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?

Step-by-step explanation:

Given:  Quadrilateral PQRS is a rectangle.

To prove: PR = QS

Proof: 1.  Quadrilateral PQRS is a rectangle(Given).

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

3. QP ≅ RS QR ≅ PS (Opposite angles of parallelogram are equal).

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).

solve for x

Step-by-step explanation: