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...

Extracted 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.