Answer to this: All equilateral triangles have interior angles equal to 60 degrees APEX
No.
The axioms are not postulates.
euclidean Geometry where the parallel line postulate exists. and the is also eliptic geometry where the parallel line postulate does not exist.
Answer The two commonly mentioned non-Euclidean geometries are hyperbolic geometry and elliptic geometry. If one takes "non-Euclidean geometry" to mean a geometry satisfying all of Euclid's postulates but the parallel postulate, these are the two possible geometries.
The ruler placement postulate is the third postulate in a set of principles (postulates, axioms) adapted for use in high schools concerning plane geometry (Euclidean Geometry).
No. Non-Euclidean geometries usually start with the axiom that Euclid's parallel postulate is not true. This postulate can be shown to be equivalent to the statement that the internal angles of a traingle sum to 180 degrees. Thus, non-Euclidean geometries are based on the proposition that is equivalent to saying that the angles do not add up to 180 degrees.
In Euclidean geometry, yes.In Euclidean geometry, yes.In Euclidean geometry, yes.In Euclidean geometry, yes.
Euclidean geometry is the traditional geometry: it is the geometry of a plane surface, as developed by Euclid. Among other things, it is based on Euclid's parallel postulate which said (in effect) that given a line and a point outside that line there could only be one line through that point that was parallel to the given line. It has since been discovered that both alternatives to that postulate - that there are many such lines possible and that there are none - give rise to consistent geometries. These are non-Euclidean geometries.
One main characteristic of non-Euclidean geometry is hyperbolic geometry. The other is elliptic geometry. Non-Euclidean geometry is still closely related to Euclidean geometry.
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One main characteristic of non-Euclidean geometry is hyperbolic geometry. The other is elliptic geometry. Non-Euclidean geometry is still closely related to Euclidean geometry.
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.