Given: PT parallel to RS; PT=RS. Prove: PQ congruent to QS

Question

the diagram looks like a giant X box

Answer 1

1. Given: PT is parallel to RS and PT = RS To prove: PQ is congruent to QS
2. We can use the transitive property of congruence to prove this. If two lines are parallel and corresponding parts of one line are congruent to corresponding parts of the other line, then the entire lines are congruent.
3. Since PT is parallel to RS and PT = RS, then by the transitive property, PQ = QS.
4. Therefore, the transitive property can prove that PQ is congruent to QS.