Prove: In Young’s geometry, for every line l, there exists exactly two lines m and n such that m//l and n//l. Use any of the following axioms: There exists at least one line. There are exactly three points on every line. Not all points are on the same line. There is exactly one line on any two distinct points. For each line l and each point P not on l, there exists exactly one line on P which is not on any point of l. Note: Do not use diagrams.

Prove: In Young’s geometry, for every line l, there exists exactly two lines m and n such that m//l and n//l. Use any of the following axioms: There exists at least one line. There are exactly three points on every line. Not all points are on the same line. There is exactly one line on any two distinct points. For each line l and each point P not on l, there exists exactly one line on P which is not on any point of l. Note: Do not use diagrams.

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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Question

Prove: In Young’s geometry, for every line l, there exists exactly two lines m and n such that m//l and n//l.

Use any of the following axioms:

There exists at least one line.
There are exactly three points on every line.
Not all points are on the same line.
There is exactly one line on any two distinct points.
For each line l and each point P not on l, there exists exactly one line on P which is not on any point of l.

Note: Do not use diagrams.

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