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Answer :
Final answer:
Considering a rotation, the sides and angles of the original shape and its image are congruent, So, just statements C (J'K' ≅ JK) and D (M∠J'K'L' = m∠JKL) are true.
Explanation:
The quadrilateral J'K'L'M' is the result of a rotation of quadrilateral JKLM about point P. When we consider a rotation, the original shape and its image after rotation are congruent, which means they have the same size and shape. Given this, let's examine the statements:
A. LM ≅ JK: This is not necessarily true, as LM and JK are two different sides of the original quadrilateral, and their relationship is not defined by the rotation.B. m∠KLM = m∠K'LM': This is not correct, because K'LM' is not an angle in the rotated image.C. J'K' ≅ JK: This is true, as the lengths of corresponding sides are preserved in a rotation.D. M∠J'K'L' = m∠JKL: This is true, each corresponding angles are congruent in a rotation process.E. K'L' ≅ ML: This is not necessarily true. K'L' and ML are not corresponding sides in the original and rotated quadrilaterals.
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Final answer:
After a rotation of quadrilateral JKLM about point P, the angles remain the same (statement B is true) and the angle measures also remain the same (statement D is true).
Explanation:
To determine the relationship between quadrilateral JKLM and its image J'K'L'M' after a rotation about point P, we need to analyze each statement.
A. LM ≅ JK: This statement is not necessarily true. The lengths of the corresponding sides may or may not be equal after the rotation.
B. m∠KLM = m∠K'LM': This statement is true. The angle measures remain the same after a rotation.
C. J'K' ≅ JK: This statement is not necessarily true. The lengths of the corresponding sides may or may not be equal after the rotation.
D. M∠J'K'L' = m∠JKL: This statement is true. The angle measures remain the same after a rotation.
E. K'L' ≅ ML: This statement is not necessarily true. The lengths of the corresponding sides may or may not be equal after the rotation.
Therefore, the true statements are B and D.
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