Question 138759
I read this as "How does one show that if line a is parallel to line b AND line b is parallel to line c, then line a is parallel to line c".

If line a and b are parallel, then they have the same slope. Let's call that m.

If line b and line c are parallel, they have the same slope. lets call that n.

Since the slope of b is constant, n = m. And the slope of a equals the slope of c.

Since a and c have the same slope, they are parallel. 

And the operation is transitive.