The Theorem of Pappus states that if A,B,C are three distinct points on one line and if A',B',C' are three different distinct points on a second line, then the intersections of AC' and CA', AB' and BA', and BC' and CB' are collinear. Prove that there are exactly two lines parallel to a given line.

The Theorem of Pappus states that if A,B,C are three distinct points on one line and if A',B',C' are three different distinct points on a second line, then the intersections of AC' and CA', AB' and BA', and BC' and CB' are collinear. Prove that there are exactly two lines parallel to a given line.

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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The Theorem of Pappus states that if A,B,C are three distinct points on one line and if A',B',C' are three different distinct points on a second line, then the intersections of AC' and CA', AB' and BA', and BC' and CB' are collinear.

Prove that there are exactly two lines parallel to a given line.

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