Answer:
Explanation:
For segment/ angle proofs:
Here’s how you can complete the proof:
1. Statement: PQ ≅ RS Reason: Given
2. Statement: m∠PQR = m∠QRS Reason: If two lines are parallel, then corresponding angles are congruent.
3. Statement: m∠PQR + m∠QRP = m∠PRS and m∠QRP + m∠RSQ = m∠QSR Reason: Angle addition postulate
4. Statement: m∠PRS = m∠QSR Reason: Transitive property of equality (from statements 2 and 3)
5. Statement: ∠PRS ≅ ∠QSR Reason: Definition of congruent angles (angles that have the same measure)
6. Statement: PQ ≅ RS Reason: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent (by ASA, Angle-Side-Angle, congruence rule). Since ∠PRS ≅ ∠QSR and PR = QS (given), PQ ≅ RS.