Olivia wrote a paragraph proof to prove that the diagonals of parallelogram M NOP 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.

Question

(2 points)

Because of the definition of a parallelogram, I know that opposite sides are congruent. I can say that MN e OP. I now have enough information to say that AMNL.* AOP L by the ASA Congruence Theorem.

I am given that quadrilateral MNOP is a parallelogram. I know that opposite sides of a parallelogram are congruent because of the definition of a parallelogram, so MN || PO and MP || NO.

By the CPCTC Theorem, I know that ML ≥ OL and NL ~ PL. MO and NP bisect each other because this is the definition of a oisector.
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When I think of the diagonals as transversals cutting parallel lines, I can see that /MOP ~ LOMN and /NPO ~ LPNM because of the Alternate Interior Angles Theorem.

Answer 1

Here is the ordered proof for Olivia's statement that the diagonals of parallelogram MNOP bisect each other:

1. Statement: I am given that quadrilateral MNOP is a parallelogram.
   Reason: Definition of a parallelogram.

2. Statement: I know that opposite sides of a parallelogram are congruent because of the definition of a parallelogram, so MN || PO and MP || NO.
   Reason: By the definition of a parallelogram.

3. Statement: When I think of the diagonals as transversals cutting parallel lines, I can see that ∠MOP ≅ ∠LOMN and ∠NPO ≅ ∠LPNM because of the Alternate Interior Angles Theorem.
   Reason: Alternate Interior Angles Theorem.

4. Statement: I can say that ΔAMNL ≅ ΔAOPL by the ASA Congruence Theorem.
   Reason: ASA Congruence Theorem.

5. Statement: By the CPCTC Theorem, I know that ML ≅ OL and NL ≅ PL.
   Reason: CPCTC (Corresponding Parts of Congruent Triangles are Congruent).

6. Statement: MO and NP bisect each other because this is the definition of a bisector.
   Reason: Definition of bisectors.

This ordering logically presents the proof that the diagonals of the parallelogram bisect each other based on the properties of parallelograms and congruence theorems.