Mathematics
Grade9
Easy
Question
What is the 6th 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.
