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converse of the corresponding angles postulate
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What postulate or theorem guarantees that there is only one line that can be constructed perpendicular to a given line from a given point not on the line?
It's the theorem that says " One and only one perpendicular can be drawn from a point to a line. "
is this statement true or falsethe converse of the alternate exterior angle theorem guarantees that line L and line n are parallel.?
true
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 an example of an postulate?
An example of a postulate is the "Parallel Postulate" in Euclidean geometry, which states that through any point not on a given line, there is exactly one line that can be drawn parallel to the given line. This postulate serves as a foundational assumption for the development of Euclidean geometry and is critical in understanding the properties of parallel lines.
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 there is only one line that can be constructed perpendicular to a given line from a given point not on the line?
It's the theorem that says " One and only one perpendicular can be drawn from a point to a line. "
is this statement true or falsethe converse of the alternate exterior angle theorem guarantees that line L and line n are parallel.?
true
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 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 the difference between a theorem and postulate?
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.
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.
Through a point not on the line exactly one line can be drawn parallel to the?
... 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.
What is another name for the Playfair Axiom?
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.
Which conjecture justifies the construction of a line parallel to a given line through a given point?
Euclid's parallel postulate.
Through a given point not on a given line there is exactly one line parallel to the given line?
The Playfair Axiom (or "Parallel Postulate")
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.
If Two lines perpendicular to the same line are perpendicular to each other?
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.
