Abstract
This chapter defines a betweenness relation and uses it to define segments, rays, and triangles. A few theorems are proved in the resulting IB geometry. These are foundational for the rest of the development.
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Notes
- 1.
In Chapter 21 we will construct Model DZIII for IB geometry and prove, in Theorem DZIII.4(A) that it is possible to have two segments
and 
such that 
and yet {A, B} ≠{C, D}, i.e., two segments which are equal but have different endpoints. - 2.
In Chapter 21 we will construct Model DZII for IB geometry and prove, in Theorem DZII.4, that all these statements are false.
and 
such that 
and yet {A, B} ≠{C, D}, i.e., two segments which are equal but have different endpoints.References
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Specht, E.J., Jones, H.T., Calkins, K.G., Rhoads, D.H. (2015). Incidence and Betweenness (IB). In: Euclidean Geometry and its Subgeometries. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-23775-6_4
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