The required prove is shown below.
Step-by-step explanation:
Consider the provided statement.
The required figure is shown below:
 Statement                       Reasons
PQ ≅ TQ; UQ ≅ QS                Given
PQ = TQ, UQ = QS Â Â Â Â Â Â Â Â Â Â Definition of Congruence
PQ + QS = PS; TQ+QU = TU Â Â Segment Addition Postulate
TQ + QS = PS               Substitution  (PQ = TQ)
TQ + QS = TU               Substitution  (QU = QS)
PS = TU Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Transitive Property
Prove: PS ≅TU              Definition of Congruence
Hence, the required prove is shown above.