangle is more than .
