Posted by Heather on .
Which of the following statements from Euclidean geometry is also true of spherical geometry?
A) A line has infinite length.
B) Two intersecting lines divide the plane into four regions.
C) Two perpendicular lines create four right angles.
D)The intersection of two lines creates four angles.
Im realy having trouble on this quesiton & I need some help:) thankyou!
Think of great circles on a sphere. Those correspond to straight lines in a plane. An arc of a great circle is the shortest distance between two points, measured along the surface of the sphere. A great circle is one whose diameter is the same as the diameter of the sphere.
not A: On a sphere, a great circle does not have infinite length.
not B: Anything pertaining to a plane has no relevance on a sphere.
not C: Two perpendicular great circles intersect twice. Think of the equator and a meridian. At each intersection there are 4 right angles.
D: This is true. Although as in C, two "lines" on a sphere always intersect twice.
By the way, that means that in spherical geometry, there are no parallel lines!