Given that r is between s and t, find each missing measure.

rs =6, tr =4.5, ts =?

TS = 10.5. 
For the purposes of this discussion, a line segment is a line that has a starting point and an endpoint. 
From the measurements given: RS = 6, TR = 4.5, it can be deduced that T is the starting point of the line segment. S is the endpoint of the line segment. TS represents the starting point and the endpoint of the line segment. This means that you add the values of RS and TR together. 
TS = RS + TRTS = 6   +  4.5TS = 10. 5
Another way to represent the above is as follows:

T          6                        R        4.5                        S