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Advanced MathQ&A LibraryConsider an incidence geometry satisfying the betweenness axioms. Let A,B,C bepoints on a line / such that A*B *C (i.e. B is between A and C). Let tA, tB, to belines through A,B,C respectively such that tA and tB are parallel and distinct andtc 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,Zrespectively. Prove that X Y *Z. Hint: Use sides of the line tB.Question

Asked Oct 28, 2019

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Step 1

Given* t _{a}* is parallel to

Step 2

(a)To prove:* t _{a}* and

Proof:

Let *θ _{1}, θ_{2 }*and

When two lines are parallel, their respective corresponding angles are equal.

So here *θ _{1}*=

It can be concluded that *θ _{1=} θ_{2=} θ_{3}*

Which implies *θ _{1 =} θ_{3}*

Which implies *t _{a}* and

Step 3

To prove: *X*Y*Z*

Given *m* be a line intersecting the line *ta*, *tb* and *tc* at the point *X...*

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