Playfair Axiom
parallel postulate
Some branches of quantum physics postulate properties and phenomena that are not observed in classical physics. The Addition Postulate is one of several in geometry that are always accepted as true and correct.
Connection Conversion Transformation Parallel
postulate
Educated guess.
parallel postulate
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.
postulate theorems tell that the lines are parallel, but the converse if asking you to find if the lines are parallel.
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.
Parallel lines are parallel. Proof they have same slopes
converse of the corresponding angles postulate
... 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.
No.
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.
That is only true of triangles and is a consequence of the parallel postulate. In fact it is an alternative way of stating Euclid's parallel postulate.
Euclid's parallel postulate.