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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.

1 answer

To help you arrange Olivia’s proof that the diagonals of parallelogram \( MNOP \) bisect each other, I will outline a standard proof structure for this theorem.

Statements and Reasons:

  1. Statement: Let \( L \) be the intersection point of diagonals \( MO \) and \( NP \). Reason: Definition of intersection point.

  2. Statement: \( MNOP \) is a parallelogram. Reason: Given.

  3. Statement: \( MO \) is parallel to \( NP \) and \( MN \) is parallel to \( OP \). Reason: Properties of a parallelogram.

  4. Statement: From the properties of parallel lines and transversals, \( \triangle MLO \cong \triangle NLP \). Reason: Alternate Interior Angles Theorem and Side-Angle-Side (SAS) Congruence.

  5. Statement: Therefore, \( ML = NL \) and \( OL = PL \). Reason: Corresponding parts of congruent triangles are congruent (CPCTC).

Complete Arrangement:

  • 1: \( MNOP \) is a parallelogram. (Given)
  • 2: Let \( L \) be the intersection point of diagonals \( MO \) and \( NP \). (Definition of intersection point)
  • 3: \( MO \) is parallel to \( NP \) and \( MN \) is parallel to \( OP \). (Properties of a parallelogram)
  • 4: From the properties of parallel lines and transversals, \( \triangle MLO \cong \triangle NLP \). (Alternate Interior Angles Theorem and Side-Angle-Side (SAS) Congruence)
  • 5: Therefore, \( ML = NL \) and \( OL = PL \). (CPCTC)

You can now rearrange the statements and reasons according to this order for Olivia’s proof. If you need further assistance on how to drag and drop, please let me know!