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 |

- Segment Addition Postulate
- Transitive Property of Equality
- Substitution Property of Equality
- 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.