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The hyperbolic parallel postulate states that given a line L and a point P, not on the line, there are at least two distinct lines through P that do not intersect L.
The negation is that given a line L and a point P, not on the line, there is at most one line through P that does not intersect L.
The negation includes the case where there is exactly one such line - which is the Euclidean space.
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What is the differences between postulate theorems and converse?
postulate theorems tell that the lines are parallel, but the converse if asking you to find if the lines are parallel.
What are the two kinds of geometry?
euclidean Geometry where the parallel line postulate exists. and the is also eliptic geometry where the parallel line postulate does not exist.
If there is a line and a point not on the line then there is exactly lines trough the point parallel to the given line?
This is Euclid's fifth postulate, also known as the Parallel Postulate. It is quite possible to construct consistent systems of geometry where this postulate is negated - either many parallel lines or none.
what postulate or theorem guarantees that line L and line N are parallel?
converse of the corresponding angles postulate
Why does a triangle have 180 degree?
It is a consequence of Euclid's parallel postulate. In fact, in some versions, the statement that "a plane triangle has interior angles that sum to 180 degrees" replaces the parallel postulate.
