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. (2 points) Arrange responses in the correct order to answer the question.

Question

Statement A: 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.
Statement B: When I think of the diagonals as transversals cutting parallel lines, I can see that ∠MOP ≅ ∠OMN and ∠NP ≅ ∠PNM because of the Alternate Interior Angles Theorem.
Statement C: Because of the definition of a parallelogram, I know that opposite sides are congruent. I can say that MN ≅ OP. I now have enough information to say that △MNL ≅ △OPL by the ASA Congruence Theorem.
Statement D: By the CPTC Theorem, I know that ML ≅ OL and NL ≅ PL. MO and NP bisect each other beacuase this is the definition of a bisector.

An image shows a rhombus with the top left angle marked as "M", the top rigth angle, "N", the bottome left, "P", and bottom right, "O". A line is drawn from the inside of the M's angle to the inside of O's angle. The same is done with angles P and N. Where the two lines intersect, it is marked as "L". Use this information to answer the question please. :) :D

Answer 1

To organize Olivia's proof that the diagonals of parallelogram MNOP bisect each other, we can arrange the statements in a logical order. Here's the correct sequence:

1. Statement A: 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.

2. Statement B: When I think of the diagonals as transversals cutting parallel lines, I can see that ∠MOP ≅ ∠OMN and ∠NP ≅ ∠PNM because of the Alternate Interior Angles Theorem.

3. Statement C: Because of the definition of a parallelogram, I know that opposite sides are congruent. I can say that MN ≅ OP. I now have enough information to say that △MNL ≅ △OPL by the ASA Congruence Theorem.

4. Statement D: By the CPTC Theorem, I know that ML ≅ OL and NL ≅ PL. MO and NP bisect each other because this is the definition of a bisector.

This order supports the logical progression of proving that the diagonals of the parallelogram bisect each other through congruence of triangles and properties of angles created by transversals.