Mathematics

Grade9

Easy

Question

# What is the 6^{th} reason?

Given: Q is between P and R, R is between Q and S, PR = QS.

Prove: PQ = RS

Proof:

Statements | Reason |

1. Q is between P and R. | 1. Given |

2. PQ + QR = PR | 2. ________ |

3. R is between Q and S. | 3. _________ |

4. _______ | 4. Seg. Add. Post |

5. PR = QS | 5. _______ |

6. PQ + QR = QR + RS | 6. ________ |

7. PQ + QR – QR = QR + RS - QR | 7. ________ |

8. ____________ | 8. Substitution |

- definition of congruence
- substitution property
- definition of midpoint
- given

Hint:

### In this question, given is PR = QS and we have to proved that PQ = RS. Here 8 total step were given and also asked the reason of 6th state. This solve by the Segment addition postulate and different equality property.

## The correct answer is: substitution property

### Here we have to find the reason of step 6.

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 PR = QS

1 . Q is between P and R ( given)

2. PQ + QR = PR (Segment addition Postulate)

3. R is between Q and S ( given )

4. QR + RS =QS ( Segment addition Postulate )

5. PR = QS ( given)

6. PQ +QR = QR + RS ( substitution )

7. PQ + QR – QR = QR + RS – QR (subtraction property , subtract from QR)

8. PQ = RS ( substitution )

Therefore, The reason of step 5 is transitive property of equality.

The correct answer is Transitive property of equality.

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