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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.

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Sure! To prove that the diagonals of a parallelogram bisect each other, we can use the following logical sequence of statements and reasons.

Here is a typical structure for such a proof:

  1. Statement: Let M, N, O, and P be the vertices of parallelogram MNOP. Reason: Given.

  2. Statement: Draw diagonals MO and NP. Reason: Diagonals of a parallelogram can be drawn.

  3. Statement: By the definition of a parallelogram, MN || OP and MO || NP. Reason: Properties of parallel lines in a parallelogram.

  4. Statement: Triangles MNO and OPN are formed by the diagonals. Reason: Diagonal segments create triangles within the parallelogram.

  5. Statement: By the Alternate Interior Angles Theorem, ∠MNO = ∠OPN and ∠MON = ∠NOP. Reason: If two lines are parallel, then the alternate interior angles are equal.

  6. Statement: MN = OP and MO = NP because opposite sides of a parallelogram are equal. Reason: Properties of a parallelogram.

  7. Statement: Triangles MNO and OPN are congruent by the ASA (Angle-Side-Angle) postulate. Reason: Two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

  8. Statement: Therefore, the segments MO and NP bisect each other at point X. Reason: Corresponding parts of congruent triangles are equal (CPCTC).

You can arrange these statements and reasons accordingly in your proof to show the logical progression leading to the conclusion that the diagonals of a parallelogram bisect each other.