Given TU is congruent to US. US is congruent to SV.
Prove ST > UV.
Are points T, U, S, and V collinear?
If so, then ST = UV.
T-----|-----U-----|-----S-----|-----V
Proof:
(1) $\displaystyle TU=US \ \ and \ \ US=SV$ GIVEN
(2) $\displaystyle TU=SV$ Transitive property of equality
(3) $\displaystyle US=US$ Reflexive property of equality
(4) $\displaystyle TU+US=SV+US$ Addition property
(5) $\displaystyle TU+US=ST \ \ and \ \ SV+US=UV$ Segment addition postulate
(6) $\displaystyle ST=UV$ Substitution (4) and (5)