Question

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 1

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).

Answer 2

The reason for the third step in this proof : Opposite angles of parallelogram are equal

Step-by-step explanation :

Given: Quadrilateral PQRS is a rectangle.

To prove: PR = QS

Proof: 1. Given that Quadrilateral PQRS is a rectangle.

2. Definition of a rectangle : Rectangle PQRS is a parallelogram

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).

Therefore, The reason for the third step in this proof : Opposite angles of parallelogram are equal