To help you arrange Olivia’s proof that the diagonals of parallelogram \( MNOP \) bisect each other, I will outline a standard proof structure for this theorem.
### Statements and Reasons:
1. **Statement**: Let \( L \) be the intersection point of diagonals \( MO \) and \( NP \).
**Reason**: Definition of intersection point.
2. **Statement**: \( MNOP \) is a parallelogram.
**Reason**: Given.
3. **Statement**: \( MO \) is parallel to \( NP \) and \( MN \) is parallel to \( OP \).
**Reason**: Properties of a parallelogram.
4. **Statement**: From the properties of parallel lines and transversals, \( \triangle MLO \cong \triangle NLP \).
**Reason**: Alternate Interior Angles Theorem and Side-Angle-Side (SAS) Congruence.
5. **Statement**: Therefore, \( ML = NL \) and \( OL = PL \).
**Reason**: Corresponding parts of congruent triangles are congruent (CPCTC).
### Complete Arrangement:
- 1: \( MNOP \) is a parallelogram. (Given)
- 2: Let \( L \) be the intersection point of diagonals \( MO \) and \( NP \). (Definition of intersection point)
- 3: \( MO \) is parallel to \( NP \) and \( MN \) is parallel to \( OP \). (Properties of a parallelogram)
- 4: From the properties of parallel lines and transversals, \( \triangle MLO \cong \triangle NLP \). (Alternate Interior Angles Theorem and Side-Angle-Side (SAS) Congruence)
- 5: Therefore, \( ML = NL \) and \( OL = PL \). (CPCTC)
You can now rearrange the statements and reasons according to this order for Olivia’s proof. If you need further assistance on how to drag and drop, please let me know!