Use the image to answer the question.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. Select a response, navigate to the desired position and insert response at that position. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can be moved using the up and down arrow keys or by dragging with a mouse.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 bisector.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.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¯¯¯¯¯¯¯¯.When I think of the diagonals as transversals cutting parallel lines, I can see that ∠MOP≅∠OMN and ∠NPO≅∠PNM because of the Alternate Interior Angles Theorem.

Question

Use the image to answer the question.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. Select a response, navigate to the desired position and insert response at that position. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can be moved using the up and down arrow keys or by dragging with a mouse.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 bisector.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.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¯¯¯¯¯¯¯¯.When I think of the diagonals as transversals cutting parallel lines, I can see that ∠MOP≅∠OMN and ∠NPO≅∠PNM because of the Alternate Interior Angles Theorem.

GPT-4o mini · Answer

To arrange the statements and reasons of Olivia's proof in the correct order, we can follow the logical progression of the argument. Here's the ordered sequence:

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 ≅ OP and MP ∥ NO.
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.
When I think of the diagonals as transversals cutting parallel lines, I can see that ∠MOP ≅ ∠OMN and ∠NPO ≅ ∠PNM because of the Alternate Interior Angles Theorem.
By the CPCTC Theorem, I know that ML ≅ OL and NL ≅ PL. This shows that MO and NP bisect each other because this is the definition of a bisector.

This sequence logically progresses from stating the properties of the parallelogram to establishing the congruence of triangles and finally concluding that the diagonals bisect each other.