The implication here goes both ways, i.e., if (a,b) in Tr and (b,c) in Tr implies (a,c) in Tr for all a, b, c, then Tr is transitive. So, this (the premise in the previous sentence) is what you need to show.I know that if it is transitive, (a,b), (b,c) element of Tr --> (a,c) element of Tr.
Fix arbitrary a, b, and c and assume that (a,b) is in Tr and (b,c) is in Tr. Write what this means according to the definition of Tr. Then write, again according to the definition, what is means for (a,c) to be in Tr. Can you show this latter fact from the previous two?