Given: Quadrilateral PQRS is a rectangle. Prove: PR = QS Reason Statement 1. Quadrilateral PQRS is a rectangle. given 2. Rectangle PQRS is a parallelogram. definition of a rectangle 3. QP ≅ RS QR ≅ PS 4. m∠QPS = m∠RSP = 90° definition of a rectangle 5. Δ PQS ≅ ΔSRP SAS criterion for congruence 6. PR ≅ QS Corresponding sides of congruent triangles are congruent. 7. PR = QS Congruent line segments have equal measures. What is the reason for the third step in this proof?

Answer: opposite sides in rectangle are congruent.

Step-by-step explanation:

It is given that Quadrilateral PQRS is a rectangle.

Since opposite sides of rectangle are congruent.

Therefore, QP ≅ RS, QR ≅ PS

Therefore, the reason for "QP ≅ RS, QR ≅ PS" in this proof is "opposite sides in rectangle are congruent."

hence, the reason for the third step in this proof is "opposite sides in rectangle are congruent."

Since, the opposite sides of parallelogram are always congruent.

With using this property, the proof is mentioned below,

Given : Quadrilateral PQRS is a rectangle.

To Prove: PR = QS

Quadrilateral PQRS is a rectangle (Given)

Rectangle PQRS is a parallelogram. (Definition of a rectangle)

QP ≅ RS QR ≅ PS (By the definition of parallelogram)

m∠QPS = m∠RSP = 90° (Definition of a rectangle)

Δ PQS ≅ ΔSRP (SAS criterion for congruence)

PR ≅ QS (Corresponding sides of congruent triangles are congruent)

PR = QS (Congruent line segments have equal measures)

Hence proved.