Olivia wrote a paragraph proof to prove that the diagonals of parallelogram MNIOP 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

a. Because of the definition of a parallelogram, I know that opposite are congruent. I can say that MN ≅ OP. I now have enough information to say that triangle MNL ≅
triangle OPL by ASA Congruence Theorem
b. I am given that quadrilateral MNOP is a parallelogram. I know that opposite sides of a parallelogram are congruent because of the definition of parallelogram, so MN ll PO and MP ll NO.
c. By the CPCTC Theorem, I know that ML ≅ OL and NL ≅ PL. MO and NP bisect each other because this the definition of bisector.
d. When I think of diagonal as transversal cutting parallel line, I can see that.
∠MOP ≅ ∠OMN and ∠NPO ≅ ∠PNM because of the Alternate Interior Angles Theorem

Answer 1

To arrange Olivia's proof in the correct order, we start with the initial given information and proceed logically through the reasoning to reach the conclusion. Here’s the correct sequential order of her proof:

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

2. d. When I think of diagonal as transversal cutting parallel line, I can see that ∠MOP ≅ ∠OMN and ∠NPO ≅ ∠PNM because of the Alternate Interior Angles Theorem.

3. a. 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 triangle MNL ≅ triangle OPL by ASA Congruence Theorem.

4. c. By the CPCTC Theorem, I know that ML ≅ OL and NL ≅ PL. MO and NP bisect each other because this is the definition of bisector.

This sequence sets out the proof clearly and logically, building upon one statement to arrive at the final conclusion about the diagonals bisecting each other.