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