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Consider an incidence geometry satisfying the betweenness axioms. Let A,B,C be points on a line / such that A*B *C (i.e. B is between A and C). Let tA, tB, to be lines through A,B,C respectively such that tA and tB are parallel and distinct and tc and tB are parallel and distinct |(a) Prove that tA and tc are parallel. (b) Let m be a line intesecting lines tA, tB, tc at points X,Y,Z respectively. Prove that X Y *Z. Hint: Use sides of the line tB.

Consider an incidence geometry satisfying the betweenness axioms. Let A,B,C be points on a line / such that A*B *C (i.e. B is between A and C). Let tA, tB, to be lines through A,B,C respectively such that tA and tB are parallel and distinct and tc and tB are parallel and distinct |(a) Prove that tA and tc are parallel. (b) Let m be a line intesecting lines tA, tB, tc at points X,Y,Z respectively. Prove that X Y *Z. Hint: Use sides of the line tB.

Elementary Geometry for College Students
Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter1: Line And Angle Relationships
Section1.6: Relationships: Perpendicular Lines
Problem 27E
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Consider an incidence geometry satisfying the betweenness axioms. Let A,B,C be points on a line / such that A*B *C (i.e. B is between A and C). Let tA, tB, to be lines through A,B,C respectively such that tA and tB are parallel and distinct and tc and tB are parallel and distinct |(a) Prove that tA and tc are parallel. (b) Let m be a line intesecting lines tA, tB, tc at points X,Y,Z respectively. Prove that X Y *Z. Hint: Use sides of the line tB.
Transcribed Image Text:Consider an incidence geometry satisfying the betweenness axioms. Let A,B,C be points on a line / such that A*B *C (i.e. B is between A and C). Let tA, tB, to be lines through A,B,C respectively such that tA and tB are parallel and distinct and tc and tB are parallel and distinct |(a) Prove that tA and tc are parallel. (b) Let m be a line intesecting lines tA, tB, tc at points X,Y,Z respectively. Prove that X Y *Z. Hint: Use sides of the line tB.
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