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17 March, 22:56

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?

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  1. 17 March, 23:08
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    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."
  2. 17 March, 23:10
    0
    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.
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