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Quadrilateral J'K'L'M' is the image of JKLM rotated about the point P. Select all true statements that describe the relationship between JKLM and J'K'L'M'.

Select all that apply:

A. LM = JK
B. [Please provide additional statements for completion]

Answer :

When a quadrilateral is rotated about a point, certain statements can be true or false. In this case, statements B and E are true, while statements A, C, and D are false.

The rotation of a quadrilateral about a point P can result in various relationships between the original quadrilateral and its image. Let's go through each statement and determine whether it is true or false.

  1. A. LM ≅ JK: This statement is false. In a rotation, the lengths of the sides do not necessarily remain the same. Therefore, LM may not be congruent to JK.
  2. B. m∠KLM = m∠K'LM': This statement is true. The measurement of angle KLM in the original quadrilateral is equal to the measurement of angle K'LM' in the rotated image.
  3. C. J'K' ≅ JK: This statement is false. While some sides may be congruent, it is not necessary for all sides to be congruent in a rotation.
  4. D. m∠J'K'L' = m∠JKL: This statement is false. The angles in the rotated image may not have the same measures as the corresponding angles in the original quadrilateral.
  5. E. K'L' ≅ ML: This statement is true. If K'L' and ML are congruent, it means that the corresponding sides in the original quadrilateral and the rotated image are of equal length.

In summary, statements B and E are true, while statements A, C, and D are false.

Learn more about Quadrilateral rotation here:

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