To check whether the given postulate of plane Euclidean Geometry has a corresponding statement in Spherical Geometry
Answer to Problem 8CYU
There doesn’t exist a corresponding statement in Spherical Geometry for the given statement.
Explanation of Solution
Given information: Perpendicular lines intersect at one point.
Formula used:
Great circle: A plane can intersect a sphere in a point or in a circle. If the circle contains the center of the sphere, the intersection is called a great circle.
As two great
That is, intersection of greater circles do not possess perpendicular angles.
Therefore, there doesn’t exist a corresponding statement for the given statement, “perpendicular lines intersect at one point” in spherical geometry
Chapter 12 Solutions
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