Which statement represents the parallel postulate in Euclidean geometry, but not elliptical or spherical geometry?

1 .Through a given point not on a line, there exists no lines parallel to the given line through the given point.

2.Through a given point not on a line, there exists exactly one line parallel to the given line through the given point.

3.Through a given point not on a line, there exists more than one line parallel to the given line through the given point.

4.Through a given point not on a line, there exists exactly three lines parallel to the given line through the given point.

The object of "Euclidean geometry" (more commonly called "plane geometry") is, in principle, the study of the shapes and properties of natural bodies. However, geometry is not an experimental science since its object is not to study certain aspects of nature but a necessarily arbitrary reproduction of it.

After the definitions, Euclid then poses his famous postulates (his requests), the fifth of which has remained Euclid's postulate, often called axiom (or postulate) of parallels and which was the subject of much research and controversy as to its necessity:

Given two points A and B, there exists a line passing through A and B.
Any segment [AB] can be extended into a straight line passing through A and B.
For any point A and any point B distinct from A, we can describe a circle with centre A passing through B.
The whole right angles are always equal to each other.
By a point outside a line, we can draw a parallel and only one to this line.

From the above explanation, we could deduce that the correct option is Option 2.

alexandermcqueen1513 alexandermcqueen1513 · Answer 2 · 2021-01-04T05:38:32+01:00

alexandermcqueen1513 alexandermcqueen1513

04-01-2021

Answer:

The answer is B, Through a given point not on a line, there exists exactly one line parallel to the given line through the given point.

Step-by-step explanation:

Answer Link