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converse of the corresponding angles postulate

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Q: What postulate or theorem guarantees that line L and line N are parallel?

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It's the theorem that says " One and only one perpendicular can be drawn from a point to a line. "

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euclidean Geometry where the parallel line postulate exists. and the is also eliptic geometry where the parallel line postulate does not exist.

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.

Although he presented it differently, the modern version is as follows:given a straight line and a point which is not on that line, there is only one line which will pass through the point and which is parallel to the line.

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It's the theorem that says " One and only one perpendicular can be drawn from a point to a line. "

true

euclidean Geometry where the parallel line postulate exists. and the is also eliptic geometry where the parallel line postulate does not exist.

Postulates are assumed to be true and we need not prove them. They provide the starting point for the proof of a theorem. A theorem is a proposition that can be deduced from postulates. We make a series of logical arguments using these postulates to prove a theorem. For example, visualize two angles, two parallel lines and a single slanted line through the parallel lines. Angle one, on the top, above the first parallel line is an obtuse angle. Angle two below the second parallel line is acute. These two angles are called Exterior angles. They are proved and is therefore a theorem.

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.

... given line. This is one version of 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.

Another name for the Playfair Axiom is the Euclid's Parallel Postulate. It states that given a line and a point not on that line, there is exactly one line parallel to the given line passing through the given point.

Euclid's parallel postulate.

The Playfair Axiom (or "Parallel Postulate")

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.

No. Two lines perpendicular to the same line are parallel to each other. I am doing this for my geometry homework right now trying to recall the name of the postulate/theorem stating it.

Although he presented it differently, the modern version is as follows:given a straight line and a point which is not on that line, there is only one line which will pass through the point and which is parallel to the line.