Given: PQ= TQ, UQ: QSProve: PS TUReasonsStatements1. PQ= TO, UQ= OS2. PQ = TQ, UQ = QS3. PQ+ QS = PS; TQ + QU = TU4. TQ + QS = PS5. TQ + QS = TU6. PS = TU7. PS = TU1. Given2. reflexive Ž3. Addition Poe4. Seament Addition post5. Seament Addition Post6. U7. Definition of CongroencelGina Wilson (All Things Algebra), 2014

Answer:The required prove is shown below.Step-by-step explanation:Consider the provided statement.The required figure is shown below:  Statement                                             ReasonsPQ ≅ TQ; UQ ≅ QS                               GivenPQ = TQ, UQ = QS                     Definition of CongruencePQ + QS = PS; TQ+QU = TU    Segment Addition PostulateTQ + QS = PS                            Substitution  (PQ = TQ)TQ + QS = TU                            Substitution  (QU = QS)PS = TU                                    Transitive PropertyProve: PS ≅TU                          Definition of CongruenceHence, the required prove is shown above.