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  • Unique line assumption. There is exactly one line passing through two distinct points.
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What is a line postulate?

The postulate that pertains to a line is:For any two points there exists only one line.


What is a postulate?

The verb "to postulate" means to assert a claim as true, with or without proof. Geometric "postulates" are basic axioms that are given or assumed in order to establish the framework of geometric relationships. An example is Postulate 1 which defines point, line, and distance as unique conditions.


what postulate or theorem guarantees that line L and line N are parallel?

converse of the corresponding angles postulate


What is the perpendicular postulate?

The perpendicular postulate states that if there is a line, as well as a point that is not on the line, then there is exactly one line through the point that is perpendicular to the given line.


What is the line intersection postulate?

The line intersection postulate states that if two distinct lines intersect, they do so at exactly one point. This fundamental principle in geometry ensures that the intersection of lines is unique, meaning that no two lines can cross at more than one point. This postulate forms the basis for understanding the relationships between lines in a plane.


What is postulate 9?

Postulate 9 is- If two planes intersect, then their intersecion is a line


Is hyperbolic parallel postulate a postulate of Euclid?

No, the hyperbolic parallel postulate is not one of Euclid's original five postulates. Euclid's fifth postulate, known as the parallel postulate, states that given a line and a point not on that line, there is exactly one line parallel to the original line that passes through the point. Hyperbolic geometry arises from modifying this postulate, allowing for multiple parallel lines through the given point, leading to a different set of geometric principles.


What was A postulate that was developed and accepted by greek mathematicians?

One postulate developed and accepted by Greek mathematicians was the Parallel Postulate, which stated that given a line and a point not on that line, there is exactly one line through the point that is parallel to the given line. This postulate was crucial in the development of Euclidean geometry. However, it was later discovered that this postulate is not actually necessary for generating consistent geometries, leading to the development of non-Euclidean geometries.


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.


What is a distance postulate?

The distance postulate is such: the shortest distance between two points is a line.(xy, x-y) The distance postulate is such: the shortest distance between two points is a line.(xy, x-y)


What does the postulate that Euclid was unable to prove deal with?

The postulate that Euclid was unable to prove is known as the Fifth Postulate or the Parallel Postulate. It states that given a line and a point not on that line, there is exactly one line parallel to the original line that passes through the given point. Despite Euclid's attempts, he could not derive this postulate from his other axioms, leading to centuries of exploration in geometry and the eventual development of non-Euclidean geometries. This postulate fundamentally shapes the nature of geometry and led to significant advancements in mathematical thought.


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.