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7.1 Using the axioms of incidence and betweenness and the line separation property, show that sets of four points A, B, C, D on a line behave as we expect them to with respect to betweenness. Namely, show that (a) A * B * C and B * C * D imply A * B * D and A * C * D. (b) A * B * D and B * C * D imply A * B * C and A * C * D.

7.1 Using the axioms of incidence and betweenness and the line separation property, show that sets of four points A, B, C, D on a line behave as we expect them to with respect to betweenness. Namely, show that (a) A * B * C and B * C * D imply A * B * D and A * C * D. (b) A * B * D and B * C * D imply A * B * C and A * C * D.

Elementary Geometry For College Students, 7e
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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[Geometry] How do you solve this? The second photo has hints

7.1 Using the axioms of incidence and betweenness and the line separation property, show that sets of four points A, B, C, D on a line behave as we expect them to with respect to betweenness. Namely, show that (a) A * B * C and B * C * D imply A * B * D and A * C * D. (b) A * B * D and B * C * D imply A * B * C and A * C * D.
Transcribed Image Text:7.1 Using the axioms of incidence and betweenness and the line separation property, show that sets of four points A, B, C, D on a line behave as we expect them to with respect to betweenness. Namely, show that (a) A * B * C and B * C * D imply A * B * D and A * C * D. (b) A * B * D and B * C * D imply A * B * C and A * C * D.
7.1 • Can you show first that A, B, D are collinear? (do you see why we need to show this first?) • Now A* B * C, translated into separation of line by point (in this case B), is equivalent to what argument? • Can you do the same thing for BC * D? • Now translate what you want to prove in the form of separation theorem as well. The consequence is now evident
Transcribed Image Text:7.1 • Can you show first that A, B, D are collinear? (do you see why we need to show this first?) • Now A* B * C, translated into separation of line by point (in this case B), is equivalent to what argument? • Can you do the same thing for BC * D? • Now translate what you want to prove in the form of separation theorem as well. The consequence is now evident
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