Olivia wrote a paragraph proof to prove that the diagonals of parallelogram MNOP
bisect each other. Drag and drop the statements and reasons of her proof to put them in the correct order, starting with the first step at the top.
1. Statement: Diagonals MO and NP intersect at point Q.
Reason: Definition of diagonals in a parallelogram.
2. Statement: Triangle MOQ is congruent to triangle QNP.
Reason: SAS congruence property.
3. Statement: Segment MQ is congruent to segment NQ.
Reason: CPCTC.
4. Statement: Diagonals MO and NP bisect each other.
Reason: If two segments bisect each other, they divide each other into two congruent segments.
5. Statement: MO is congruent to NP.
Reason: Given that MNOP is a parallelogram.
6. Statement: Triangle MOQ is congruent to triangle MPQ.
Reason: Reflexive property of congruence.
7. Statement: Triangle MOQ is congruent to triangle MPQ.
Reason: ASA congruence property.
8. Statement: Triangle NQP is congruent to triangle MQP.
Reason: CPCTC.
9. Statement: Triangle MOQ is congruent to triangle NQP.
Reason: Transitive property of congruence.
10. Statement: Triangle MQP is congruent to triangle NQP.
Reason: Reflexive property of congruence.
11. Statement: MQ is congruent to QN and MP is congruent to PN.
Reason: CPCTC.
12. Statement: Diagonals MO and NP bisect each other.
Reason: If two segments bisect each other, they divide each other into two congruent segments.