Interpret point to mean one of the four vertices of square, line to mean one of

Question

Interpret point to mean one of the four vertices of square, line to mean one of the sides of the square, and lie on to mean that the vertex is an endpoint of the side. Consider the incidence axioms:

I-1: For any two distinct points there exists a unique line that passes through both of them.

I-2: For any line there exists at least two distinct points incident with it

I-3: There exist three distinct points with the property that no line is incident with all three of them

a) Which parallel postulates hold in this interpretation? What about other geometries? Explain

b) Could this be a model of Euclidean or Elliptical or Hyperbolic geometry? Justify

Explanation / Answer

Square is a geometric figure(satisfying all norms of euclidean geometry) with 4 sides or more precisely line segments connected to each other at 90*.Line segment is a set of points.From axiom 2 For any line there exists at least two distinct points incident with it.So the endpoints of each side are points

This implies the vertices of square are points and also endpoints of the line segments.

This model is even satisfied by other geometric figures(triangles,rectangles).

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