Consider the Euclidean plane, and instead of ordinary lines, let the line segments PQ for all pairs of distinct points P, Q be taken as the “lines.” Show that this system of points and lines satisfies Axioms 0–2. What seems unnatural to you about this geometry?

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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  1. Consider the Euclidean plane, and instead of ordinary lines, let the line segments PQ for all pairs of distinct points P, Q be taken as the “lines.” Show that this system of points and lines satisfies Axioms 0–2. What seems unnatural to you about this geometry?

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