Which statement represents the parallel postulate in Euclidean geometry, but not elliptical or spherical geometry?
Through a given point not on a line, there exists no lines parallel to the given line through the given point.
Through a given point not on a line, there exists exactly one line parallel to the given line through the given point.
Through a given point not on a line, there exists more than one line parallel to the given line through the given point.
Through a given point not on a line, there exists exactly three lines parallel to the given line through the given point.

Question

22-08-2017
Mathematics

contestada

Which statement represents the parallel postulate in Euclidean geometry, but not elliptical or spherical geometry?
Through a given point not on a line, there exists no lines parallel to the given line through the given point.
Through a given point not on a line, there exists exactly one line parallel to the given line through the given point.
Through a given point not on a line, there exists more than one line parallel to the given line through the given point.
Through a given point not on a line, there exists exactly three lines parallel to the given line through the given point.

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gchaching gchaching · Answer 1 · 2017-08-24T21:29:15+02:00

gchaching gchaching

24-08-2017

B.) Through a given point not on a line, there exists exactly one line parallel to the given line through the given point.

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chisnau chisnau · Answer 2 · 2019-06-18T07:49:41+02:00

Answer:

Option B is the right answer.

Step-by-step explanation:

Which statement represents the parallel postulate in Euclidean geometry, but not elliptical or spherical geometry?

The correct statement is - Through a given point not on a line, there exists exactly one line parallel to the given line through the given point.

The parallel postulate in Euclidean geometry states that through any given point not on a line there passes exactly one line parallel to that line in the same plane.