Mathematics
Grade9
Easy

Question

The steps of a proof are shown.
Given PQ = RS
Prove PR = QS

What is the reason for step 5?
Statements Reasons
1. PQ = RS 1. Given
2. PQ + QR = RS + QR  
3. PQ + QR = PR  
4. RS + QR = QS  
5. PR = QS  

  1. Segment Addition Postulate
  2. Transitive Property of Equality
  3. Substitution Property of Equality
  4. Subtraction Property of Equality

Hint:

In this question, given is PQ = RS and we have to proved that PR = QS . Here 5 total step were given and also asked the reason of 5th state. This solve by the Segment addition postulate .

The correct answer is: Transitive Property of Equality


    Here we have to find the reason of step 5 .
    Firstly , we must consider that PQRS as a straight line, and P,Q, R and S are point on it one after another.
    Here given is 1 .PQ = RS
    2. PQ + QR = RS + QR ( by using addition postulate)
    3. PQ + QR = PR ( by segment addition )
    4. RS + QR = QS ( by segment addition )
    5. PR = QS ( by substitution property both are equal)
    Therefore, The reason of step 5 is substitution property of equality.
    The correct answer is Substitution property of equality.
    Or,
    Transitive Property of Equality. The whole proof is as following:
    Statements Reasons
    1. PQ = RS 1. Given
    2. PQ + QR = RS + QR 2. Addition Property of Equality
    3. PQ + QR = PR 3. Segment Addition Postulate (Post. 1.2)
    4. RS + QR = QS 4. Segment Addition Postulate (Post. 1.2)
    5. PR = QS 5. Transitive Property of Equality
     
     

    In this question , Most of steps are used as segment addition property to prove that PR = QS . In substation property , If A =B and A = C then we can write A = C.

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