Question

Statements1. PQ = TQ,UQ = QS2. PQ = TQ, UQ = QS3. PQ + QS = PS, TQ + QU = TU4. TQ+ QS = PS5. TQ + OS = TU6. PS= TU7. PS=TU

Answer 1

3.

• 1.

`PQ\cong TQ,UQ\cong QS`

Reason: Given

• 2.

`PQ=TQ,UQ=QS`

Reason: Definition of Congruence

• 3.

`PQ+QS=PS;TQ+QU=TU`

Reason: Segment Addition Postulate

• 4.

`TQ+QS=PS`

Reason: Substitution (PQ = TQ)

• 5.

`TQ+QS=TU`

Reason: Substitution (QU = QS)

• 6.

`PS=TU`

Reason: Transitive Property

• 7.

`PS\cong TU`

Reason: Definition of Congruence