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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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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