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Parallelogram upper M upper N upper O upper P is shown with base upper O upper P larger than height upper N upper O. Diagonals are drawn from upper M to upper O and upper N to upper P to meet at upper L.

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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1 answer

To create a valid proof that the diagonals of the parallelogram MNOP bisect each other, we can follow a logical sequence of statements and reasons. Here is a potential correct order for the proof:

  1. Statement: In parallelogram MNOP, diagonals MO and NP intersect at point L. Reason: Definition of a parallelogram (having diagonals).

  2. Statement: M and N are opposite vertices, and O and P are opposite vertices of parallelogram MNOP. Reason: Definition of a parallelogram (opposite sides are equal and parallel).

  3. Statement: MO || NP and MN || OP (since opposite sides of a parallelogram are equal and parallel). Reason: Opposite sides of parallelograms are parallel.

  4. Statement: Triangle MOL and triangle NPL are formed. Reason: Definition of point of intersection creates two triangles.

  5. Statement: MO = NP (since they are opposite sides of the parallelogram). Reason: Opposite sides of a parallelogram are equal.

  6. Statement: OL = PL and ML = NL (we need to show that both pairs are equal). Reason: By using the properties of the triangles formed at intersection.

  7. Statement: By the Side-Side-Side (SSS) criterion, triangle MOL is congruent to triangle NPL. Reason: Triangles are congruent by SSS (side-side-side congruence).

  8. Statement: Since the triangles are congruent, each pair of corresponding parts is congruent. Reason: Corresponding Parts of Congruent Triangles are Congruent (CPCTC).

  9. Statement: Therefore, OL = PL and ML = NL, proving that the diagonals bisect each other at point L. Reason: Definition of bisection (each segment is equal).

Make sure the statements and reasons align correctly to complete Olivia's proof logically and clearly!